This post serves as a primer for future posts related to topics in economics. While not necessarily core to a critical thinking curriculum, economic concepts are vital for understanding a modern policy environment. I cannot begin to describe the vast disconnect between basic economic literacy and the folk models held by large swaths of the general public. As an economist myself, perhaps I am biased in thinking many of our problems in society are in some way, caused by this illiteracy. However, I think there is a strong case to be made that obsolete, ideologically laden, underdeveloped, and empirically unsound economic mental models held by various groups, are contributing significantly to the deterioration of the nations welfare. Therefore, I think it's important to lay out how professional or academic economists come to their conclusions. The public broadly has no idea what economists do; how they reason, their models of the economy, what a model even is, their sources of information etc. This post introduces some of the most basic concepts implicit in most economic theory and regularly used by applied economists. Lets start with some basics. These might seem abstract initially, so I'll try to concretize them:
Table of Contents
Economy
Is defined as:
"a system of interactions among agents (households, firms, and governments) in which scarce resources are allocated through markets and institutions to produce, distribute, and consume goods and services."
This is actually a lot to unpack; what is a system? what is a market? what is an agent? what are goods? Each of these terms within this definition are just as abstract as the definition itself. Its also important to point out that different schools of economics will often define an economy differently, emphasizing certain aspects they find to be of crucial importance. For our purposes here, just note that this definition will likely be broadly accepted by most economists and is consistent with definitions within textbooks.
After years if study, I've come to appreciate the conceptualization discussed by George E. Mobus in "Systems Science: Theory, Analysis, Modeling, and Design". It is defined here as an instance of the broader class of systems called Complex Adaptive Evolutionary Systems (CAES). The author conceives of a "generic economic system", that is usually embedded within a larger system (like an ecosystem), characterized by certain elements such as the way in which the system obtains resources in energy/materials, how they do internal work to grow/replicate/maintain themselves, and how they export waste back into their environment. In other words, an economy is a type pattern within a broader set of CAES. Specifically, he states:
"What all of these systems do internally is to use the energy and material imports in work processes that build and maintain essential internal structures. Waste products are inevitable in all such products in nature. The organization of the work processes and their ongoing management (which collectively we can call the governance of the system) is the pattern of which we spoke. Whether we are talking about the internal organization and dynamics of a living cell, of the multicellular organism of a Neolithic tribe, a single household, a complex organization, or a modern nation state, the patterns of organization and dynamics follow them. These patterns cluster under the title 'economy'."
This is an even more generic definition that invokes concepts from system science. It's analogous to a biological subsystem that performs that performs vital functions that ensure the survival of the supersystem in which it is embedded. Doyne Farmer, a complexity economist, has drawn an analogy between an economic system and a metabolic system. The economic system functions like a metabolic system, in that it consumes resources, processes energy & information, and adapts over time. It is always changing, growing, or decaying. It's primary function is the flow of energy and matter. Using this analogy, we can conceive of the economic metabolism; how economies transform inputs into outputs, similarly to how living organisms metabolize food into energy and biomass.
I'll admit that this is definitely a heterodox approach but you can see the parallels with how mainstream economists define an economy. You might see in standard textbooks the etymology of the term "economy". It originally derives from "oikonomia", a Greek term meaning "management of a household". In ancient Greece, the "masters" of the household had to practice "economic activities", like raising sufficient food to support the household. Mobus states that "this meant managing processes so that the household recognizes an accumulation of wealth that would ultimately provide for the support of subsequent generations." In modern times, these households are embedded within a broader complex system and interact with institutions such as "markets" to achieve these ends. Mobus offers another abstraction:
"At an abstract level, an economy is a fabric of transactions, a network of sub-processes of resource acquisition , transformation (value added), production, and consumption, in which biological beings are sustained.... In the systems view, an economy is a way of managing the flows of high potential energy and of the transformation of high entropy materials into low entropy assets via work processes that use that high potential energy to do useful work. The low entropy assets support the existence and stability of the system."
The key thing to note with these definitions, is that economists are concerned with the flow and utilization of scarce resources, typically within some national boundary, but increasingly at a global scale.
Models (Modeling)
So, what is a model? At its core, a model is a simplified representation of reality. It’s a tool we use to describe, explain, or predict how something works. Consider a map; it's not the territory, rather its a simplified version that leaves out irrelevant details, allowing you to navigate the terrain efficiently. A model is a map of a system of interest. Many different models can describe the same system. A single system like the economy, or climate, or a human body can be described in many different ways, depending on what you want to understand or predict, the data you have access to, and generally speaking the question you are asking. In economics, there are a plethora of models that describe the same economy. The choice of model depends on the question, context, and needed level of accuracy. The level of fidelity or granularity of the model also depends on these considerations. Low fidelity models are fast, easy to understand, captures big-picture behavior. They are good for teaching, quick decisions, or back-of-the-envelope estimates. Medium fidelity models capture more details; attempting to balance tractability and accuracy. High fidelity models are very detailed, often computational, can model complex interactions; they are used when precision really matters. Many economic models are "coarse grained models"; coarse-graining means reducing a system’s complexity by grouping together small-scale components and modeling only the aggregate behavior. Think of it like pixels on a screen; fine grained would be something like ultra HD while coarse grained would be something lower resolution, but you can still make out the general objects in the screen.
Everyone has a model of reality in their mind. Our brains construct maps of reality, which we use to navigate the terrain. The deliberate act of modeling, allows us to interrogate, investigate, and revise these models. This is particularly useful for explicating our assumptions. Models are highly sensitive to their underlying assumptions. If we are not aware of these assumptions, our model will be inaccurate and useless. Every mathematical model starts with assumptions about what variables matter, how the variables relate, what is constant vs what can change, the environment in which the system is embedded, and assumptions about the fundamental unit of analysis (in economics, our "agents"). Even if our model is not mathematical, it still depends on these sorts of assumptions. The use of mathematics in the physical sciences and economics is for clarity. Language is incredibly ambiguous and vague; mathematization allows us to be incredibly precise with our definitions; leaving little room for ambiguity when we must interpret the model. Model assumptions define the world. Models don’t discover truth, they operate within a truth you’ve defined. So if your assumptions are flawed, your model will produce misleading results, even if the math is perfect. Some models are relatively unaffected by slight changes in the underlying assumptions, other models are highly sensitive. In finance, models like the Black-Scholes equation assume no transaction costs and continuous trading. In the real world, these assumptions break down and so does the model’s accuracy. Our assumptions also guide the interpretation of the model results. Therefore, the economist (ideally) should be constantly asking “What’s this model assuming? And is that reasonable for the question I care about?”
I would argue that many economics students don't fully appreciate the rationale behind mathematical modeling in economics or more broadly across disciplines. The very essence of economics is to treat the economy as a system governed by universal laws. We invoke modeling notions such as equilibrium to describe how markets stabilize over time in response to external perturbations. We construct analogies like "market forces" which help explain movements in some quantity of interest, typically price. We use differential equations to model the dynamics of quantities like inflation or interest over time. Much of these techniques are inspired by physical sciences. In fact, many economists are simply mathematicians who apply this math to questions about economics.
The problem I've recognized within economics departments, is that students pay less attention to the process of modeling, and focus more on the results of a particular economic model. It is easier to memorize the implications of a model, rather than to interrogate the structure and assumptions governing a model. I've simultaneously recognized an overemphasis on formalisms and equation solving within economics departments. What I mean is, students are evaluated by their abilities to solve a particular set of equations, rather than by the model thinking required to solve economic problems. Both of these miss the point of what were doing. The first set of students is primarily interested in the answers while the latter set of students is treating economics as if its mathematics.
Educators really need to stress why we even model to begin with. I've explained briefly what a model is, while only alluding to the many reasons why we might want to model. The "why" we model is core to scientific inquiry. Much of the "Why" I'll be describing comes from
Why Model by Joshua Epstein and
Different Modeling Purposes by Bruce Edmonds.
Epstein argues that modeling is an inherent part of human cognition. Whenever individuals make projections or imagine scenarios, such as the spread of an epidemic or the outcome of a war, they are effectively running mental models. These are implicit models with hidden assumptions, untested internal consistency, and unknown logical consequences. The distinction lies in making these models explicit, allowing for scrutiny, replication, and validation. Building explicit models involves clearly stating assumptions, which facilitates understanding their implications. Explicit models can be shared, tested against data, and refined. They enable sensitivity analysis, allowing researchers to explore how changes in parameters affect outcomes. This process is crucial for identifying uncertainties, robust regions, and critical thresholds, particularly in policy-making contexts. Epstein also describes the value of modeling beyond out of sample prediction. He lists 16 different uses:
- Explain (very distinct from predict)
- Guide data collection
- Illuminate core dynamics
- Suggest dynamical analogies
- Discover new questions
- Promote a scientific habit of mind
- Bound (bracket) outcomes to plausible ranges
- Illuminate core uncertainties.
- Offer crisis options in near-real time
- Demonstrate tradeoffs / suggest efficiencies
- Challenge the robustness of prevailing theory through perturbations
- Expose prevailing wisdom as incompatible with available data
- Train practitioners
- Discipline the policy dialogue
- Educate the general public
- Reveal the apparently simple (complex) to be complex (simple)
Explanation is distinct from prediction. When scientists use the word "predict", they do not necessarily mean "forecast". A quote attributed to Neils Bohr says "Prediction is hard, especially about the future!" This highlights the distinction between prediction "within sample" vs prediction "out of sample", the latter being something more akin to a forecast; an extrapolation based on historical trends. To predict in a scientific sense, means given a model of a system, some input (X) is expected to produce output (Y) within some margin of error. So for example, if I know the mass of a solid and its acceleration, then I can predict what the force will be; it is determined by the formalization of the system. I can then conduct an experiment to verify whether my description corresponds to observations. In economics, if i know the quantity demanded and the quantity supplied of a product, I can determine the market price. Sometimes prediction is very hard given the complexity of a system. This is fine, because the model can still be explanatory. Epstein gives the example of plate tectonics being explanatory of earthquakes, despite not predicting the time and location of any specific earthquake.
Epstein critiques the naïve inductivist view of science, which assumes that researchers first gather data and then build models to explain it. This view is common among both non-modelers and some modelers, especially in the social sciences, where it's often believed that one should "collect lots of data and run regressions." While data-driven research can be valuable, Epstein argues that this is not how science typically works. In many significant scientific breakthroughs, theory came before data and actually guided what data should be sought. Models are not just tools for explaining existing data, they are invaluable for shaping and guiding data collection. Without models, researchers might not know what data is most relevant or worth collecting in the first place.
Models don’t have to be precisely accurate to be incredibly useful. In fact, all the best models are technically "wrong", they are simplifications or idealizations of reality. But this wrongness doesn’t diminish their value. On the contrary, their simplicity and abstraction make them powerful tools for understanding the core dynamics of complex systems. Though models are idealizations and approximations, they nevertheless enable us to describe broad qualitative behavior of a system such as feedback loops, threshold effects, tipping points etc. The real question isn't whether a model is idealized (all models are), but whether the model is a fertile idealization, does it generate insight, understanding, and foundational intuition; hence George Box famously stating that “All models are wrong, but some are useful.” When first introduced to modeling, it can seem absurd to deliberately simplify, ignoring potentially relevant details. The truth of the matter is that we simply have to ignore things, we do all the time, without realizing it. We simply cannot function in the world without ignoring most facts about the world. We have limited cognitive resources; we could not possibly consider the mountains of information bombarding our senses at any given moment. Formal modeling forces us to be very explicit with what we are considering; meaning that it's clearly communicated what's not being considered, thus providing deeper intellectual engagement with the question at hand.
Paul Smaldino gives an thoughtful anecdote illustrating the precision of a formalism provided by modeling. Remember from earlier, verbal models suffer from ambiguity. Formalizing theories in terms of mathematical models helps us be precise with our concepts. Smaldino recounts an experience from his undergraduate days when he and a friend, while waiting in a theater basement, constructed a whimsical LEGO figure they dubbed a "Cubist chicken." Both agreed on its identity until a third friend questioned its features. Upon attempting to explain, they realized each had a different interpretation of which parts represented the chicken's head, body, and tail. This divergence highlighted that their shared understanding was more assumed than actual. The parable serves as a metaphor for the pitfalls of relying solely on verbal models in science. While verbal descriptions can seem comprehensive, they often harbor ambiguities that lead to misinterpretations. In contrast, formal models, despite being simplifications, require explicit definitions and assumptions, fostering clearer communication and understanding among researchers. Smaldino emphasizes that the "stupidity" or simplicity of models is a strength, as it forces clarity and facilitates the testing of specific hypotheses. Models force us to make sure we are all talking about the same thing. A corollary to precision is tractability. Formal models are logical engines that transform assumptions into conclusion. Stating assumptions precisely allows us to know what necessarily follows from those assumptions, which helps us find potential gaps in our explanations.
Mainstream economics frequently gets criticized by its approach to modeling. This brings us to the distinction between as-is and as-if modeling. As-if models assume that agents behave "as if" they are behaving a certain way (optimizing) even if they don't do so in reality. For example, the classic rational actor model in economics assumes individuals maximize utility as if they were calculating costs and benefits precisely, even though real humans may not. Friedman famously defended this in "The Methodology of Positive Economics" (1953), arguing that the realism of assumptions is less important than the accuracy of predictions. Mainstream economics often uses as-if models for their analytical tractability and predictive usefulness. On the other hand, "as-is" models try to represent how agents actually behave based on empirical observation, often including heuristics, bounded rationality, learning, or psychological factors. These models are often less mathematically neat but aim to be more descriptive of real-world behavior. An example might be an agent based model that computationally encodes more complex decision rules an agent might adaptively utilize, within an evolving system. Economists like J. Doyne Farmer and others in the complexity economics tradition (at the Santa Fe Institute, inspired by Herbert Simon) are strong proponents of as-is modeling, especially using agent-based models and data-driven simulations. They reject the representative agent:, emphasizing heterogeneity and micro-level interaction. They emphasize emergence of macro-level phenomena from simple decentralized rules. They place a heavy emphasis on empirical validation; models must fit and explain data, not simply derive from axioms. From the mainstream economist perspective, the goal is to predict behavior, so highly unrealistic idealizations are fine if they aid in prediction. They deemphasize descriptive realism.
Systems
When describing "the economy", we are describing an economic system. This was somewhat alluded to in the definition of economics. We are interested in studying aspects about a particular system of interest. Sometimes we are interested in studying the "global economic system". Other times, we are interested in studying a proper subsystem of the global economic system, like the financial system. But what exactly is a "system"? How do economists think about systems? I'll first start with a broad definition of "system" from systems science, before modifying it to encapsulate how economists broadly think of "systems". Economists are usually not this explicit when conceiving "systems"; in fact, in all my years of study I rarely find economists formally defining "system". Mainstream economists certainly do not formalize the notion. Heterodox approaches like complexity economists tend to be more descriptive. The following formalization is consistent with heterodox approaches taken by someone like Brian Arthur. But we will see broadly, economists are concerned with these elements.
Mobus and Kalton describe a system as a cohesive, organized whole composed of interrelated components that work together to produce behaviors or functions not reducible to those of the individual parts. A system exists within a boundary, interacts with its environment, and processes inputs and outputs in structured ways. It exhibits emergence, meaning the behavior or purpose of the whole cannot be understood merely by analyzing its parts in isolation. Systems can be open or closed, adaptive or rigid, and operate across multiple scales and timeframes. They maintain internal organization through feedback, control, and governance mechanisms, and are often hierarchically embedded in larger systems.
Formally, a system at identity and hierarchical level is defined as the 9-tuple:
Each component of this tuple describes a key aspect of what constitutes a system in precise, structural terms.
1. : Components
This is the set of parts or elements that make up the system. Each component may itself be a system (a subsystem), reflecting the hierarchical nature of systems in general. Components are defined by their roles and characteristics within the system, and their inclusion in the system may not always be binary—it is sometimes useful to model their membership as “fuzzy,” meaning that components may participate in the system to varying degrees or under specific conditions. For instance, in an ecosystem, a migratory species might only be part of the system seasonally, making its membership conditional.
The components of an economy include a vast array of agents and institutions—households, firms, banks, government agencies, and markets. Each of these components has a defined role: households provide labor and consume goods, firms produce goods and services, banks manage financial intermediation, and governments set fiscal and monetary policy. These entities interact within and across sectors, forming the basic building blocks of the system. Some components, like multinational corporations or informal economies, may participate across boundaries, making them partially included or fuzzy in membership.
2. : Network of Relations
This element represents the structural or functional connections between components. It defines how parts of the system influence, support, or depend on each other. These relationships can be bidirectional or unidirectional, physical (like wires connecting electrical components) or abstract (like authority or influence in a social organization). The network structure determines the topology of the system and underlies many dynamic behaviors, such as cascades, feedback loops, and resilience to disruption.
In an economy, components are linked through a dense network of financial, legal, and social relationships. Firms are connected to consumers through market exchanges, to suppliers via supply chains, and to banks through credit and investment. Governments interact with all other components through taxation, regulation, and public spending. These relationships define flows of goods, services, money, labor, and influence. The structure of these connections—centralized or distributed, robust or fragile—has a strong impact on economic performance and resilience to shocks.
3. : Sources
Sources refer to the inputs that enter the system from its environment. These might include material resources, energy, or information—anything required for the system to function and persist over time. In a manufacturing system, for example, raw materials are sources. In a cognitive system, sensory stimuli are inputs. The nature and availability of these sources can have a profound impact on how the system behaves or whether it can sustain itself.
The sources of an economy are the external inputs that support its functioning. These include natural resources (like oil, minerals, or water), imported goods and services, foreign investments, immigrant labor, and technological innovation originating abroad. These sources flow into the system and are transformed, consumed, or circulated internally. For a closed economy, these sources would be limited, but in reality, most modern economies are highly open and reliant on continuous input from the global system.
4. : Sinks
Complementary to sources, sinks are the outputs of the system—where its products, wastes, or by-products go. Sinks represent how the system interacts with and impacts its external environment. In an ecological system, this could be the dispersal of nutrients or the release of waste products. In an economic system, sinks might be the markets that receive goods or the environment that absorbs pollution. A system’s outputs can affect not only its own stability but also the systems it interfaces with.
Sinks are where the economy’s outputs go, including exports, emissions, and waste. For example, manufactured goods might be sold to international markets, information products consumed globally, or pollutants expelled into the environment. These outputs affect external systems—ecological, social, and economic. Negative sinks, like environmental degradation, can feed back as costs to the system, making them crucial to sustainability and long-term modeling.
5. : Flow Graph
The flow graph represents the directed movement of resources—whether energy, matter, or information—between components within the system. It formalizes the system's internal dynamics and enables modeling of how internal processes operate, such as transport, transformation, or communication. Flow graphs are typically weighted and directional, capturing both the pathways and intensities of flows, and are critical for analyzing systemic phenomena like bottlenecks, delays, and accumulation.
The flow graph of an economy maps how resources circulate between components—money flows from consumers to producers, taxes from businesses to government, subsidies from government to agriculture, and so on. It includes supply chains, labor markets, investment flows, and trade routes. This graph allows us to trace bottlenecks, feedback loops (like inflationary spirals), and cyclical behaviors (like recessions). Monetary policy and interest rates, for instance, are interventions into specific flow patterns meant to influence broader systemic outcomes.
6. : Boundary
The boundary distinguishes what is part of the system from what is not. It may be physical (like the hull of a ship), functional (such as firewall rules in a network), or even conceptual (the defined scope of a scientific model). Boundaries determine the scope of analysis and define where inputs enter and outputs exit. They are essential for understanding how a system maintains its integrity, interfaces with its environment, and evolves over time. In some cases, boundaries may shift, blur, or be contested, especially in social or conceptual systems.
An economic system’s boundary defines what is considered part of the national or regional economy and what lies outside it. For example, the boundary of the U.S. economy would include all production and consumption activities within its jurisdiction, but also interactions with foreign economies through trade and capital flows. The boundary is often fuzzy—offshore accounts, black markets, or informal economies may blur the lines of inclusion. How we define the boundary impacts the scope of data collection (GDP, for instance) and policy-making.
7. : Knowledge
Knowledge is the information stored, encoded, or maintained within the system. This might be in the form of data, memory, genetic information, operating rules, or even learned behaviors. Knowledge enables the system to regulate itself, adapt, and evolve in response to internal or external conditions. In biological systems, this could be DNA; in human organizations, it could be culture or institutional memory. Knowledge may also define how the system models itself or anticipates its environment, enabling more sophisticated forms of control.
Knowledge in an economy includes institutional memory, laws, technologies, business practices, education, and even cultural norms. It resides in human capital, embedded in institutions, and codified in technologies and systems of production. This internal knowledge base enables innovation, guides decision-making, and supports coordination across vast distances and organizational layers. A highly developed economy typically has dense knowledge structures that promote adaptability and efficiency.
8. : Governance
Governance encompasses the mechanisms, rules, and feedback processes that guide the system’s behavior and maintain its stability. This may include control systems, management structures, or algorithms. It can be centralized or distributed, rigid or adaptive. Governance ensures that the system responds to changes, corrects errors, and aligns its operations with desired outcomes. In ecosystems, governance might take the form of natural feedback loops; in engineered systems, it might be a set of protocols or a software routine managing operations.
Economic governance is exercised through central banks, treasuries, regulatory bodies, legal frameworks, and international institutions like the IMF or WTO. It includes fiscal policy (spending and taxation), monetary policy (interest rates, money supply), and regulatory actions (banking laws, labor protections). These governance mechanisms manage inflation, employment, growth, and inequality. Effective governance keeps the system stable, resilient to shocks, and aligned with societal goals. Poor governance can lead to systemic crises.
9. : Time Interval
Finally, the time interval refers to the period over which the system is observed, modeled, or understood. It provides temporal context, distinguishing between fast, transient processes and long-term, evolutionary changes. Some systems operate over milliseconds (e.g., electronic circuits), others over centuries (e.g., climate systems). Time determines not only how the system behaves but also how we interpret causality, feedback, and system lifecycle stages such as growth, decay, and renewal.
The time interval for studying an economy could vary dramatically depending on the question—short-term intervals might focus on quarterly business cycles, while long-term intervals could examine industrial development, technological evolution, or demographic shifts over decades. Time plays a critical role in understanding lag effects, feedback delays, and compounding dynamics like debt accumulation or climate-related economic changes. Economies are dynamic systems that evolve, adapt, and sometimes collapse across different time horizons.
Given all of this, it's clear that economists are concerned with "economic systems". They are certainly concerned with governance, knowledge structures, network relations etc. However, they do not use formalisms like what's used in systems science. When referring to "systems", they will use designations like "capitalist system" or "mixed system"; highlighting different aspects of these systems that are present or absent. In mainstream economics, the concept of a “system” is only partially formalized, it’s often used metaphorically or descriptively (often ideologically laden), but elements of it are embedded in formal models without always being explicitly labeled as “systems.” For example,
dynamic stochastic general equilibrium (DSGE) models, used in macroeconomics, formalize how an economy responds over time to shocks. They're system-like in structure, with
state variables,
feedback, and evolution over time. In systems, equilibrium is a state of balance or homeostasis. In economics,
equilibrium is central; markets “clear” when supply equals demand; economists typically assume there to be some
homeostasis absent external perturbations. This is a central analogy used in economics to physical systems. Systems are defined by what’s inside (
endogenous) and what’s outside (
exogenous inputs); more on this later because these are absolutely critical concepts you must understand to understand the practice of economics. In economics, models clearly separate endogenous variables (explained within the model) and exogenous ones (shocks, policy, technology); this mirrors the "system boundary" concept. In many applications, like
game theory or
IO analysis, “system” means a set of interrelated equations that represent how different variables (like prices, consumption, wages) influence each other. It’s a structural or computational sense of a system, closer to engineering or
control theory. Economic agents are modeled like controllers
optimizing an objective (utility, profit) subject to constraints (budget, production function). Very similar to
optimal control or
operations research. Central banks have access to the systems control variables, which are the levers used to influence the systems behavior. Monetary policy is modeled with feedback rules (like the
taylor rule), which is essentially a
PID controller. DSGE models are analyzed for stability around a
steady state, and then
impulse response functions are used to study how these systems react to shocks (impulses). Every agent has an objective function they're seeking to optimize and follow simple rules for optimizing these function over time. When I was in graduate school, I learned quite a lot about
state space models. The difference between a systems science approach, is that economists typically do not consider emergence, adaptation, agent heterogeneity, network interactions, path dependence, tipping points, learning, or evolution. It primary uses a
rational agent framework (more on this later) which assumes away the possibility of these phenomenon.
When economists are speaking more loosely about "systems", they are using the term in the broad metaphorical sense rather than the rigorous mathematical sense. They are essentially shorthand for institutional arrangement, decision making structures, and norms of organization. They refer to who owns resource, how decisions are made, and the role of the government. I personally think we can juxtapose the systems science formalism onto these terms. For example, "Capitalist system" would by an instance of a broader class of related systems that can be described using the 9-tuple above. I really wish the discipline went this way because there is so much confusion around these ideologically loaded terms; can't imagine how much of humanity is wasted speaking past each other because they have no conceptual foundations. "Systems" in this loose sense, refers to broad institutional configurations, typically involving the following:
- Ownership of the means of production
- Coordination mechanisms (think prices)
- Incentive Structures (think the profit motive)
- Role of the state (think of "laissez faire")
- Allocation of Resources (budgeting, planning, markets)
- Legal and Institutional Framework (property rights, taxation etc)
Samuelson uses "capitalist" and "market economy" pretty much interchangeably; emphasizing property rights, private enterprise, and markets. Other economists emphasize "price signals" as what determines the allocation of resources, based on decentralized choice of individual agents. Honestly, given these loose definitions, anything can be capitalist. Not going down that rabbit hole, but I think it depends on which aspects of the system we are primarily focused on.
One last concept I think is important; system decomposition. I'll quote Smaldino from Modeling Social Behavior:
"What are the parts of the system we are interested in? What are their properties? What are the relationships between the parts and their properties? How do those properties and relationships change? Decomposition consists of usable answers to these questions"
This is relevant to the modeling section above, because when you want to hypothesize something about your system, you first must articulate the parts of that system. Economists are primarily concerned with causal hypotheses, meaning the level of description must be sufficient to capture the parts of the system relevant to the question. There is no right level of decomposition; it fundamentally depends on the question, and the value of the model depends on how well it's decomposition answers the question. Oh and remember, assumptions are behind all of this.
Optimization
Optimization is not only a cornerstone method in economics but also a conceptual lens to view systems and agents interacting within those systems. It is the engine of economic reasoning and is at the heart of every economic analysis. Whether it's a consumer choosing between products, a firm deciding how much to produce, or a government allocating a budget, economics assumes that agents make the best possible choices given their objectives and constraints. Consumers are modeled as maximizing utility given their income and the prices of goods. Firms aim to maximize profits by choosing how much labor and capital to employ. Policymakers often try to optimize welfare, balancing trade-offs like equity and efficiency. This framework allows economists to derive predictions and policy implications from first principles. It's not that everyone consciously solves equations, but the optimization lens provides a consistent method to analyze decisions in a world of scarce resources. Optimization connects economics with mathematics, especially calculus and linear programming, turning abstract choices into solvable problems from the economists perspective, to make predictions about real world scenarios. From marginal analysis to game theory, the logic of "best choice under constraints" drives much of economic reasoning. It frames the way economists see the world: as a series of trade-offs, decisions, and outcomes shaped by rational pursuit of goals within limits.
Most modern economic research begins with a simple, core idea: individuals and institutions make purposeful decisions to achieve their objectives as best they can, given constraints. This assumption allows economists to use optimization to build formal models of behavior (utility maximization, profit maximization, more on these later), derive testable implications from these models and simulate outcomes under different assumptions or scenarios. For example, a paper studying household consumption might assume that people maximize lifetime utility subject to a budget constraint. This provides a structured, solvable problem whose solution can be compared with real-world data. Optimization gives the model its internal logic and empirical tractability. By using optimization, these theories don't just describe behavior they provide a mechanism to explain why certain outcomes occur, and how changes in conditions (prices, income, technology) lead to changes in behavior. Because economic models are grounded in optimization, the policy advice that emerges from them is, by design, about improving outcomes—maximizing welfare, minimizing inefficiencies, or designing better incentives. For instance tax policy is analyzed through models where households optimize labor supply decisions, allowing economists to estimate optimal tax rates, monetary policy uses models where central banks optimize over inflation and output trade-offs and environmental regulation applies optimization to balance economic costs with ecological benefits. If the models are robust, the policy recommendations derived from them aim to move the system closer to an optimal state, given real-world constraints and trade-offs.
You can think of optimization as a way of thinking; a framework for formulating, analyzing, and solving decision problems across economics, operations research, and decision sciences. At its core, optimization thinking involves Decision variables (what can be chosen), Objective functions (what is to be maximized or minimized), and Constraints (rules that must be satisfied):
- Identify objectives
- What is the agent (a person, a firm, a policymaker) trying to achieve?
- Make the goals explicit
- Clarify constraints
- What limits the available choices—budget, time, regulations, technology?
- Map feasible alternatives
- What are the real options available?
- Evaluate trade-offs
- How do changes in one choice affect the outcome or cost of another?
- Choose the best course of action
- What’s the most effective or efficient choice given the above?
- Evaluate the costs and benefits of alternatives.
Economists are not just thinking about these concepts devoid of practical application. Often they are hired by employers to engage in prescriptive modeling on behalf of the firm. They migh construct a model of business operations within the firm to ask what should be done to acheive an optimal outcome (usually maximizing profits). Within academic economics, we use optimization primarily for explanatory and predictive purposes to describe features of a whatever unit of analysis we are concerned with. But outside of academics, economists often work in a prescriptive decision making capacity under conditions of uncertainty, risk, or resource limits where they must identify optimal course of action in situations involving strategic interaction.
Most economists should have this generic formulation internalized:
Let \( x \in \mathbb{R}^n \) be the vector of decision variables. A standard constrained optimization problem is formulated as:
\[
\begin{aligned}
\text{Minimize (or Maximize)} \quad & f(x) \\\\
\text{subject to} \quad
& g_i(x) \leq b_i, \quad i = 1, \dots, m \\\\
& h_j(x) = c_j, \quad j = 1, \dots, p \\\\
& x \in X
\end{aligned}
\]
Where:
- \( f(x) \) is the objective function to be minimized or maximized (e.g., cost, utility, profit).
- \( x \) is the vector of decision variables (e.g., quantities to produce, allocate, consume).
- \( g_i(x) \leq b_i \) are inequality constraints, representing resource limits or bounds.
- \( h_j(x) = c_j \) are equality constraints, such as balance conditions or conservation laws.
- \( X \) is the feasible set—the domain of allowable solutions (e.g., \( x \geq 0 \), or \( x \) must be integer-valued).
Whether you're modeling a consumer’s utility maximization, a firm’s cost minimization, or a government's resource allocation, almost all applied optimization problems in economics and decision science can be framed in this form.
Dynamic optimization is also very pervasive within economics. Dynamic optimization models capture decisions that unfold over time, where today’s choice affects tomorrow’s possibilities. These can be broken down into discrete time models or continuous time models; where the major difference is whether the time variable can be discretized. Economists use dynamic optimization to model:
- How consumers smooth consumption across life (life-cycle hypothesis)
- How firms invest in capital over time (investment theory)
- How governments plan fiscal or monetary policy (dynamic programming)
- How agents form expectations and adjust behavior (rational expectations models)
- How does a shock today (e.g., a technology shock or policy change) propagate over time?
- What’s the optimal investment plan when capital is costly to adjust?
The key ingredients are:
- A state variable that summarizes the relevant "current condition" (e.g., wealth, capital stock)
- A control variable (or decision variable) that the agent chooses (e.g., how much to consume or invest)
- A transition equation that describes how today’s decision shapes tomorrow’s state
- An objective function that evaluates the total value of decisions over time
Dynamic optimization is MUCH harder to explain succinctly and I struggled with it (and still do) when in graduate school. I am not going to provide the generic mathematical setup but i'll provide a very common problem macroeconomists should be familiar with. The Cake Eating Problem, a problem of intertemporal choice, asks: how much of X should I enjoy today and how much of X should I leave for the future (where X is cake)? This sounds really trivial at first until you realize it's an extremely general problem; a trade-off between current and future utility. Imagine you have a fixed-sized cake, say, one whole cake. You can eat some of it now, and save the rest for later. But once you eat a piece, it’s gone. The challenge is: How should you allocate consumption of the cake over time to maximize your total satisfaction (utility)? Is it optimal to eat it all now? Should you eat a small piece a day? If you eat more today, you'll have less tomorrow, and therefore lower future utility. The goal is to find an optimal policy (the best sequence of decisions), a specific plan for how much cake to eat at each period that balances current and future satisfaction. Economists use this idea to study decisions where you have a limited resource and you have to decide how to use it over time; like money, food, energy, or natural resources. The goal is to make choices today that don't ruin your happiness tomorrow. So here is the formal model:
- Let \( W_t \) be the amount of cake (or wealth) at time \( t \).
- You choose how much cake to eat: \( c_t \), with \( 0 \leq c_t \leq W_t \).
The remaining cake becomes:
\[
W_{t+1} = W_t - c_t
\]
- You derive utility from eating: \( u(c_t) \), where \( u(\cdot) \) is a utility function (e.g., \( u(c) = \ln(c) \)).
- You discount future utility with a factor \( \beta \in (0, 1) \), meaning you value today’s consumption more than tomorrow’s.
Your goal is to choose the sequence \( \{c_t\}_{t=0}^{\infty} \) to maximize lifetime utility:
\[
\max_{\{c_t\}} \sum_{t=0}^{\infty} \beta^t u(c_t)
\]
subject to:
\[
\begin{aligned}
W_{t+1} &= W_t - c_t \\\\
W_0 &> 0, \quad c_t \in [0, W_t]
\end{aligned}
\]
A brief note on the discount factor; this is essentially a scaling factor that tells you how much you value future consumption compared to current consumption. This is such a core concept in economics and finance that I cannot possibly do it justice in this section, so I'll save it for later. But for now just see it as a scaling factor that reduces the weight of future utility compared to current utility. If it is less than zero, you eat more now. If it is closer to one, you save more for the future. It models the idea that people usually prefer good things sooner and bad things later, something very intuitive. This pops up literally everywhere in economics and is conceptually (almost identical) to the idea of an interest rate.
Rationality
Economists describe "agents" as "rational". I've made use of the term "agent" in earlier sections but haven't explicitly defined how economists use it. The "agent" is the fundamental unit of analysis shared by most economists. This is the basic building block or elementary unit in many economic models; the lowest level at which behavior is assumed or described. In disciplines like physics, the fundamental unit might be a particle. In Sociology, it might be a group or institution. It's important to note that, some people self described as economists, take the institution to be fundamental. The fundamental unit doesn't have to be the "smallest" per se, it's typically just the starting point for a specific line of inquiry. In economics, it is an "agent"; an individual decision making entity. We build models by specifying how these agents behave.
"Agents" in economics have ordered and complete preferences, respond to incentives, make choices given constraints, and are modeled to optimized an objective like utility (more on that in a bit) or profit. A "consumer" is an agent that maximizes utility from consumption of finished products, goods, services etc. A firm is an "agent" that maximizes profit or minimizes costs. A government is an agent that maximizes "welfare" (more on that later). Macroeconomists make use of the "representative agent", encapsulating the average behavior of a collection of homogenous agents. We often assume that agents are rational (the point of this section), forward looking, self interested, autonomous and atomistic. You may think you know what these terms refer to, but economists tend to use them in very specific ways. For example, self interest need not mean "selfishness". Atomistic is pretty much an assumption about how behaviors are influenced by peer groups.
In behavioral economics, agents are conceptualized differently. For example, in the classical conceptualization, economists assume transitive preferences, meaning if I prefer A to B and B to C, then I prefer A to C. There is a well orderedness that follows classical laws of logic. Behavioral economists on the other hand, relax this assumption, frequently showing empirically that this assumption doesn't hold in reality. They also use a model of bounded rationality, in which cognitive resources are fundamentally constrained, implying we engage in suboptimal behavior utilizing simple decision rules like heuristics. These heuristics are influenced by framing, emotions, social norms. They can be inconsistent intertemporally and context dependent. They are subject to cognitive biases that may have been evolutionary inherited. Notice how this becomes extremely more complex to model. In agent based modeling, the "atomistic" and "homogenous" assumptions are relaxed. Agents are conceived as heterogenous and adaptive. They don't "optimize" anything, rather they follow simple rules of thumb and use learning algorithms (implicitly). Macroeconomic phenomenon are the emergent patterns arising from this underlying heterogeneity. In other words, there is no "representative agent". In game theory, agents are fundamentally strategic. They form Nth order beliefs about other peoples beliefs, updating these beliefs as games (situations of strategic integration) evolve. They project signals to competitors to influence their competitors beliefs. They can be both cooperative and competitive dependent on perceived payoffs. In social theory, agents are inherently inseparable from their social structures. Decisions aren't made based on constrained optimization and are shaped by culture, norms, and institutions. Preferences aren't a "given"; they are not taken for granted.
Notice how assumptions about the fundamental unit of analysis literally determines the conclusions we draw about "the economy". The choice of how to model an agent, determines what behavior is explain, what can be predicted, and what policies are recommended. Mainstream economists use the classical conceptualization of an agent, reflecting methodological individualism. There is nothing inherently wrong with this approach, insofar as it is a useful model of agency. It is becoming increasable augmented and challenged by more pluralistic conceptions of agency.
The foundational view of rationality in economics is the idea that agents make decisions that are consistent with their preferences and goals, given the information they have access to and their constraints. This is a form of "
instrumental rationality", a practical rationality that describes how people choose efficient means to achieve their goals. Economists assume preferences are consistent. This means they are complete, transitive, independent and monotone. Completeness refers to the idea that, given a complete set of choices, it is possible for the agent to rank all the options, according to some preference mapping (i.e. utility). Transitivity was mentioned earlier. Independence refers to the idea that preferences are formed in isolation and that a persons choice between two options are not influenced by the presence or absence or a third option. In economics, we call this "Independence of Irrelevant Alternatives", or IIA. This is a crucial assumption ensuring preferences are well defined and consistent; meaning that if it fails then we can't model agents as optimizers. The IIA assumption implies that choices can be predicted based solely on the properties of the options being considered, not on irrelevant circumstances or other options that might be available. Monotone preferences, or "Non-Satiation", means that "more is better". An agent will always choose a bundle of goods that contains more of every good, subject to their constraints. I cannot stress how foundational this assumption is. It assumes that consumers always prefer more of a good or service to less; and that there are no limits to their potential satisfaction of consuming more. Satisfaction might increase at a decreasing rate, this is called diminishing marginal utility, something I'll write about later.
Monotone functions are functions that either always increase or decrease within their domain. This is what we assume about consumer utility with respect to consuming a product. An important implication of this is that preferences are
convex .
Convexity refers to a feature of a mathematical function. Why is this important in economics? Simply put, preferences must be convex, because if not then its pretty frickin hard to optimize.
It's so easy to take this for granted when studying economics. It's also why many people struggle with studying economics; they're unfamiliar with the foundational assumptions of the fundamental unit of analysis. Every economic theory, recommendation, policy proposal, analysis etc in some form or another, builds off this. Many economists literally take it for granted; they do not recognize these as simplifying assumptions for the model, but see them as eternal truths about human behavior. One of my main contentions with economics, is the economists who are incapable of critically analyzing these central assumptions. When I was in highschool, I remember taking an economics class where on one day, the teaching was so dogmatic that in hindsight, the best description of the situation was child abuse. For the record, the instructor was not an economist. He probably had no familiarization with mathematical modeling. But he was trying to indoctrinate us with the monotonicity assumption by insisting that it's an eternal truth of "homo economicus" that we have infinite wants, and that we would act on these infinite wants if it werent for scarcity (constraints). This was not a discussion, this was not interactive, it was taught as a central dogma; literally like a Sunday School session. It's always been interesting to me how a modeling formalization has literally become ideology.
I have no problem with this rationality assumption in principle. It makes modeling choice mathematically tractable. It can offer some predictive power. It provides a normative benchmark, allowing us to make comparisons between different policies because it serves as a baseline for efficiency. However, I am a pluralist when it comes to economic methodology. I think this framework is a special instance of a broader set of possible descriptions of human behavior. It's unable to explain many real world phenomena like bubbles, crises, and persistent unemployment. It is inconsistnt with behavioral predictions like loss aversion, framing effects, and time inconsistency. It's not capable of predicting how agents will respond to policy and price changes universally. It's really contrived; I prefer as-is modeling to as-if modeling. Assuming perfect information and infinite computation is kind of absurd and obviously not empirically valid. Rationality is useful in that it provides coherence and rigor to models, but it abstracts away human psychology, institutional aspects, and computational limits (more on this later).
Nevertheless, like I mentioned, this is foundational in economics. It informs how the models are constructed, and the subsequent policy recommendations. For example, the supply and demand model imply rent control is economically inefficient. Since the framework is deductive in nature, the implications of the model would recommend removing this policy. If A then B, A therefore B. If rent control, then inefficiency, rent control therefore inefficiency. These deductions literally fall out of the assumptions about our fundamental unit of analysis and how agents aggregate. In macroeconomics, a representative agent stands in as the single agent who can represent the economy. Heterogeneity is very difficult to model because aggregation is impossible (well, technically its possible, but its not possible to have a stable single equilibrium). This agent is assumed to solve intertemporal optimization problems. They also have
rational expectations about the future, this is the forward looking assumption. Specifically, it means that individuals gather all the available information, including past trends and economic data. They form expectations based on this historical data. These are statistical expectations about key macroeconomic measures such as inflation and interest rates. Therefore, central banks set interest rates based on forward looking inflation expectations falling directly out of the DSGE model assuming rational expectations.
There are a variety of different conceptualizations of rationality, as I've touch on briefly above. Some of these highlight the importance of cognitive resources. I think this is absolutely crucial for understanding rationality. Dan Sperber and Deirdre Wilson present a concept of "Relevance" in their book "Relevance: Communication and Cognition" which I think implies a model of rationality that is not only realistic, but consistent with definition of rationality in computational fields, and therefore cross disciplinary agreed upon. To me, this is an important sign of a concepts usefulness; if other disciplines converge on something similar. The authors introduce the cognitive principle of relevance. Human cognition is geared towards the maximization of relevance. In other words, we tend to pay attention to information that yields the most cognitive effect (like new insights or changes in belief) for the least processing effort. This leads to the communicative principle of relevance; Every act of communication carries with it the presumption of its own relevance. When someone says something, the listener expects that it is worth the mental effort to understand — i.e., it will be relevant enough to justify the attention. Communication is not just about encoding and decoding messages (as traditional code models suggest), but about inferring intentions. Listeners use context and assumptions to figure out what the speaker meant, not just what they said. They define communication as a two part process: Ostension, in which a speaker signals they want to communicate, and inference, the lister inteprets the signal, guided by the assumption it will be relevant. Communication and thought are guided by the search for relevance, and this means acheiving the most meaningful impact with the least amount of cognitive effort.
How is a theory of relevance, well, relevant to rationality? Well, their theory gives us a description about how cognitive faculties function. Rationality and decision making are obviously interconnected with that. Their theory implies something about rationality because it gives us a description of cognitive information processing, something fundamental to the concept of rationality. Rememeber, economists simply assume infinite processing power. How absurd is that? If you are in anyway familiar with computational complexity, supercomputing, or scientific computing, you'll be very aware of the fact that some of the fastest computers in the world still can only provide approximations to even relatively simply computations. And yet, economists think its safe to assume that, the human brain is capable of handling some of the most computationally complex problems. The theory of relevance highlights the fact that communication is an inferential process, which depends on cognitive resources. We cant possibly attend to all information, or even determine which information is relevant to a decision problem, without simplfying assumptions. This implies a model of bounded rationality. Humans are not perfectly logical agents. Instead of maximizing truth or utility in a strict sense, we use heuristics (mental shortcuts) to make satisficing decisions — ones that are good enough given our cognitive limitations. According to Sperber and Wilson, rationality is driven by the search for relevance. A person is rational if they pursue thoughts, beliefs, and interpretations that provide high cognitive effects (like useful inferences or knowledge) with minimal effort; this can be completely independent of utility. Their model of rationality is inferential, we interpret others not just by decoding language, but by inferring their intentions in context, guided by relevance. So communication is rational when it makes those inferences easy and rewarding.
Tom Griffiths, a cognitive scientist at Princeton, has a computational model of reality that is consistent with the rationality implied by Sperber and Wilsons communication model. Griffiths argues that to understand human rationality, we should think in terms of optimal use of limited resources; including time, information, and cognitive capacity. His work blends Bayesian inference, machine learning, and resource-bounded computation to model how people make decisions and draw conclusions. Tom Griffiths’ theory of rationality sees humans as computationally rational agents; not perfectly logical, but using clever approximations, heuristics, and probabilistic reasoning to solve problems efficiently under real-world constraints.
His approach is very interesting in my opinion because elements of it still incorporate the "as-if" modeling approach taken by economists while also incorporating insights from artificial intelligence, psychology, and computer science. For example, he assumes that at some level, humans reason as if they're doing bayesian inference. At some general level, they handle uncertainty by weighing evidence and prior beliefs to update their understanding of the world. Our cognitive process approximate bayesian reasoning. Other researchers in neuroscience like Karl Friston take this approach also. He also takes the resourc-rational approach, meaning that human thought and behavior should be understood as the best possible use of limited computational resources. So instead of optimizing, like in economics, people are bound by computational resources such that hueristics and approximations take place of a potentially resource intensive optimization. Think of it this way, economists assume that preference are complete. This means that agents are capable of enumerating all possible choices and rank ordering them according to which choices maximize utility. They do this intertemporally, meaning they are aware of how the choice space will look N years in the future. They also are aware of the secondary effects of choosing action A over action B, meaning they have counterfactual knowledge of the decision space. For any given decision, they can compute the optimal solution. Kind of hilarious when you pose it this way. But a more realistic approach, is to model people as cognitively resource constrained, not just physical resource constrained. Griffiths emphasizes computational-level analysis, following David Marr’s idea that we should ask: What is the goal of the computation? What is the optimal solution, and how close are humans to achieving it under real-world limits? His work connects to the idea that human cognition is adapted to the structure of the environment; we make the best decisions possible based on the patterns we’ve learned from experience (like machine learning models trained on data). This is known as
ecological rationality.
Obviously, I'm not here to reconcile the differences between Griffiths and Sperber/Wilsons theories. Strictly speaking there isn't anything to reconcile, the latter aren't advancing a model of rationality. But I think their communicative model implies many elements in Griffiths approach to rationality. For sperber/wilson, agents seek to maximize relevance and minimize cognitive load during communication. From a rational agent perspective, agents must engage with other agents to acquire information relevant to their decision problem. They obviously do not exhaustively inquire with other agents over the space of possible information sources and level of depth when engaging with the information. They are bound by cognitive resources and update their posterior beliefs accordingly. The mind is a relevance engine that is evolved to make inferential leaps based on minimal effort; I think this is literally what a heuristic is. I suppose the main difference between the two is that, since communication is inherently contextual and social, interpretation is bound by expectations of relevance, which are socially generated. In other words, rationality itself is something bound to the social. Griffiths approach is still individual based.
Below are some more non-classical approaches to modeling rationality that have inspired this section:
- Herbert Simon – Bounded Rationality: Humans are not fully rational due to cognitive and informational limits. Instead, they are boundedly rational; they make satisficing (satisfy + suffice) decisions rather than optimizing. People choose the first acceptable solution, not necessarily the best one. Memory, attention, and time restrict decision-making. Behavior is shaped by the structure of the environment; people adapt, rather than optimize.
- Gigerenzer – Ecological & Heuristic Rationality: In many environments, simple heuristics can be more effective than complex reasoning. Rationality is adaptive, not absolute. Fast and frugal heuristics are quick, efficient mental shortcuts that exploit environmental structure. Ecological rationality means What’s rational depends on the match between the mind’s heuristics and the structure of the environment.
- Amos Tversky & Daniel Kahneman – Heuristics and Biases: Humans rely on heuristics, which often lead to systematic biases, deviations from ideal rationality. There are many catalogued biases and heuristics including the Availability heuristic (Judging likelihood by ease of recall) and Representativeness heuristic (Judging similarity over base rates). Prospect theory is also central. This states that people evaluate gains/losses relative to a reference point and are loss-averse. This is where the idea "predictably irrational" comes from.
Implicit within all of this is the concept of
self interest. I didn't designate a section specifically for this concept because its normally covered by many definitions of rationality; although sometimes glossed over. Self interest does not mean selfish. Let's just establish that. It primarily refers to a specific vantage point of an individual within a broader economic system. This really goes back to Adam Smith. In The Theory of Moral Sentiments, Smith argues that our moral sentiments (feelings of empathy, sympathy, approval etc.) are stronger toward people who are closer to us, whether emotionally, socially, or physically. Smith talks about a hierarchy of concern, such that the literal proximity determines how much we care; the closest is ourselves, then family/friends/community, and then countrymen/strangers, finally humanity at large. Smith is providing an explanatory account of emotional distance, not evaluative. He is saying that it takes work to extend our sympathies beyond our immediate circles. Self interest refers to the fact that individuals attend to things that are more immediately salient, more directly important to them, or within a more proximal frame of reference. Smith never referred to self-interest as a dog-eat-dog kind of behavior; on the contrary, he repudiated that.
Self interest and altruism tend to operate simultaneously. Likewise, competition and cooperation tend to operate in conjunction. Many people confuse these concepts, juxtaposing them against one another, thinking they are mutually exclusive. However, economists understand these concepts like the following: for a rational agent pursuing self preservation, very often its necessary to engage in altruistic and cooperative behavior. We engage in this behavior not in begrudgingly, but because its part of a broader self preservation goal that encompasses a wide range of ethical behaviors. But can we be perfectly altruistic, by showing a high level of empathy for those outside your immediate proximity? The answer is probably no. We are oriented toward our own immediacy, and sometimes this comes at the expense of showing empathy towards the out group. Since we cant empathize with all possible vantage points (we cant put ourselves in everyones shoes), we tend to place our cognitive effort towards our immediate groups. This is in essence how economists think of self interest. I should qualify that last statement actually. Many economists who have actually read Adam Smith will think this. Other economists reduce self-interest to mere utility maximization. Smith’s insight that our sympathy weakens with distance shows that he saw self-interest not as a cold, calculating force, but as entangled with the limits of our emotional imagination. The economist’s self-interest is abstract and constant; Smith’s self-interest is human, fallible, and bound up with emotion and moral perception.
Opportunity Cost
This is a fundamental concept used by economists to understand the allocation of some scarce resource. The resource can be time, energy, money, something physical like land, etc. Opportunity cost refers to a decision about the scarce resource and the implicit tradeoff you are making relative to alternative uses. For example, suppose you have some resource called X, that can be used for purposes, ranked in descending order, (a,b,c). By selecting option (a), your opportunity cost is (b); it represents what you have to "give up" in order to devote those resources to option (a). The opportunity cost is the actual value (usually defined in terms of utility, something we will define later) someone must give up.
Let's concretize this with an example. Suppose you have a portfolio of financial assets, with a mixture of fixed income and equities. You can imagine a scenario where you have 1000$ to spend on different mixtures, or combinations of these assets. Call these mixtures M1, M2 and M3. Lets say M1 gives expected profits of 100$, M2 90$ and M3 85$. Your opportunity cost will be the difference between M1 and M2.
This seems like a rather useless concept at first, but I cannot stress how essential it is within the economists toolkit. It is fundamentally about how agents identify, rank, and select among alternative uses of some resource; which is at the core of economic behavior. Opportunity cost focuses on the single most valuable thing you had to give up, when making your choice. Here is an example you might see in a textbook. Suppose a company owns a building. It can choose to rent it out for 50k a year or use it for its own operations. If the company decides to use it, it is forgoing 50k dollars of rent they could have earned. So they will not use the building unless they expect they can make more than 50k on the alternative use.
Consider another example. Imagine a group of citizens under an oppressive regime. They’re frustrated, hungry, overtaxed, but they haven’t revolted yet. Why might this be? Revolting involves opportunity costs. To participate in a revolution, people must give up their current income (even if its low), relative safety, and the time/effort that could go into something else like fleeing. So the opportunity cost of revolting is the stability and limited benefits of not revolting. Now suppose those current benefits diminish, the opportunity cost of not revolting will increase. So from an economists perspective, when the opportunity cost of action becomes lower than the opportunity cost of inaction, a revolution might spark.
I'm not here to argue about whether revolutions are made based on an economic calculus. All I am attempting to do is show how the concept is applied. Obviously, ideological factors strongly influence the nature of revolutions. Also, even within a business context, someone might not pick the better alternative (from a financial perspective) for reasons such as sentimentality, or emotional connection to one alternative. Opportunity costs are intimately connected with incentives, which we'll learn about next.
Incentives
These are broadly thought to be factors that influence the choices people make by altering the perceived costs and benefits of different actions. Economists use an extremely broad definition; incentives are anything that motivate or influence human behavior by means of altering the cost-benefit structure. When an incentive lowers the opportunity cost of an action, that action becomes more attractive. If it raises the opportunity cost, it's less likely to be chosen. Opportunity cost is what’s given up when making a choice. Incentives are what shift the relative attractiveness of those choices by influencing opportunity costs.
From a systemic perspective, we normally refer to "incentive structures". This refers to the framework of rewards and penalties built into a system that shapes how people behave. It is the underlying setup that determines which actions are encouraged and discouraged, and what outcomes are rewarded or punished. The system itself can be formal, in the form of laws, contracts and policies. It can also be informal, in the form of cultural norms, social pressure, and status.
For example, imagine a corporate bonus system. Managers might get bonuses for short term profits. This might result in cost cutting behavior like laying off workers or slashing R&D. So the stock prices of that corporation rise in the short term, at the expense of long term innovation and employee maturation. This would be characterized as an incentive structure flaw. Or consider an environmental policy that subsidizes gasoline to the poor. The well intentioned incentive structure might have the unintended consequences of increasing pollution; since people are incentivized to drive more. Also, if there is no long term plan to phase out the program, driving can become so entrenched within the economic system, that transitioning to renewals becomes near impossible in the future because there are no incentives to adjust.
This might be one of the most fundamental concepts economists use to characterize human behavior. We are constantly asking whether a certain policy distorts economic incentives. There is even a subset of economics called
Mechanism Design, which studies how to construct rules or institutions, to reverse engineer incentives to get the outcomes you want. It studies how to create systems or rules (mechanisms) so that individuals, acting in their own self-interest, will still produce a desirable overall outcome. A traditional "economics as an observational science" approach is interested in studying how people behave within a given system, while a "economics as a field of engineering" uses mechanism design to design the system itself. Given the outcome we want, what rules should we write?
Directly related to mechanism design, and more broadly, incentive structures, is the field of
Law & Economics. The field is fundamentally about designing legal rules and institutions that align individual incentives with socially desirable outcomes. For example, in tort law (accidents, negligence, and liability), our goal might be to reduce harm while not stifling productive activity. A mechanism to achieve this, might be to select liability rules that create optimal care incentives for injurers and victims. This would be highly relevant in a situation where employers might be accountable for employee injuries. The main idea is that we want to write rules such that people can act in their own self interest but this does not result in a
tragedy of the commons (more on that later). Property rights are also a fundamental concept in economics. I'll write more about that later, but the rules of ownership will dramatically determine the resulting allocation and distribution of resources.
I hope this begins to show how these basic concepts have fundamentally shaped our modern institutions. Interestingly, I became aware of Law & Economics through its critics. I frequently read a legal theorist named
Richard Wright, who specializes in tort law, and is highly critical of what he sees as the degradation of legal theory due to the introduction of economic concepts into the discipline. In particular, he is critical of
Richard A. Posner, who might be the most influential figure in Law & Economics. Essentially, Wright and others argue that Posner's view reduces law to cost-benefit analysis, ignoring justice, rights, and duties. Law is not just a tool for efficient outcomes—it’s a normative system rooted in justice, fairness, and moral responsibility. I am not going to elaborate any further on this, but if interested, I definitely recommend reading about these two people. You'll begin to see how prolific economic thinking has penetrated the most fundamental institutions governing our lives. The nature of the legal system directly impacts incentive structures and opportunity costs, and hence how the economic metabolism of society functions.
Utility
This might be one of the most underappreciated concepts in economics, among non-practitioners. Utility is a core concept in decision theory, economics, and operations research, representing a way to model and quantify preferences, satisfaction, or value that an agent (individual or organization) assigns to outcomes. It's used to guide rational choices under conditions of uncertainty, scarcity, or competing alternatives. Utility is a numerical representation of preferences. Higher utility values represent more preferred outcomes. Its used to model rational choices under uncertainty (e.g., expected utility theory) and to describe consumer behavior, market demand, and welfare economics. A major principle in economics is that people try to maximize utility; agents choose options that yield the highest point on the utility curve. Another important concept is marginal utility; the additional utility derived from consuming one or more unit of a good or service. This is typically understood by analyzing the derivative of the utility function; the function mapping input combinations (typically combinations of goods and services) to utility space. A utility function is typically written as:
where:
-
is the consumption set or set of possible bundles (e.g., combinations of goods).
-
is the real-valued utility assigned to a bundle .
This function represents the preferences of a consumer over bundles of goods. Here are a few examples of utility functions used in economics:
Cobb-Douglas Utility:
-
Perfect Substitutes:
-
Perfect Complements:
-
Quasilinear Utility:
-
CES (Constant Elasticity of Substitution) Utility:
The famous "demand curve" in economics is indirectly derived from the utility function. Utility functions represent a consumers preferences over a bundle of goods. Since economics is about scarcity, this utility is constrained by the household budget (we do not have infinite resources to satisfy every desire). The global maximum U(.) might be outside the feasible set. So the consumers goal is to maximize utility subject to the budget constraint (which is a constrained optimization problem). Solving these equations, gives the optimal quantities as functions of price and income, which correspond to the demand curve. Economists typically assume diminishing marginal utility, meaning the first derivative of the utility function is a decreasing function. The utility function increases at a decreasing rate, while the marginal utility function (first derivative) asymptotically approaches some constant. The demand curve falls out of the budget constraint problem (p*x < I). In plain English, the demand curve (partly) is downward sloping because of diminishing marginal utility.
This might sound extremely abstract and unremoved from practice but its at the very core of how economists model the economy. Consider a real example. The Federal Reserve has a core set of monetary policy tools it can use to influence interest rates, inflation, employment, and economic stability:
1. The Federal Funds Rate (Main Tool): The interest rate banks charge each other for overnight loans of reserves. The Fed doesn't directly set this rate but targets it by adjusting the supply of reserves in the banking system via open market operations (OMO) or interest on reserves. This rate affects all other short-term interest rates — from savings accounts to business loans to mortgage rates. Changing it influences consumption, investment, and inflation.
2. Open Market Operations (OMO): Buying or selling government securities (like Treasury bills) in the open market.
- Buy securities → inject money → lower interest rates (stimulate economy)
- Sell securities → pull money out → raise interest rates (cool economy)
3. Interest on Reserve Balances (IORB): The interest rate the Fed pays banks on their reserves held at the Fed. Banks won’t lend at rates lower than what they can earn risk-free from the Fed. So this effectively sets a floor for the Fed Funds Rate.
4. Discount Rate (Lender of Last Resort): The interest rate the Fed charges commercial banks for short-term loans from the Fed's discount window. Mostly used in emergencies when banks can’t get funding elsewhere. It’s a backup liquidity tool, not a regular lever for setting monetary conditions.
5. Forward Guidance (Communication Tool): Public statements about future policy intentions, e.g. "Rates will remain low for an extended period. Expectations drive behavior. Clear guidance can influence long-term interest rates and financial market conditions.
Based on a model of consumer utility, the fed adjusts these policy tools, influencing consumption choices, by changing the incentives embedded within the utility function. In monetary theory, utility functions shape how people make choices about consumption today vs. in the future. The Euler equation formalizes that tradeoff.
The Core Euler Equation (in real terms):
Where:
It says households will only give up consumption today if they’re compensated by enough expected utility tomorrow , which depends on the real return (how much they can get by saving). The curvature of the utility function directly controls how much consumption will shift if rates change. Let’s map the tools to the equation:
1. Federal Funds Rate (nominal rate )
Appears in the Euler equation indirectly, via the real interest rate:
So:
2. Open Market Operations (OMO)
OMO are used to hit the Fed’s interest rate target. So they influence , and thus , the same way. They’re the operational tool to implement changes that show up in the Euler equation.
3. Interest on Reserve Balances (IORB)
IORB affects bank incentives to lend, which influence the actual market interest rates (including ). If banks can earn more by parking money at the Fed, they tighten lending → market interest rates go up → higher in the Euler equation.
4. Forward Guidance
Even if the Fed doesn’t change today, if it signals future rate hikes, that changes:
So expectations of higher rates reduce current consumption — directly through the expectations operator in the Euler equation.
5. Quantitative Easing (QE)
QE works by reducing long-term interest rates, including , especially when short-term rates are at zero.
Lower → higher current consumption → economic stimulus.
The form of determines how strongly households respond to changes in . For example:
-
If , then:
-
If utility is more curved (higher in CRRA), they are less responsive.
So Fed economists calibrate utility functions in DSGE models to match observed behavior, how much households change consumption in response to interest rate changes. Households maximize utility subject to constraints (budget, cash-in-advance, etc.). Solving this yields Euler equations and money demand functions, which help predict how interest rates affect savings/consumption, how inflation expectations influence money holdings (which affects output), and how policy changes influence economic behavior.
So as you can see, utility builds off of the more basic notions of incentives and opportunity costs.
Supply/Demand Functions and Ceteris Paribus
I think we have all the basics necessary to derive the supply and demand model. This is cornerstone in economics. Before diving into any derivations, I'd first like to explain two concepts that are critical for understanding how economists analyze the resulting
model. Economists want to answer questions such as:
- How does a change in one variable affect others?
- What happens to employment if the minimum wage increases?
- What are the effects of policy interventions or external shocks?
- How does a tax affect consumer prices and producer revenue?
- What are the conditions for equilibrium?
- At what price do supply and demand balance?
- How do markets and agents react to changes in incentives or constraints?
- How do consumers respond to a change in interest rates?
In economic analysis, comparative statics and ceteris paribus are fundamental analytical and conceptual tools used to understand how changes in one variable affect others within an economic model. Comparative statics is the method economists use to compare two different equilibrium states resulting from a change in an exogenous variable (something determined outside the model, like government policy or consumer preferences). It compares before-and-after outcomes and does not focus on the process of adjustment or dynamics over time. For example, if the price of gasoline increases, comparative statics would look at how this affects the quantity of gasoline demanded, holding everything else constant. It compares the original equilibrium (before the price change) with the new equilibrium (after the price change). Ceteris paribus is a Latin phrase meaning “all other things being equal” or “holding everything else constant.” It is a simplifying assumption used to isolate the effect of a single variable. For example, when analyzing how the demand for apples changes with price, economists assume ceteris paribus; that income, prices of other goods, and consumer preferences remain unchanged. Very often, comparative statics often asks counterfactual questions that explore outcomes in alternative states of the world. Comparative statics uses counterfactual reasoning to compare equilibria before and after a change in an exogenous factor, holding everything else constant (ceteris paribus). This is implemented by analyzing the partial derivatives of the resulting model, which I'll show shortly. Ceteris paribus is powerful: it lets you isolate these effects clearly, and see whether your model produces intuitive or surprising behavior. Partial derivatives are the mathematical formalization of a comparative static analysis.
So now that we understand what we are trying to do, lets derive a supply curve, demand curve, and analyze equilibrium by doing comparative statics. Remember, we are assuming economic agents are maximizers. Individual consumers will be seeking to maximize utility and firms will be seeking to maximize profit (minimize cost). Choice variables are at the heart of any optimization problem. They represent the things the decision maker can control or choose to adjust in order to acheive these goals. For a consumer, the choice variables are quantities of a good to buy. For a firm, these are the factors of production (labor or capital) or the output level. For a policy maker, it might be tax rates or subsidy levels. These are "variables" because the decision maker is free to choose the values, under some set of constraints, to optimize the objective.
Remember, an optimization problem has three main components:
- Objective function: what you're trying to maximize or minimize (e.g., profit, utility)
- Choice variables: the variables you control (e.g., \(x_1, x_2, \dots, x_n\))
- Constraints: limits or requirements (e.g., budget, production technology)
Example 1: Consumer Choice
\[
\max_{x_1, x_2} \ u(x_1, x_2) \quad \text{subject to } p_1 x_1 + p_2 x_2 \leq I
\]
- Choice variables: \(x_1\), \(x_2\) — quantities of goods
- Objective: maximize utility
- Constraint: budget
Example 2: Firm Profit Maximization
\[
\max_{L, K} \ \pi = p f(L, K) - wL - rK
\]
- Choice variables: \(L\) (labor), \(K\) (capital)
- Objective: maximize profit
- Constraints: often none in short-run, or include capacity or cost restrictions
Choice variables enter the objective function, so changing them changes the value the decision-maker cares about. They are adjusted subject to constraints; you can’t just pick anything, but you choose what’s best from what’s allowed. In mathematical optimization, they are what you're solving for. Without choice variables, there's no decision to make. The solution to an optimization problem is always a value (or set of values) for the choice variables that maximizes or minimizes the objective.
Let’s derive the market supply curve from the firm’s profit maximization problem using the Lagrangian method:
- Start with a single firm facing a cost constraint (cost minimization problem as dual)
- Derive the firm's supply function
- Aggregate to get the market supply curve
1. Setup: Firm’s Profit Maximization Problem
Let’s assume the firm has:
- A production function: \(f(x)\), where \(x\) is the input
- Input price: \(w\)
- Output price: \(p\)
The firm chooses input \(x\) to maximize profit:
\[
\max_{x} \ \pi(x) = p \cdot f(x) - w \cdot x
\]
2. Cost Minimization Problem via Lagrangian
We now minimize cost subject to producing a fixed amount \(q\):
\[
\min_{x} \ w \cdot x \quad \text{subject to} \quad f(x) \geq q
\]
This is suitable for Lagrangian optimization. Define the Lagrangian:
\[
\mathcal{L}(x, \lambda) = w x + \lambda (q - f(x))
\]
First-Order Conditions (FOCs):
- \(\frac{\partial \mathcal{L}}{\partial x} = w - \lambda f'(x) = 0 \Rightarrow \lambda = \frac{w}{f'(x)}\)
- \(\frac{\partial \mathcal{L}}{\partial \lambda} = q - f(x) = 0 \Rightarrow f(x) = q\)
So, the cost-minimizing input \(x^*(q)\) solves:
\[
f(x) = q \quad \Rightarrow \quad x = f^{-1}(q)
\]
Then cost function:
\[
C(q) = w \cdot f^{-1}(q)
\]
3. Derive Supply Function
Now switch back to the profit maximization side.
Profit:
\[
\pi(q) = p q - C(q) = p q - w \cdot f^{-1}(q)
\]
Maximize with respect to \(q\):
\[
\frac{d\pi}{dq} = p - w \cdot \frac{d}{dq} f^{-1}(q) = 0
\]
But from inverse function rule:
\[
\frac{d}{dq} f^{-1}(q) = \frac{1}{f'(x)} \quad \text{where } x = f^{-1}(q)
\]
So:
\[
p = \frac{w}{f'(x)} \Rightarrow p \cdot f'(x) = w
\]
This matches the first-order condition from profit maximization: value of marginal product = input price.
Solve this equation for \(q\), via \(x\), to get the firm's supply function:
\[
q = f(x^*(p)) \quad \text{where } f'(x^*) = \frac{w}{p}
\]
4. Example: Cobb-Douglas Production
Say: \(f(x) = x^\alpha\), \(0 < \alpha < 1\)
- \(f'(x) = \alpha x^{\alpha - 1}\)
- Set: \(p \cdot f'(x) = w \Rightarrow p \cdot \alpha x^{\alpha - 1} = w\)
- Solve for \(x\):
\[
x = \left( \frac{p \alpha}{w} \right)^{\frac{1}{1 - \alpha}}
\]
So output: \(q = f(x) = \left( \frac{p \alpha}{w} \right)^{\frac{\alpha}{1 - \alpha}}\)
This is the individual firm’s supply function:
\[
q(p) = A p^{\frac{\alpha}{1 - \alpha}}, \quad A = \left( \frac{\alpha}{w} \right)^{\frac{\alpha}{1 - \alpha}}
\]
5. Market Supply Curve
If all firms are identical (simplifying assumption by economists) and there are \(N\) of them:
\[
Q(p) = N \cdot q(p) = N A p^{\frac{\alpha}{1 - \alpha}}
\]
This is the market supply curve. The inverse supply function expresses price as a function of quantity supplied rather than the other way around. This is useful because it tells us what price is required to induce a given level of output. It’s particularly helpful for market analysis, equilibrium modeling, and comparative statics.
Recall from earlier:
\[
q(p) = A \cdot p^{\frac{\alpha}{1 - \alpha}}, \quad \text{where } A = \left( \frac{\alpha}{w} \right)^{\frac{\alpha}{1 - \alpha}}
\]
Let’s solve for \(p\) in terms of \(q\): Start with:
\[
q = A \cdot p^{\frac{\alpha}{1 - \alpha}}
\]
Solve for \(p\):
- Divide both sides by \(A\):
\[
\frac{q}{A} = p^{\frac{\alpha}{1 - \alpha}}
\]
- Take both sides to the power \(\frac{1 - \alpha}{\alpha}\):
\[
p = \left( \frac{q}{A} \right)^{\frac{1 - \alpha}{\alpha}}
\]
Substitute back in the expression for \(A\):
\[
A = \left( \frac{\alpha}{w} \right)^{\frac{\alpha}{1 - \alpha}} \quad \Rightarrow \quad \frac{1}{A} = \left( \frac{w}{\alpha} \right)^{\frac{\alpha}{1 - \alpha}}
\]
So:
\[
p(q) = \left( q \cdot \left( \frac{w}{\alpha} \right)^{\frac{\alpha}{1 - \alpha}} \right)^{\frac{1 - \alpha}{\alpha}}
\]
Or more cleanly:
\[
p(q) = B \cdot q^{\frac{1 - \alpha}{\alpha}}, \quad \text{where } B = \left( \frac{w}{\alpha} \right)
\]
(Note: the exponent is positive because \(0 < \alpha < 1\).)
How do we interpret this? As \(q\) increases, \(p\) must increase to induce more output. This reflects increasing marginal cost; typical of most realistic production settings. The elasticity of supply depends directly on the exponent \(\varepsilon\), which comes from technology (i.e., how easily output increases with input).
\[
p(q) = B \cdot q^{\varepsilon}, \quad \varepsilon = \frac{1 - \alpha}{\alpha} > 0
\]
If market supply is \(Q(p) = N \cdot q(p)\), then:
\[
Q(p) = N A p^{\frac{\alpha}{1 - \alpha}} \Rightarrow p(Q) = \left( \frac{Q}{N A} \right)^{\frac{1 - \alpha}{\alpha}}
\]
Now economists can make statements about what a market of firms will do under various conditions such as an unforseen policy shock or perhaps a natural disaster.
Now let’s now derive the market demand function from the consumer’s utility maximization problem.
1. Conceptual Setup: Consumer Choice
A consumer wants to choose a bundle of goods that gives the highest utility subject to a budget constraint.
Let:
- \(x_1, x_2\): quantities of two goods
- \(p_1, p_2\): prices of goods 1 and 2
- \(I\): income
- \(u(x_1, x_2)\): utility function
2. Consumer’s Problem (Utility Maximization)
\[
\max_{x_1, x_2} \ u(x_1, x_2) \quad \text{subject to } p_1 x_1 + p_2 x_2 \leq I
\]
We’ll assume the constraint binds (no free money), so:
\[
p_1 x_1 + p_2 x_2 = I
\]
We’ll use the Lagrangian:
\[
\mathcal{L}(x_1, x_2, \lambda) = u(x_1, x_2) + \lambda (I - p_1 x_1 - p_2 x_2)
\]
3. Solve Using Cobb-Douglas Utility (Example)
Let’s use a classic Cobb-Douglas utility function:
\[
u(x_1, x_2) = x_1^{\alpha} x_2^{1 - \alpha}, \quad \text{where } 0 < \alpha < 1
\]
First-Order Conditions (FOCs)
- \(\frac{\partial \mathcal{L}}{\partial x_1} = \alpha x_1^{\alpha - 1} x_2^{1 - \alpha} - \lambda p_1 = 0\)
- \(\frac{\partial \mathcal{L}}{\partial x_2} = (1 - \alpha) x_1^{\alpha} x_2^{-\alpha} - \lambda p_2 = 0\)
- \(\frac{\partial \mathcal{L}}{\partial \lambda} = I - p_1 x_1 - p_2 x_2 = 0\)
4. Solve the FOCs
Take the ratio of (1) and (2):
\[
\frac{\alpha x_1^{\alpha - 1} x_2^{1 - \alpha}}{(1 - \alpha) x_1^{\alpha} x_2^{-\alpha}} = \frac{\lambda p_1}{\lambda p_2}
\Rightarrow
\frac{\alpha}{1 - \alpha} \cdot \frac{x_2}{x_1} = \frac{p_1}{p_2}
\]
Solve for \(x_2\) in terms of \(x_1\):
\[
x_2 = \frac{1 - \alpha}{\alpha} \cdot \frac{p_1}{p_2} \cdot x_1
\]
Now plug into the budget constraint:
\[
p_1 x_1 + p_2 x_2 = I
\Rightarrow
p_1 x_1 + p_2 \left( \frac{1 - \alpha}{\alpha} \cdot \frac{p_1}{p_2} \cdot x_1 \right) = I
\]
Simplify:
\[
p_1 x_1 \left(1 + \frac{1 - \alpha}{\alpha} \right) = I
\Rightarrow
p_1 x_1 \cdot \frac{1}{\alpha} = I
\Rightarrow
x_1 = \frac{\alpha I}{p_1}
\]
Plug back into \(x_2\):
\[
x_2 = \frac{(1 - \alpha) I}{p_2}
\]
5. Marshallian (Ordinary) Demand Functions
\[
x_1(p_1, p_2, I) = \frac{\alpha I}{p_1}, \quad x_2(p_1, p_2, I) = \frac{(1 - \alpha) I}{p_2}
\]
These are the individual demand functions: they show how much of each good the consumer will demand, as a function of prices and income. This function is Homogeneous of degree 0 in \((p_1, p_2, I)\): If all prices and income double, demand stays the same. It is Downward sloping: As \(p_1\) increases, \(x_1\) decreases. Demand for each good is proportional to the budget share: \(\alpha\) and \(1 - \alpha\).
Now lets derive the Inverse demand function, expressing price as a function of quantity demanded, holding income and other prices constant and Market demand, aggregating individual demand functions across consumers. From earlier, we have the Marshallian demand, these express the maximum price the consumer is willing to pay for a given quantity. Demand is downward-sloping: as quantity increases, the price the consumer is willing to pay falls. These functions reflect the marginal utility per dollar, the more you have of a good, the less you're willing to pay for more.
Suppose there are \(N\) identical consumers with the same utility function and income \(I\). Then the market demand is just the sum of individual demands. These are aggregate demand curves for goods 1 and 2 in the market.
\[
X_1(p_1) = N \cdot x_1 = N \cdot \frac{\alpha I}{p_1} = \frac{N \alpha I}{p_1}
\]
\[
X_2(p_2) = N \cdot x_2 = N \cdot \frac{(1 - \alpha) I}{p_2} = \frac{N (1 - \alpha) I}{p_2}
\]
Rewriting in inverse form:
\[
p_1(X_1) = \frac{N \alpha I}{X_1}, \quad p_2(X_2) = \frac{N (1 - \alpha) I}{X_2}
\]
We are almost there. We have the two major ingredients for establishing an equilibrium needed to do comparative statics! In a competitive market, equilibrium occurs at the price \(p^*\) and quantity \(q^*\) where:
\[
\text{Quantity demanded} = \text{Quantity supplied}
\quad \Rightarrow \quad Q_d(p^*) = Q_s(p^*)
\]
It’s the point where buyers and sellers agree: no excess demand, no excess supply. Assume a single good, \(q\), and a Cobb-Douglas utility and production structure. Recall the market demand and market supply functions from earlier:
\[
Q_d(p) = \frac{N \alpha I}{p}
\]
\[
Q_s(p) = N A p^{\frac{\alpha}{1 - \alpha}}
\]
This shows upward-sloping supply and downward-sloping demand. Set quantity demanded equal to quantity supplied:
\[
Q_d(p) = Q_s(p)
\quad \Rightarrow \quad
\frac{N \alpha I}{p} = N A p^{\frac{\alpha}{1 - \alpha}}
\]
Cancel \(N\) on both sides:
\[
\frac{\alpha I}{p} = A p^{\frac{\alpha}{1 - \alpha}}
\]
Multiply both sides by \(p\):
\[
\alpha I = A p^{\frac{\alpha}{1 - \alpha} + 1}
\]
To solve for equilibrium price \(p^*\), let’s simplify the exponent:
\[
\frac{\alpha}{1 - \alpha} + 1 = \frac{\alpha + (1 - \alpha)}{1 - \alpha} = \frac{1}{1 - \alpha}
\]
So:
\[
\alpha I = A p^{\frac{1}{1 - \alpha}} \Rightarrow
p^{\frac{1}{1 - \alpha}} = \frac{\alpha I}{A}
\Rightarrow
p^* = \left( \frac{\alpha I}{A} \right)^{1 - \alpha}
\]
Now we want to find the Equilibrium Quantity \(q^*\). Plug \(p^*\) back into either supply or demand. Using demand:
\[
q^* = Q_d(p^*) = \frac{N \alpha I}{p^*}
= N \alpha I \cdot \left( \frac{A}{\alpha I} \right)^{1 - \alpha}
= N \cdot A^{1 - \alpha} \cdot (\alpha I)^\alpha
\]
What determines the equilibrium?
- On the demand side:
- \(N\): number of consumers
- \(I\): income
- \(\alpha\): preference weight on good 1
- On the supply side:
- \(A\): a function of technology (\(\alpha\)) and input cost \(w\)
- \(N\): number of firms
Comparative Statics:
- Increase in income \(I\):
- Demand shifts right
- \(p^*\) increases
- \(q^*\) increases
- Decrease in input cost \(w\):
- Supply shifts right (A increases)
- \(p^*\) falls
- \(q^*\) rises
- More consumers or firms:
- Increasing \(N\) on the demand side raises \(q^*\) and \(p^*\)
- Increasing \(N\) on the supply side increases \(q^*\) but reduces \(p^*\)
This is a theoretical model that makes predictions about what will happen empirically. Typically what an economist would do next is collect data and fit an econometric model to test whether the theoretical model matches reality. This is also known as the "Validation" stage of applied mathematical modeling. If the empirical estimates align with the predictions made by the theoretical model, this would act as confirmation of the model; it describes economic reality to a sufficient degree. I'll say more about empirics in later posts. For now, just remember that many economists consider an empirical model to be successful if the signs of the coefficients align with the theoretical model. For example, if the empirical model suggests that an increase in income decreases demand for a product, that would indicate something is wrong with the model. If the model fits poorly to the data (based on econometric criteria of model fit), economists might revise or relax their assumptions, consider alternative functional forms, or move to more advanced methods like non-parametric estimation.
It should also be clear that policy implications flow naturally from economic models. Once a model is formalized and possibly validated empirically, it becomes a tool for counterfactual reasoning; "What would happen if something changes"? The "something" is typically a policy. If something shifts, it gives us a predictive framework for understanding how the system will respond. The model identifies key variables that influence market outcomes so economists can use this to figure out the direction and magnitude of effects of some policy based on the structure of the model. This is where the common textbook examples of policy derive: tax policy, price controls, subsidies etc. I've not yet talked about efficiency, but this is a common theme in economics. Efficiency is a deviation from the optimal market solution. But efficiency is conceptualized very specifically in economics and derives from the assumptions governing these standard models (welfare economics). More on that later. These models also help economists run cost-benefit analyses, compare trade-offs between the short-run and long-run, and allow them to draw conclusions about who will be effected by something.
The model provides clarity about mechanisms and outcomes, it makes our assumptions explicit, and allows simulation of alternatives without trial-and-error in the real world. Policy implications are not just guesses; they are disciplined logical consequences of the structure of the model. The more grounded the model is in both theory and data, the more reliable its guidance becomes for shaping public policy. Often in economics, much dispute arises at the level of assumptions. Differing assumptions lead to differing policy implications, which have a real effect on people. These assumptions ought to be interrogated. Unfortunately, in the public sphere, economic discourse is polluted by ideology. Models are just maps of reality; they are necessarily wrong but can be useful. They are useful for gaining analytical clarity and are fundamental tools of inquiry, not conversation stoppers. Often times, these models become justifications for dogmatic economic ideology. This was the major motivation driving me to write about this because nothing pisses me off more than ideologues at think tanks who pollute the broader public dialogue.
Assumptions
We have made reference to the notion of "assumption" many times throughout this post. There are many assumptions fundamental to what might be referred to as "orthodox economics". Often, these assumptions are what divide economists into varying heterodox "schools of economics". They are essentially different starting points of analysis which lead to different sets of methods and many times, rapidly divergent descriptive and prescriptive conclusions. I first want to discuss more generally the role of assumptions in everyday life. Then we will dive into the most core assumptions fundamental to much of economics.
An assumption is a proposition that is accepted without proof (at least temporarily), often as a starting point for further reasoning, action, or communication. In modeling, assumptions are simplifications or idealizations that are used to abstract away complexity, make problems mathematically tractable, and define boundary conditions of the model. They are often not intended to be true in the real world, but are meant to produce useful insights under controlled or ideal conditions. Many times, they are required because we have insufficient information or data about the system under consideration. There are different types of assumptions that arise in modeling contexts. Structural assumptions define the form of the model; like linear or nonlinearity, more broadly functional form. There are simplifying assumptions that are used to eliminate complications, such as ignoring friction in simple physical models. There are boundary and initial condition assumptions that define the system limits; such as defining edge cases. There are assumptions about homogeneity or independence; such as iid assumption in statistical models to ignore network effects. In everyday situations, we often have culturual and social assumptions such as "smiling signalling friendliness"; necessary for navigating social life. We have ontological assumptions such as objects persisting through time. We have foundational epistemic assumptions such as the existence of other minds. We assume object permanence, causal relations, and spatial continuity; these are "hardwired"assumptions.
Assumptions are a necessary part of all human reasoning. We cannot scrutinize every proposition at every moment. If we do not assume something, reasoning cannot begin; we simply couldn't infer anything because all reasoning, argument, and proof requires a starting point. Assumptions are crucial for communication because conversations require shared background context, definitions, and social norms. In modeling, you cannot model everything; and thats the very point of a model anyway, we want to simplify and abstract irrelevant details. Modeling allows us to make our assumptions explicit; often times disagreement arises because of unknown divergent implicit assumptions. Assumptions are heuristics, mental shortcuts that allow rapid decision making in uncertain environments. But unexamined assumptions can lead to bias, error, or dogma. To assume is to bet on something being provisionally true so that we can function, think, or communicate. But all assumptions are contextual, and being aware of them is the key to clarity and critical thinking.
Economics is assumption-heavy due to its abstract nature and the complexity of what we are modeling (human behavior). We often make behavioral assumptions about agents, such as what information they have access to, their goal structure, and whether they're inclined to cooperate or compete. We make assumptions about the environments agents operate within; such as market assumptions about transaction costs, adjustments, and structure. We often make many technical assumptions about continuity, convexity, differentiability, and equilibrium. We also make many assumptions about the dynamics of economic systems. All theories rest on assumptions (uniformity of nature, observer independence etc.); there is simply no way around it. The necessity of assumptions comes with many benefits. Models become tractible; solving equations and running simulations becomes feasible. Assumptions provide clarity; we can focus our attention on core mechanisms and not irrelevant details. Probably one of the most important benefits is comparaibility; shared assumptions make our models comparable. They also enable counterfactual analysis. But there are known risks as well. We could be oversimplifying reality, missing essential real world dynamics. Assumptions may give us a sense of false precision. In economics, there can often be normative smuggling; assumptions about rationality, efficiency, or fairness may be ideologically laden. Incorrect assumptions can also lead to disasterous policy misguidance.
Given the known risks of assuming something incorrect, the obvious next question becomes: When should we revise our assumptions? Assumption revision is the process of modifying, rejecting, or reaffirming the background beliefs or premises on which a system of thought or action is based. It arises under various scenarios. For example, when new evidence contradicts existing conclusions. This is an application of Poppers falsifiability criterion. If a model fails, we revise the assumption. But this obviously begs the questions; what does it mean for a model to fail? This is not always clear cut. Another example is when internal inconsistencies emerge. If two or more assumptions yield incompatible outcomes, we must revise at least one in order to maintain consistency. More generally, its rational to revise an assumption when New data falsifies the predictions derived from the assumption, The assumption leads to incoherence or contradiction within the model, The assumption creates systematic prediction errors across contexts, Better alternative assumptions produce more robust or simpler explanations, The assumption is based on outdated concepts or technologies (e.g., assuming infinite computation power), or when Stakeholders or society reject the normative basis of the assumption (e.g., utility maximization at all costs). It is irratinoal to stick to an assumption when you ignore contrary evidence due to ideological commitment/convenience/tradition, the assumption is unfalsifiable or immune to revision (dogma), the models predictive failures are blamed on everything else except the assumptions, or when the assumption serves to protect power structures and not explain reality. This is often driven by motivated reasoning, status quo bias, or confirmation bias; all forms of epistemic irrationality. Being rational means being attuned to evidence, willing to adapt, and humble about certainty. Assumption revision is not a weakness; it's a sign of intellectual maturity and rigor. There are many different theories of
belief revision; since it is outside the scope of the purpose of my objective here, we can move on to the core assumptions in economic theory.
Microeconomic theory is based on a set of fundamental assumptions about consumer and firm behavior. These assumptions provide the foundation for economic models and help in deriving demand and supply functions, equilibrium conditions, and welfare implications. For now we will just look at microeconomic fundamentals, but the assumptions underlying modern macroeconomic models (DSGE models and Rational Expectations Theory) are very similar.
- Rationality: Economic agents (consumers and firms) act rationally, meaning they seek to maximize their utility or profit given constraints. For example, a consumer chooses the combination of goods that provides the highest satisfaction within their budget. For a consumer maximizing utility:
\[
\max_{x} U(x)
\]
subject to:
\[
p \cdot x \leq w
\]
where:
\(U(x)\) is the utility function,
\(x\) is the consumption bundle,
\(p\) is the price vector,
\(w\) is the consumer’s wealth.
For a firm maximizing profit:
\[
\max_{q} \pi(q) = R(q) - C(q)
\]
where:
\(q\) is output,
\(R(q)\) is revenue,
\(C(q)\) is cost.
- Complete Preferences: Consumers can rank all possible consumption bundles. For example, a consumer can compare apples and oranges and decide whether they prefer one to the other or are indifferent. A preference relation \(\succsim\) satisfies completeness if:
\[
\forall x, y \in X, \quad x \succsim y \text{ or } y \succsim x.
\]
where \(X\) is the set of all consumption bundles.
- Transitivity: If a consumer prefers bundle \(A\) to \(B\) and \(B\) to \(C\), then they must prefer \(A\) to \(C\). If a consumer prefers coffee to tea and tea to soda, then they should prefer coffee to soda.
\[
\forall x, y, z \in X, \quad x \succsim y \text{ and } y \succsim z \Rightarrow x \succsim z.
\]
- Non-Satiation (Monotonicity): More of a good is always preferred to less, assuming no negative effects. A consumer prefers 5 chocolates over 4 chocolates. If \(x'\) has at least as much of each good as \(x\) and strictly more of at least one good, then:
\[
x' \succ x.
\]
- Convex Preferences: Consumers prefer a balanced mix of goods rather than consuming only one type. A consumer prefers a mix of apples and bananas over consuming only apples or only bananas. If \(x \sim y\), then for \(0 \leq \lambda \leq 1\),
\[
\lambda x + (1-\lambda)y \succsim x, y.
\]
- Diminishing Marginal Utility: As consumption of a good increases, the additional utility gained from consuming one more unit decreases. The first slice of pizza is highly satisfying, but the tenth slice provides much less additional satisfaction. Mathematically:
\[
\frac{\partial^2 U}{\partial x^2} < 0.
\]
- Perfect Information: All economic agents have full knowledge of prices, product quality, and available alternatives. For example, a consumer knows the price of apples at every store and always buys from the cheapest source.
- Perfect Competition: Markets have many buyers and sellers, no single agent has market power, and goods are homogeneous. For example, the wheat market has many sellers, and no single farmer can influence the price. Mathematically, each firm is a price taker:
\[
P = MC(q)
\]
- No Externalities: All costs and benefits of a transaction are borne by the buyer and seller, with no third-party effects. For example, a factory polluting a river affects nearby residents, violating this assumption. Mathematically, market efficiency is:
\[
MC_{\text{private}} = MC_{\text{social}}.
\]
- No Barriers to Entry or Exit: Firms can freely enter or exit the market based on profitability. For example, if the coffee shop industry becomes highly profitable, new competitors can enter the market. Mathematically this means long-run equilibrium requires zero economic profits:
\[
P = AC.
\]
- Time-Invariant Preferences: Consumer preferences do not change unpredictably over time. If a person prefers Coke to Pepsi today, they will likely prefer it tomorrow. Mathematically:
\[
U(x,t) = U(x) \text{ for all } t.
\]
- Well-Defined Property Rights: Resources have clear ownership, allowing markets to function efficiently. A farmer owns land and can decide how to use or sell it. If \(x\) is owned by agent \(i\), then:
\[
x \in X_i.
\]
- Continuity of Preferences: A small change in consumption does not cause abrupt changes in preferences. For example, if a consumer slightly increases the quantity of an orange, their utility does not change dramatically. Mathematically, this means:
\[
\lim_{x \to x'} U(x) = U(x').
\]
- Production Function Assumptions: Firms use inputs efficiently and experience diminishing returns to inputs. Doubling workers in a factory may not double output due to inefficiencies. For a production function \(f(L, K)\), where \(L\) is labor and \(K\) is capital:
\[
\frac{\partial^2 f}{\partial L^2} < 0, \quad \frac{\partial^2 f}{\partial K^2} < 0.
\]
Many of the assumptions in standard microeconomic theory do not hold in real-world settings. Violating these assumptions has significant implications for economic models, often necessitating alternative approaches. Many standard microeconomic assumptions fail in practice, leading to market failures, inefficiencies, and suboptimal decision-making. Alternative models—behavioral economics, game theory, contract theory, and institutional economics—provide more realistic approaches to understanding real-world behavior. Relaxing these assumptions makes economic models more complex but also more applicable to real-world problems. Below are key microeconomic assumptions that are frequently violated and the implications of their violations:
- Rationality (Utility and Profit Maximization): Behavioral economics shows that individuals frequently exhibit bounded rationality (Simon, 1955). People rely on heuristics and biases (Kahneman & Tversky, 1979) rather than maximizing expected utility. Firms may satisfice instead of maximizing profit, meaning they aim for a satisfactory rather than the optimal outcome. Standard demand and supply models may fail when consumers make suboptimal choices.
- Standard models may overpredict rational behavior in decision-making
- Markets may not clear efficiently due to systematic errors in decision-making
- Firms can exploit consumer biases for profit
- Bubbles and irrational behaviors (such as excessive risk-taking) may arise
- Perfect Information: Consumers and firms often have incomplete or asymmetric information. A few examples are the lemons problem (Akerlof, 1970), moral hazard, and adverse selection in insurance markets. Search costs and information-processing limitations can also affect choices.
- Markets may fail due to information asymmetries
- Firms may exploit consumers using advertising, leading to suboptimal consumption
- Government intervention may be required (e.g., regulations on truth-in-advertising or financial disclosures)
- Transitivity of Preferences: People’s preferences are inconsistent over time (Tversky & Kahneman, 1981). Often they have context-dependent preferences (e.g., framing effects): choices depend on how alternatives are presented. They frequently have cyclical preferences: People may prefer A over B, B over C, but C over A.
- Standard utility maximization fails because preference orderings are not well-defined
- Choices may be intransitive, leading to unstable market equilibria
- The Revealed Preference Theory fails when choices change with context
- Perfect Competition (Price Taking Behavior): Many markets have monopolies, oligopolies, and monopolistic competition. Firms engage in strategic pricing, branding, and product differentiation. Market power allows firms to set prices above marginal cost.
- The first welfare theorem (which states that competitive markets lead to efficiency) does not hold
- Price distortions lead to deadweight loss
- Firms engage in rent-seeking behavior (more on this later)
- No Externalities: Real-world markets generate negative externalities (pollution) and positive externalities (innovation spillovers). Firms and consumers do not internalize the full social cost/benefit.
- Market outcomes are not Pareto efficient
- Public goods (e.g., clean air) are underprovided
- Tragedy of the commons occurs (Hardin, 1968)
Obviously, there are economists that relax these assumptions if the situation calls for it. You can think of these as default assumptions, or a base case. Economists will make adjustments if this methodological individualism fails to describe the system. For systemic risk, macro crises, and institutional evolution, individual-level analysis is insufficient. Newer models increasingly blend individual and collective dynamics, incorporating social networks, heuristics, and institutional effects. For example, complexity economics rejects many of these assumptions. Here is a table for comparison:
| Assumption |
Standard Micro & Macro Theory |
Complexity Economics |
| Rationality |
Agents are fully rational, optimizing utility or profit |
Agents have bounded rationality and use heuristics (Adaptive Expectations) |
| Homogenous Representative Agent |
A single agent represents an entire sector or economy |
Heterogeneous agents interact and adapt (Agent Based Models) |
| Equilibrium |
Systems converge to a stable equilibrium |
Systems are out-of-equilibrium, evolving over time (Positive Feedback Dynamics) |
| Perfect Information |
Agents have full or at least rational expectations |
Information is localized and incomplete |
| Linear Dynamics |
Small shocks lead to small effects (predictable responses) |
Systems exhibit nonlinear dynamics and tipping points |
| Exogenous Shocks |
Crises are caused by external factors (e.g., policy mistakes) |
Crises emerge endogenously from network effects (Financial Contagion, Technology Diffusion) |
| Aggregate Behavior |
Macro outcomes result from simple aggregation of individual behavior |
Emergence: Macro outcomes arise from micro interactions (Non-Linear and Evolutionary) |
When I began heavily questioning the assumptions of economic models in graduate school, I came across a well-known result in computer science and computational complexity theory that demonstrates the inherent computational difficulty of finding equilibrium in economic models. The result shows that many equilibrium problems in economics, particularly those based on fixed-point theorems, are NP-hard or even in the complexity class PPAD-complete (Polynomial Parity Argument on Directed graphs). It took a while for me to wrap my head around this because Economists typically do not study computational complexity, and hence would never imagine questioning the equilibrium assumption in economics. Theoretical economic models assume that equilibrium exists (e.g., Walrasian general equilibrium, Nash equilibrium). However, from a computational complexity perspective, actually computing these equilibria is often infeasible in practice. Several studies have shown that finding general equilibrium prices or Nash equilibria is at least NP-hard. This means It may take exponentially long computation time to find an equilibrium, making it impractical for real-world markets. This implies that markets may not reach equilibrium in reasonable time scales, meaning market equilibrium assumptions might not hold in practice. I think Kenneth Arrow proved that under certain assumptions, economies described by the competitive model will have a unique equilibrium. But then (Daskalakis, Goldberg & Papadimitriou, 2006) showed that, even if an equilibrium exists (by Nash’s theorem), finding it is as hard as any problem in the PPAD class. Nash's theorem relies on Brouwer's fixed-point theorem but Daskalakis et al. showed that computing such a fixed point is PPAD-hard, meaning there is no polynomial-time algorithm unless PPAD problems are easy. In large markets or games, even if an equilibrium theoretically exists, it may be computationally impossible to find. This questions the practical relevance of equilibrium-based economic models. (https://people.cs.pitt.edu/~kirk/CS1699Fall2014/lect4.pdf)
I also began asking about what happens if we have heterogenous utility functions across the collection of consumers and whether utility functions are strictly independent from one another. How can we do any aggregation? Turns out, aggregation under heterogenous preferences is a known issue. We cannot aggregate individual behavior cleanly unless very specific conditions hold. If each consumer \( i \) has their own utility function \( U_i(x_i, y_i) \), we can’t, in general, assume that aggregate demand behaves like a “representative” consumer’s demand. Why?
- Income Effects Differ Across Consumers: Suppose one consumer has a strong income effect, another has a weak one. As total income or prices change, aggregate demand won’t behave like any single demand function — the composition of demand changes.
- Preferences Might Not Be Homothetic: If utilities are non-homothetic (e.g., demand depends on income in nonlinear ways), the shape of aggregate demand depends on the income distribution — not just total income. That makes aggregate demand non-representable by a single utility function in general.
- Non-Separability & Interdependence: If consumers' utilities interact (e.g., network effects, social preferences), you can’t even write their problem as separate maximization problems. For example: \( U_i(x_i, y_i; x_j) \) — consumer \( i \)'s utility depends on what consumer \( j \) does. Aggregation fails hard in this case; the economy is strategic, not just additive.
In comes The Sonnenschein-Mantel-Debreu (SMD) Theorem: Almost any shape of market demand can be generated by aggregating rational individual demands, even if each consumer behaves "nicely" (i.e., maximizes utility, has well-behaved preferences). Aggregate demand functions need not satisfy The law of demand, Uniqueness, Smoothness, or Downward-sloping structure. Even if all individual preferences are convex, continuous, monotonic, etc., aggregate demand can be wild. There are special cases where you can cleanly aggregate.
Case 1: Identical, Homothetic Preferences: Everyone has the same utility function, and it’s homothetic (e.g., Cobb-Douglas, CES). Then aggregate demand depends only on total income, not its distribution. A representative consumer exists.
Case 2: Gorman Polar Form: The Gorman form shows when individual demands can be aggregated: If each consumer’s indirect utility function is quasi-linear in income, i.e.,
\[
v_i(p, m_i) = a_i(p) + b(p) \cdot m_i
\]
and all consumers share the same marginal utility of income function \( b(p) \), then aggregate demand can be represented as if from one representative consumer. This condition is very restrictive. If utility functions differ, especially non-homothetically, and income effects vary, then aggregation fails. You cannot represent aggregate demand with a single utility function. The distribution of income and preferences matters deeply. And if preferences are not independent (e.g., they depend on others), then you are no longer even in a “representative agent” world, you’re in game-theoretic territory. This is fascinating; Arrow and Debreu have shown that in most cases (because of aggregation problems), there will probably not be a unique stable equilibrium. In the ideal case, where there is a stable equilibrium, Papadimitriou essentially shows that it will take an economy exponentially long to find it. So what are economists doing with their time? Who knows. Earlier I mentioned the rationality of assumption revision, and the general drawbacks of assuming something false. I think the implications are clear. I should specify that these results are applicable in macroeconomics, but I don't see how they wouldn't also be applicable to single markets which are just localized instantiations of the general problem.
"Almost a century and a half after Léon Walras founded general equilibrium theory, economists still have not been able to show that markets lead economies to equilibria. We do know that — under very restrictive assumptions — equilibria do exist, are unique and are Pareto-efficient. But — what good does that do? As long as we cannot show that there are convincing reasons to suppose there are forces which lead economies to equilibria — the value of general equilibrium theory is nil. As long as we cannot really demonstrate that there are forces operating — under reasonable, relevant and at least mildly realistic conditions — at moving markets to equilibria, there cannot really be any sustainable reason for anyone to pay any interest or attention to this theory."
In order to have a coherent market demand function, you typically need these assumptions:
| Assumption |
Why It's Needed |
What Happens if It Fails |
| 1. Homothetic preferences |
So Engel curves (income → quantity) are straight lines through the origin — demand only depends on relative prices and total income. |
Demand becomes sensitive to income distribution, not just total income — aggregation fails. |
| 2. Identical preferences |
Ensures that income effects and substitution effects are similar across individuals. |
Different preferences create non-canceling income effects, making demand shapes unpredictable. |
| 3. No wealth effects (or quasi-linear utilities) |
Gorman polar form requires linear Engel curves with the same slope across consumers. |
Consumers react differently to income changes → aggregation fails. |
| 4. Independent preferences |
Each consumer’s utility is independent of others’. |
Interdependent preferences (e.g., externalities, network effects) destroy separability. No meaningful aggregation. |
| 5. Complete markets & no rationing |
Ensures each agent optimizes fully. |
If constraints exist (e.g., liquidity, quantity rationing), individual demands don’t reflect preferences alone. |
| 6. Convex preferences |
Makes individual demands well-behaved (single-valued, continuous, responsive). |
Non-convexity introduces multiple optima, discontinuities, or non-monotonic demand — invalidates aggregation. |
| 7. Perfect information and price-taking behavior |
Ensures individual demands are responsive only to prices and income. |
If strategic behavior or uncertainty exists, individual choices reflect beliefs, not pure preferences. |
Generally these are the issues:
- Different marginal propensities to consume across individuals → income redistribution changes aggregate demand.
- Presence of luxuries and necessities → demand depends on income distribution, not just totals.
- Social preferences, peer effects, positional goods → utility is not separable.
- Price-dependent wealth effects → demand depends on who holds wealth, not just how much exists.
- Differential exposure to prices (e.g., subsidies, taxes, discrimination) → different consumers face different effective prices.
- Behavioral heterogeneity (bounded rationality, reference dependence, etc.) → violates utility maximization assumptions.
- Multiple equilibria or discontinuities → market demand can't be summarized by a stable function.
Efficiency
Risk and Uncertainty
Nash Equilibrium
Elasticity
Time Preference and Discounting (Present Value, Discount Rate)
More Reading (Highly Recommended):
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