52.01.01 · economics / microeconomics

Microeconomics — scarcity, choice, and equilibrium

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Anchor (Master): Mas-Colell, Whinston & Green Microeconomic Theory; Debreu Theory of Value

Intuition Beginner

Microeconomics studies how individuals and firms make choices under scarcity, and how those choices interact through markets to set prices and allocate goods. Its core insight is that constrained optimisation — doing the best you can within limits — describes behaviour across buyers, sellers, workers, and firms.

A consumer with limited income chooses among goods to maximise satisfaction. A firm with limited inputs chooses output to maximise profit. Markets bring these choices together: prices adjust until the quantity buyers want equals the quantity sellers offer.

Microeconomics is the foundation of every applied economic question, from tax policy to climate policy to platform competition.

Visual Beginner

The supply-and-demand diagram: two curves crossing at the equilibrium price where the quantities offered and sought coincide.

Above the equilibrium, surplus; below it, shortage. The crossing is the market clearing point.

Worked example Beginner

A market has demand $Q_{d} = 100 - 2 P$ and supply $Q_{s} = 20 + 2 P$ , where $P$ is price. Find the equilibrium.

Step 1. Set $Q_{d} = Q_{s}$ : $100 - 2 P = 20 + 2 P$ .

Step 2. Solve: $80 = 4 P$ , so $P = 20$ .

Step 3. Quantity at equilibrium: $Q = 20 + 2 (20) = 60$ .

What this tells us: equilibrium is the price at which the plans of buyers and sellers are mutually consistent; neither surplus nor shortage remains.

Check your understanding Beginner

Formal definition Intermediate+

A consumer's preference relation $⪰$ on a consumption set $X$ is complete, transitive, and continuous; under standard regularity it is representable by a utility function $u : X \to R$ such that $x ⪰ y$ iff $u (x) \geq u (y)$ ^{[Mas-Colell Whinston Green Ch. 1–3]}. The consumer's problem is

x \in X max u (x) subject to p \cdot x \leq m, x \geq 0,

where $p$ is the price vector and $m$ is income. The solution defines the Marshallian demand $x (p, m)$ and the indirect utility $v (p, m) = u (x (p, m))$ .

A firm produces output $y = f (z)$ from inputs $z$ via a production function $f$ . Profit $π = p_{y} y - w \cdot z$ is maximised over feasible inputs; the solution gives input demands and output supply.

A competitive equilibrium is a price vector $p^{*}$ and allocations $(x_{i}^{*})$ , $(y_{j}^{*})$ such that every consumer maximises utility, every firm maximises profit, and markets clear: $\sum_{i} x_{i} = \sum_{j} y_{j}$ .

Counterexamples to common slips

Utility is ordinal, not cardinal. Only the ranking matters for demand; doubling the utility function leaves choices unchanged.
Equilibrium need not be efficient without further assumptions. Externalities and public goods can make competitive outcomes Pareto-inefficient.
Demand curves slope down only under restrictions. Giffen goods, though rare, are demand curves that slope up.

Economic theory Intermediate+

First welfare theorem. Under completeness, transitivity, continuity, and local non-satiation of preferences, every competitive equilibrium is Pareto efficient.

Argument sketch. Suppose an allocation $(x_{i})$ is feasible and Pareto-dominates the equilibrium $(x_{i}^{*})$ . Then each consumer $i$ weakly prefers $x_{i}$ to $x_{i}^{*}$ , and at least one strictly prefers. Local non-satiation implies each $x_{i}$ costs at least as much as $x_{i}^{*}$ at equilibrium prices, with one strict inequality. Summing gives that the dominating allocation costs strictly more than the equilibrium allocation — contradicting feasibility. $□$

Bridge. This result builds toward 52.04.01 (game theory), where strategic interaction replaces price-taking and the welfare theorems need re-examination, and appears again in 52.03.01 (econometrics), where the competitive model's predictions are tested empirically. The foundational reason the welfare theorem matters is that it gives the competitive market a normative defence — efficiency without a planner — and putting these together, this is the bridge from the positive description of markets to the normative analysis of policy, and the pattern generalises to the mechanism-design results that extend the competitive framework to informationally constrained environments.

Exercises Intermediate+

Lean formalization Intermediate+

lean_status: none. Microeconomics uses optimisation machinery drawn from 44.02.01 (convex duality and KKT conditions); its correctness gate is model consistency and empirical evidence, not formal proof.

Advanced results Master

The competitive model extends in several directions. General equilibrium (Walras, Arrow, Debreu) establishes existence and welfare properties of simultaneous equilibrium across all markets; the Arrow-Debreu model handles uncertainty and time via contingent-claim markets ^{[Debreu Theory of Value]}. Mechanism design (Hurwicz, Maskin, Myerson) characterises the institutions that implement desired outcomes under private information, formalising the trade-offs the Second Welfare Theorem surfaces.

Market failures — externalities, public goods, asymmetric information, market power — are the standard cases where the First Welfare Theorem's assumptions fail. Pigouvian taxes, Coasian bargaining, and auction design address them respectively. Behavioural economics (covered in 52.06.01) documents systematic deviations from the rational-agent model, motivating richer preference specifications.

Synthesis. Microeconomics is the load-bearing analytical framework of the economics curriculum: the constrained-optimisation framework established here builds toward 52.02.01 (macroeconomics), where aggregates of micro-decisions produce macro-outcomes, appears again in 52.03.01 (econometrics), where the model's predictions are estimated empirically, the foundational reason the welfare theorems matter is that they give a precise normative benchmark against which real markets and policies are judged, the bridge is that the same optimisation-and-equilibrium pattern recurs from individual choice to general equilibrium to mechanism design, and the pattern generalises to the game-theoretic analyses of strategic interaction in 52.04.01; putting these together, microeconomics is the foundation of every applied economic question, the chapter whose results the other economics chapters presuppose.

Full proof set Master

Proposition (Existence of consumer optimum). If the consumption set $X \subset R_{+}^{n}$ is closed, convex, and bounded below, and the utility function $u$ is continuous, then for any price vector $p ≫ 0$ and income $m > 0$ , the budget set ${x \in X : p \cdot x \leq m}$ is compact and the consumer's problem attains its maximum.

Argument. The budget set is closed (intersection of closed sets) and bounded (because all prices are strictly positive and income is finite), hence compact by Heine-Borel. A continuous function on a compact set attains its maximum (Weierstrass). Hence an optimal consumption bundle exists. $□$

Connections Master

Macroeconomics 52.02.01. Aggregate outcomes — output, employment, inflation — are built up from microeconomic decisions of consumers and firms; modern macro models are explicitly micro-founded.
Econometrics 52.03.01. The empirical estimation of supply, demand, and consumer-preference parameters uses the structural predictions developed here.
Game theory 52.04.01. When agents are large enough to affect prices, the competitive paradigm gives way to strategic analysis, the subject of game theory.
Optimisation and duality 44.02.01. The mathematical machinery of constrained optimisation (Lagrangian, KKT, duality) that microeconomics deploys is the formal subject of the optimisation chapter.

Historical & philosophical context Master

Adam Smith's Inquiry into the Nature and Causes of the Wealth of Nations (1776) introduced the idea that self-interested agents in a competitive market produce socially coordinated outcomes — the "invisible hand" ^{[Smith 1776]}. The formalisation of this intuition into the welfare theorems was the work of the twentieth-century general-equilibrium school: Walras's Éléments d'économie politique pure (1874), Arrow and Debreu's 1954 existence proof, and Debreu's Theory of Value (1959).

The constrained-optimisation approach to consumer theory was systematised by Hicks (Value and Capital, 1939) and Samuelson (Foundations of Economic Analysis, 1947), who made the Lagrangian and duality framework standard. Mas-Colell, Whinston, and Green's Microeconomic Theory (1995) is the canonical graduate synthesis, integrating general equilibrium, game theory, and information economics into a single framework.

The discipline's ongoing development — behavioural economics, mechanism design, market design — continues to refine the rational-agent foundation while preserving the optimisation-and-equilibrium core that the First Welfare Theorem crystallises.

Bibliography Master

@book{MasColellWhinstonGreen1995,
  author = {Mas-Colell, Andreu and Whinston, Michael D. and Green, Jerry R.},
  title = {Microeconomic Theory},
  publisher = {Oxford University Press},
  year = {1995},
}

@book{Varian2014,
  author = {Varian, Hal R.},
  title = {Intermediate Microeconomics},
  edition = {9},
  publisher = {W. W. Norton},
  year = {2014},
}

@book{Debreu1959,
  author = {Debreu, Gérard},
  title = {Theory of Value: An Axiomatic Analysis of Economic Equilibrium},
  publisher = {Yale University Press},
  year = {1959},
}

@book{Smith1776,
  author = {Smith, Adam},
  title = {An Inquiry into the Nature and Causes of the Wealth of Nations},
  year = {1776},
}