elasticity¶
How many percent quantity changes when price changes by — a gauge of responsiveness. Steeper curves are more elastic.
Key terms from the scenes, grouped by chapter. Each term links to the scene where it is introduced.
How many percent quantity changes when price changes by — a gauge of responsiveness. Steeper curves are more elastic.
The boundary of affordable bundles with income — . The happiest point on this line is the choice.
A binary relation on a set of alternatives. means the consumer likes at least as much as . A rational preference is complete and transitive.
The axiom that for any two alternatives , either or (or both) holds — the consumer can compare any pair.
The axiom that and imply — it guarantees the consistency of preferences.
when and both hold — the two alternatives are equally good.
A function representing : . Any monotone transform represents the same preference, so it is an ordinal concept.
A rule assigning to each budget set (a subset of feasible alternatives) the set of alternatives actually chosen.
The consistency condition: if is chosen when was available, then must not be available whenever is chosen. Choice derived from rational preferences satisfies WARP.
The set of affordable consumption bundles at prices and wealth : . Its boundary is the budget line.
Under locally nonsatiated preferences the optimum spends the whole budget: . If money were left over, a better bundle would be affordable.
The good serving as the price standard — its price is normalized to . Demand is unaffected by the numeraire choice thanks to homogeneity in prices and wealth.
The solution of the utility maximization problem — demand as a function of prices and wealth. Also called Marshallian demand.
Walrasian demand is homogeneous of degree zero in prices and wealth: . A proportional rise in all prices and income changes nothing real.
The set of bundles yielding equal utility. Under monotonicity and convexity it slopes downward and is convex to the origin.
The slope (in absolute value) of an indifference curve — how much of good 1 the consumer needs at the margin to give up one unit of good 2. .
subject to . Its solution is Walrasian (Marshallian) demand ; its value is indirect utility .
The value function of the UMP, . Nonincreasing in prices, nondecreasing in wealth, homogeneous of degree zero.
The formula recovering Walrasian demand from indirect utility: .
Decomposes a price effect into substitution and income effects: . The substitution effect is always nonpositive.
The effect of a price change on demand holding utility compensated — the slope of Hicksian demand. Always nonpositive for the own price.
The effect of a price change on demand through changed real purchasing power. Same direction as the substitution effect for normal goods, opposite for inferior goods.
The solution of the expenditure minimization problem — the cheapest bundle achieving utility . Homogeneous of degree zero in prices, nonincreasing in own price.
A good whose demand rises when its price rises — happens when a strong inferior-good income effect overwhelms the substitution effect.
subject to . Its solution is Hicksian demand ; its value is the expenditure function .
The value function of the EMP, . Homogeneous of degree one in prices, concave, nondecreasing — and yields Hicksian demand via Shephard's lemma.
Differentiating the expenditure function in a price gives Hicksian demand: .
The UMP and EMP mirror each other: , . Each problem's solution recovers the other's.
The sum of individual demands . Walras' law and homogeneity of degree zero survive aggregation, but WARP generally does not.
A fictional consumer whose demand reproduces aggregate demand. Exists (independently of the wealth distribution) when indirect utilities take the Gorman form.
— indirect utility with a common marginal utility of wealth . Makes aggregate demand depend only on total wealth.
The set of input bundles producing output . Convex to the origin when the production function is concave.
The slope (in absolute value) of an isoquant — how much of input 1 marginally replaces one unit of input 2 holding output fixed. .
How output scales when all inputs scale by : increasing if , constant if equal, decreasing if smaller.
The solution of the cost minimization problem — the inputs chosen at factor prices to produce target output .
— the minimum cost of producing . Homogeneous of degree one in factor prices, concave, nondecreasing.
The extra cost of making one more unit — discretely , continuously . Profit maximization sets price equal to marginal cost, pinning down supply.
— cost per unit. The marginal cost curve passes through the minimum of the average cost curve.
A probability distribution over outcomes — the mathematical form of an uncertain prospect. A simple lottery puts probabilities on finitely many outcomes.
The utility of a lottery — the expectation of Bernoulli utility . Under continuity and independence, preferences take this form.
If then for any and — a common mixture never reverses the ranking. The Allais paradox breaks it.
Preferring a sure amount over a lottery with the same expected value — equivalent to a concave Bernoulli utility .
The sure amount indifferent to lottery : . For a risk averter, .
— the slice of expected value the agent would give up to avoid the lottery. The price of risk aversion.
The coefficient of absolute risk aversion — a local gauge of how strongly risk is disliked.
A premium equal to the expected loss — zero expected profit for the insurer. At a fair premium, a risk averter buys full insurance.
A strategy profile where no player can gain by unilaterally deviating, holding others' strategies fixed. Each strategy is a best response to the rest.
A strategy that randomizes over pure strategies. In equilibrium every pure strategy in the mix yields the same expected payoff (the indifference condition).
A strategy that is best no matter what others do. Iterated elimination of strictly dominated strategies (IEDS) simplifies a game but can miss Nash equilibria.
A strategy profile that is a Nash equilibrium in every subgame. It rules out non-credible threats and is found by backward induction.
The gap between what consumers are willing to pay and what they actually pay — the triangle under demand and above price.
Total surplus destroyed when quantity deviates from the efficient level (taxes, monopoly) — measured by the Harberger triangle.
A tax that corrects an externality — setting equal to marginal damage brings the market back to the social optimum.
Non-rival, non-excludable goods. The Samuelson condition (vertical sum of marginal benefits = marginal cost) sets optimal supply, but free-riding causes underprovision.
A single seller maximizing profit at — price exceeds marginal cost and deadweight loss arises.
An oligopoly model where firms choose quantities simultaneously. Reaction functions intersect at the Cournot-Nash equilibrium, converging to competition as the number of firms grows.
A box plotting two consumers' endowments and indifference curves together. Points on the contract curve are Pareto efficient allocations.
A state where no one can be made better off without making someone worse off. The First Welfare Theorem says competitive equilibrium is Pareto efficient.
The set of allocations no coalition can profitably block. In a replica economy the core shrinks to competitive equilibrium as the economy grows (Debreu-Scarf).
Equilibrium with complete markets in state-contingent commodities. With no aggregate risk, full insurance (risk sharing) obtains.
No social welfare function satisfies universality, Pareto, independence of irrelevant alternatives, and non-dictatorship all at once.
Market unraveling when the informed side selects in — Akerlof's market for lemons is the canonical case.
Costly revelation of type by the informed side — Spence's education model yields a separating equilibrium.
The problem that the agent's post-contract action (effort) is unobservable. Risk sharing trades off against incentives under the incentive-compatibility constraint.
The condition that truth-telling is optimal for participants. By the revelation principle, design can be restricted to direct mechanisms.
The second-price auction — bidding truthfully is a weakly dominant strategy. The canonical incentive-compatible mechanism.