Lecture 2 - Exchange Economy Flashcards
(21 cards)
What is an exchange economy?
An economy with a finite set of individuals and goods, each individual has an initial endowment of goods and preferences over bundles, and they trade to reach mutually beneficial allocations.
What does an individual’s initial endowment represent in an exchange economy?
The bundle of goods the individual starts with before any trade occurs.
What are the axes of the Edgeworth box?
Horizontal axis: total quantity of good 1; Vertical axis: total quantity of good 2.
In the Edgeworth box, whose origin is at the lower-left corner?
Person 1’s origin is at the lower-left corner.
Where is Person 2’s origin located in the Edgeworth box?
At the upper-right corner, opposite Person 1’s origin.
What does a point inside the Edgeworth box represent?
An allocation: coordinates from the lower-left give Person 1’s bundle, and the residual to the upper-right gives Person 2’s bundle.
Define Pareto efficiency in the context of the Edgeworth box.
An allocation where you cannot make one person better off without making the other person worse off.
What condition must indifference curves satisfy at a Pareto-efficient allocation?
They must be tangent: MRS₁(x₁,x₂) = MRS₂(x₁,x₂).
What is the marginal rate of substitution (MRS)?
The rate at which a consumer is willing to trade one good for another, equal to the negative ratio of marginal utilities: –MU₁/MU₂.
What is the contract curve?
The locus of all Pareto-efficient allocations (points of tangency) in the Edgeworth box.
For a Cobb-Douglas utility U(a,b)=a×b, what is MRS?
MRS = –b/a.
For a utility function U(a,b)=a + 2b, what is MRS?
MRS = –1/2.
What is a competitive (Walrasian) equilibrium?
A set of prices and an allocation such that each individual maximizes utility given their budget constraint and markets clear for all goods.
What are the two conditions for a competitive equilibrium?
- Utility maximization subject to budget constraint. 2. Market clearing: total demand equals total endowment for each good.
What is an offer curve?
The locus of demanded bundles by an individual as the price ratio varies.
How is the equilibrium price ratio represented in the Edgeworth box?
By the slope of the line through the origin and the equilibrium allocation point.
What does the First Welfare Theorem state?
Every competitive equilibrium allocation is Pareto efficient.
What does the Second Welfare Theorem state?
Any Pareto-efficient allocation can be achieved as a competitive equilibrium through appropriate redistribution of initial endowments.
Under what assumptions does a competitive equilibrium exist?
Under standard convexity and continuity assumptions on preferences and endowments.
Why might a competitive equilibrium be non-unique?
If offer curves cross more than once, there can be multiple equilibrium intersections.
What is general equilibrium?
A framework that includes consumers and firms, where prices adjust to clear all goods and factor markets simultaneously.
