Questions: Edgeworth Box Analysis

Question 1

In an Edgeworth box, the initial endowment is at a point where Consumer A's MRS(X for Y) = 2 and Consumer B's MRS(X for Y) = 5. What can we conclude about this allocation?

• A. The allocation is Pareto efficient because both consumers' MRS values are defined
• B. The allocation is on the contract curve because the MRS values are both positive
• C. There are mutually beneficial trades available — A values X at 2Y per unit but B values X at 5Y per unit, so trading X from A to B benefits both
• D. Only Consumer B benefits from further trade since B values X more highly

Answer: (C)

When MRS values differ between consumers, gains from trade exist. Consumer A values X at 2 units of Y; Consumer B values X at 5 units of Y. A trade where B gives A some amount between 2 and 5 units of Y for each unit of X transferred would make both better off. This is not Pareto efficient — we are not on the contract curve. Pareto efficiency requires MRS equality (the tangency condition): if A and B value X differently at the margin, resources can be reallocated to increase both utilities simultaneously. The contract curve traces exactly the allocations where MRS_A = MRS_B, meaning no further mutually beneficial trade exists.

Question 2

What does the contract curve in an Edgeworth box represent?

• A. The unique efficient allocation that maximizes the sum of both consumers' utilities
• B. All allocations where both consumers are better off than at the initial endowment
• C. All Pareto efficient allocations, from A receiving everything to B receiving everything
• D. The set of allocations reachable through voluntary trade starting from the endowment

Answer: (C)

The contract curve is the locus of all tangency points between consumers' indifference curves — every allocation where MRS_A = MRS_B. This includes every Pareto efficient allocation in the box, from the corner where A gets nearly everything to the corner where B gets nearly everything. Option A is wrong: there is no single allocation that 'maximizes total utility' in the ordinal utility framework — utility is not interpersonally comparable. Option B describes the lens-shaped region of Pareto improvements from the endowment (a subset of the contract curve). Option D describes the core of the economy — the allocations reachable through voluntary trade — which is a segment of the contract curve, not the whole thing.

Question 3

In an Edgeworth box, the competitive equilibrium is one specific point on the contract curve. Other points on the contract curve are equally Pareto efficient but differ only in their distributional consequences.

• T. True
• F. False

Answer: True

This is the core insight separating efficiency from equity in the Edgeworth framework. Every point on the contract curve is Pareto efficient — at each point, no reallocation can benefit one consumer without harming the other. The competitive equilibrium at given prices lands on one particular point on the contract curve, but the entire contract curve consists of efficient allocations. Points closer to A's corner are efficient but favor A in distribution; points closer to B's corner are efficient but favor B. The Second Welfare Theorem formalizes this: any efficient allocation on the contract curve can in principle be achieved as a competitive equilibrium — you just need to redistribute the initial endowment appropriately first. Efficiency tells us nothing about who deserves what.

Question 4

Most point inside the lens-shaped region between the two indifference curves through the endowment is Pareto efficient.

• T. True
• F. False

Answer: False

Points inside the lens are Pareto improvements over the endowment — they make both consumers better off than they were initially. But Pareto improvements and Pareto efficiency are different concepts. A point inside the lens is Pareto efficient only if no further mutually beneficial trade is possible from that point, which occurs only when the two consumers' indifference curves are tangent (i.e., on the contract curve). Most points inside the lens are NOT on the contract curve: at those points, the consumers' indifference curves cross, and the lens shape around that crossing contains further Pareto improvements. Efficiency requires that you have exhausted all mutual gains from trade, which is achieved only at tangency points.

Question 5

Why can two consumers in an Edgeworth box reach the contract curve through voluntary trade but not necessarily reach any specific pre-determined point on it?

Model answer: Voluntary trade requires both parties to agree. From the initial endowment, both consumers will trade until they reach the contract curve — because as long as their indifference curves are not tangent, there exist further mutually beneficial trades. But which point on the contract curve they reach depends on the bargaining process: relative bargaining power, information, patience, and negotiation strategy determine the final split of the gains from trade. Without a price mechanism, there is no reason for the outcome to land at one specific point rather than another on the curve segment inside the lens. Competitive equilibrium pins down the outcome by introducing prices and letting both consumers optimize simultaneously — but in pure bilateral bargaining, the outcome is indeterminate within the lens.

This indeterminacy is one motivation for introducing the price-taking equilibrium concept. Prices coordinate decentralized decisions without requiring bilateral negotiation: everyone faces the same prices, each consumer independently optimizes, and in equilibrium, markets clear. The Edgeworth box makes visible that the competitive equilibrium is just one of many efficient outcomes — its selection is justified by the institutional framework of competitive markets, not by any intrinsic superiority over other points on the contract curve.