Answer to Question #247283 in Microeconomics for Chilu

Question

The two people in a pure exchange economy have identical utility functions. Will they ever want to trade? Why or why not?

Answer 1

Yes, they may want to trade. If two individuals, A and B, have identical preferences but are consuming dierent bundles, their marginal rates of substitution may be unequal and they may gain by trading.

For example, if each had the utility function U = XY , an initial allocation of (4X; 2Y ) for individual A and (2X; 4Y ) for individual B, each would have a utility level of 8, and their marginal rates of substitution would dier (MRS(A/XY) =(1/2) and

MRS(B/XY) = 2). By trading 1 unit of X for 1 unit of Y each could achieve a utility level of 9. Each individual would now have a bundle of (3X; 3Y ) and a marginal rate of substitution equal to 1. Gains to trade would now be exhausted. Candidates needed to use an Edgeworth consumption-box diagram to illustrate their answer.

The straight line between OA and OB is the consumption contract curve | the locus of

Pareto-ecient consumption allocations where marginal rates of substitution for any pair of consumers are equalised. Points o the contract curve are inecient: individuals may gain from trade until an allocation on the curve is reached, where the gains from trade are exhausted. The initial endowment position is at S with levels of utility for A and B of U1A and U1B, respectively. At S, MRS(A/XY) < MRS(B/XY ) so B is willing to give up more units of Y for an additional unit of X than A is. In our example, the nal, Pareto-ecient, allocation of consumption is at T, where MRS(A/XY) = MRS(B/XY) . At T, A and B reach the higher levels of utility U2A and U2B, respectively.