Question

Suppose there are two consumers, A and B, and two goods, X and Y. The consumers have the following initial endowments and utility functions:

W X A = 2 W Y A = 9 U A ( X , Y ) = X 1 3 Y 2 3 W X B = 6 W Y B = 2 U B ( X , Y ) = 3 X + 4 Y

Suppose the price of X is P_X=2 and the price of Y is P_Y=3. Suppose each consumer sells their initial endowment and buys back their optimal bundle.

a) (39 points) Using a clearly and accurately labeled Edgeworth Box, illustrate:

• the initial endowment, labeled "W"
• A's optimal bundle, labeled "A" and B's optimal bundle, labeled "B"
• both consumers' indifference curve through the initial allocation
• the budget constraint, the contract curve, and the core

b) (4 points) For the situation above, determine for each market if there is excess demand, excess supply, or the market is in equilibrium (write your answer). If there is excess demand or excess supply, determine how much it is.

• Market for good X:  
• Market for good Y:

c) (4 points) Is the initial endowment Pareto efficient? How do you know?

d) (4 points) Can consumers benefit from trade at the current prices? Why or why not?

Answer 1

we are also given that current prices of good x and good y are 2 & 3 respectively

person A has cobb douglas utility preferences whereas person B has perfect substitutes preferences

income of person A and person B is the monetary value of their endowments repsectively

person A's optimal point of consumption where the above condition is fulfilled

substituting this in budget constraint for person A

person B would consume only the cheaper good

Convex indifference curves, there will be a set of prices such that each Pareto efficient outcome is a competitive market equilibrium. If it is felt that the equilibrium at e' is somehow better than that at e, a lump-sum transfer of goods can be made from consumer A to consumer B, the endowment changing from W to W'

Here , at the current prices pareto efficiency is achieved

Therefore consumers donot benefit from trade at current prices