Version:0.9 StartHTML:0000000105 EndHTML:0000002562 StartFragment:0000000141 EndFragment:0000002522 Suppose there are two consumers, A and B. The utility functions...

Version:0.9 StartHTML:0000000105 EndHTML:0000002562 StartFragment:0000000141 EndFragment:0000002522

Suppose there are two consumers, A and B.

The utility functions of each consumer are given by:

UA(X,Y) = X^1/2*Y^1/2

UB(X,Y) = 3X + 2Y

The initial endowments are:

A: X = 4; Y = 4

B: X = 4; Y = 12

a) (10 points) Using an Edgeworth Box, graph the initial allocation (label it “W”) and draw the

indifference curve for each consumer that runs through the initial allocation. Be sure to label your graph

carefully and accurately.

b) (3 points) What is the marginal rate of substitution for consumer A at the initial allocation?

c) (3 points) What is the marginal rate of substitution for consumer B at the initial allocation?

d) (2 points) Is the initial allocation Pareto Efficient?

Solutions

Expert Solution

Consider the images above for the graphical and numerical solution to the problem. The initial allocation is denoted in the Edgeworth box at point W, where the IC's of A and B interest. Therefore, this is not a pareto efficient solution to the problem. Moreover, as shown above, the MRS of the two consumers are not equal at this point.

Rahul Sunny answered 1 year ago

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