Question

1.Suppose there are two consumers, A and B. The utility functions of each consumer are given...

1.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) What is the marginal rate of substitution for consumer A at the initial allocation?

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

d)is the initial allocation Pareto Efficient?

2. For Each of the following situations,

i) Write the Indirect Utility Function

ii) Write the Expenditure Function

iii) Calculate the Compensating Variation

iv) Calculate the Equivalent Variation

a) U(X,Y) = X^1/2 x Y^1/2. M = \$288. Initially, PX= 16 and PY

= 1. Then the Price of X changes to PX= 9.

i) Indirect Utility Function: __________________________

ii) Expenditure Function: ____________________________

iii) CV = ________________

iv) EV = ________________

b) U(X,Y) = MIN (X, 3Y). M = \$40. Initially, P

X= 1 and PY= 1. Then the Price of X changes to PX= 3.

i) Indirect Utility Function: __________________________

ii) Expenditure Function: ____________________________

iii) CV = ________________

3. Suppose A consumer's utility function is given by U(X,Y) = 3X + Y. The consumer has

\$120 to spend (M = \$120). Sketch the graph of the consumer's demand function for Good X. Please put

the Price of X, PX, on the vertical axis, and the quantity of Good X, X, on the horizontal axis. Scale the

Price axis up to \$12, and scale the quantity axis up to 120

iv) EV = ________________

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