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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