### How much money require in order maximize the utility

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##### Reference no: EM131244

1. Suppose a consumer's preferences are represented by the utility function U = MIN(X,4Y). The price of Y is PY = 2, and the consumer has income, M = 210.

a) Graph the consumer's Price consumption curve for prices, PX = 1, PX = 2, and PX = 3. Be sure to label your graph carefully and accurately.

b) Graph the consumer's demand curve for X. Be sure to label your graph carefully and accurately.

2. Suppose a consumer's utility function is given by U(X,Y) = X*Y. Also, the consumer has \$576 to spend, and the price of X, PX = 16, and the price of Y, PY = 4.

a) (4 points) How much X and Y should the consumer purchase in order to maximize her utility?

b) (4 points) How much total utility does the consumer receive?

c) (4 points) Now suppose PX decreases to 9. What is the new bundle of X and Y that the consumer will demand?

d) (4 points) How much money would the consumer need in order to have the same utility level after the price change as before the price change?

e) (4 points) Of the total change in the quantity demanded of X, how much is due to the substitution effect and how much is due to the income effect?

3. Suppose there are two consumers, A and B.

The utility functions of each consumer are given by:

UA(X,Y) = X*Y
UB(X,Y) = 2X + Y

The initial endowments are:

A: X = 4; Y = 2
B: X = 6; Y = 8

a) Using an Edgeworth Box, graph the initial allocation 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?

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