problem 1: Assume that a consumer’s preferences are represented by the utility function U = MIN(X, 4Y). The price of Y is P_{Y} = 2, and the consumer has income, M = 210.
a) Graph the consumer’s Price consumption curve for prices, P_{X} = 1, P_{X} = 2, and P_{X }= 3. Be sure to label your graph cautiously and precisely.
b) Graph the consumer’s demand curve for X. Be sure to label your graph carefully and correctly.
problem 2: Assume that a consumer’s utility function is given by U(X, Y) = X*Y. As well, the consumer has $576 to spend and the price of X, P_{X} = 16 and the price of Y, P_{Y} = 4.
a) How much X and Y must the consumer purchase in order to maximize her utility?
b) How much total utility does the consumer receive?
c) Now assume that PX reduces to 9. What is the new bundle of X and Y that the consumer will demand?
d) How much money would the consumer require in order to have the same utility level after the price change as before the price change?
e) 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?
problem 3: Assume that there are two consumers, A and B.
The utility functions of each consumer are provided by:
UA(X, Y) = X*Y
UB(X, Y) = 2X + Y
The initial endowments are as follows:
A: X = 4; Y = 2
B: X = 6; Y = 8
a) By using an Edgeworth Box, graph the initial allocation and draw the indifference curve for each consumer which runs via the initial allocation. Be sure to label your graph carefully and correctly.
b) Determine the marginal rate of substitution for consumer A at initial allocation?
c) Determine the marginal rate of substitution for consumer B at the initial allocation?
d) Is the initial allocation Pareto Efficient?