Suppose that a consumer=s preferences over two goods, x and y, are represented by a Cobb-Douglas utility function:
U(x,y) = x1-β yβ
a. Find the expenditure function of the consumer, and the compensated demand functions.
b. Suppose that β = 1/4 and that initially a consumer is in equilibrium with px = 1, py = 1, I = 100. What are the demands for x and y.
c. Starting from the position in part b, the price of good y rises to 2. What is the increase in the "consumer price index" (CPI) for this consumer?
d. What is the minimum increase in income necessary for the consumer to be as well off under price px = 1, py = 2, as she/he was at prices px = 1, py = 1? Explain why the percentage increase is smaller than the increase in the CPI for the consumer that you derived in part c.