Assume that a consumer maximizes his/her utility, S.T. their budget constraint by purchasing good x and good y. Let P_xbe the price of good x, P_y be the price of good y, and M be income.

A. Given the following utility function U(x,y) = x²y find the demand functions for good x and good y.

B. If P_x=P_y=$1 and M=$30 how many units of good x and good y will maximize this consumers utility S.T. the budget constraint? What is U^*?

C. Assume now the price of good y rises to P_y' = $2 and nothing else changes, redo part B.

D. Graph your solution to parts B) and C) VERY carefully and find the change in consumer surplus when the price of good y increases from $1 to $2. Assume that the Marshallian demand curve for good y is linear between $1 and $2, otherwise you will need to use integration to calculate the change in consumer surplus.

E. Find the compensating variation (CV) when the price of good y increases from $1 to $2 and illustrate it on your graph ExplainHint: Find the Hicksian compensated quantity demanded of good x and y (x, y)

F. Find the equivalent variation (EV) when the price of good y increases from $1 to $2 and illustrate it on your graph? Explain Hint: Find the Hicksian compensated quantity demanded of good x and y (x,y).

G. Compare CV, EV, andCS