Jim derives utility from fine wine w (in liters) and wine cellar space c (in cubic meters). (The wine cellar space is desirable both for the storage of fine wine and for the ambiance it provides). His utility function is given by

u(w, c) = w c^5/2

a) With w on the x-axis and c on the y-axis, write the expression for Jim's marginal rate of substitution (MRS) over these two goods. Interpret the value when w = 20 and c = 50.

b) Derive Jim's demand functions for both w and c, given that he has income Y .

c) Using the demand functions from b), compute the income elasticities for w and c. Comment on whether w or c are normal goods.

d) Using the demand functions from b) as a guide, Draw the price-consumption curve for w. Comment on whether Jim's demand for fine wine w is affected by the price of wine cellar space c.

e) Suppose p_w = 4 and p_c = 2. Draw Jim's income-consumption curve with w on the x-axis and c on the y-axis. Calculate the bundle chosen if Y = 350, and label it on your drawing.