3.2 Suppose the utility function for two goods, Xand Y, has the Cobb-Douglas form utility = U(X, Y) = Vx- Y.

a. Graph the U = 10 indifference curve associated with this utility function.

b. If X— 5, what must F equal to be on the U— 10 indifference curve? What is the MRS at this point?

c. In general, develop an expression for the MRS for this utility function. Show how this can be interpreted as the ratio of the marginal utilities for X and Y.

d. Consider a logarithmic transformation of this utility function:

U' = log U where log is the logarithmic function to base 10. Show that for this transformation the U' — 1 indifference curve has the same properties as the U= 10 curve calculated in parts

(a) and (b). What is the general expression for the MRS of this transformed utility function?