Suppose the utility function for two goods , X and Y, has the Cobb-Douglas utility form:

U(X,Y) = xy^0.5

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

a.If X = 5, what must Y equal to be on the U = 10 indifference curve? What is the MRSx ,Y at this point?

b.In general, develop an expression for the MRSx,y for this utility function. Show how this can be interpreted astheratio ofthe marginal utilities for X and Y.

c.Consider a logarithmic transformation of this utility function:

U'= logU

where log is the logarithmic function to base 10. Show that for this transformation the U' = 1 indifference curve has the same proper ties as the U = 10 curve calculated in parts (a) and (b). What is the general expression for the M RSx,Y of this transformed utility function?