Suppose the utility function for two goods, x1 (meat) and x2 (vegetables), has the Cobb-Douglas form: U(x1; x2) = (9x1 x2)1/2
a) Graph the U = 9 indifference curve associated with this utility function.
b) What is the marginal rate of substitution (MRS) at x1 = 3?
c) Develop a general expression for the MRS of this utility function.
d) Consider a logarithmic transformation of this utility function: W = log9 U(x1; x2) where log9 is the logarithmic function using base 9. Show that for this transformation the W = 1 indifference curve has the same properties as the U = 9 curve calculated in parts (a) and (b). Hint: What is the general expression for the MRS of this transformed utility function? e) If you could adopt one of these utility functions, which would you choose? Explain.