What is the general expression for the MRS of this transformed utility function?

(Vegetables) has the Cobb-Douglas Show more .(1) Suppose the utility function for two goods x1 (meat) and x2 (vegetables) has the Cobb-Douglas form: U(x1; x2) = (91 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. Show less