George has a Cobb-Douglas utility function: U(x, y) = xa y1–a where 0 < a < 1. The budget constraint is pxx + pyy = I.

a. Using marginal utilities, find the formula for the MRS (= – dy/dx). Draw a typical IC.

b. Give the equation for the tangency condition and use it to express y as a function of x.

c. Using your answer in b and the budget constraint, show that the demand functions for x and y (i.e., the expressions for the optimal quantities) are: x^d = aI/px and y^d = (1–a)I/py.