THEOREM 1.8 Relations Between Indirect Utility and Expenditure Functions Let v(p. y) and e(p, u) be the indirect utility function and expenditure function for some consumer whose utility function is continuous and strictly increasing. Then for all p > 0, y 2 0, and u El: I. e(p. v(p. y)) = y. 2. v(p, e(p, u)) = u. 3. Use the following Utility function to derive the corresponding indirect utility function and expenditure function and verify theory 1.8 (Advanced Microeconomic Theory, Jehle and Reny). a. log U(x1, X2) = a log x1 + Blog X2 b. U (X1, X2) = min {a x1, b x2}