Suppose we have a representative consumer with a utility function U(x, y) = x02y 0.8, industry x with a production function x = f(kxlx) = (kxls) 0.25, and industry y with a production function y = f(ky, ly) = ky + 41. Total capital and labor endowments are described by the constraints lx + y = 1;ky + ky = 1. a. Find the RTS for industries x and y. b. Find the equation governing the PPF (Hint: Technical efficiency). c. Using your answer from part (b), find the rate of product transformation (RPT). d. Find the representative consumer's Marginal Rate of Substitution. e. Find the efficient x and y. f. What will be the competitive market output price ratio, ? Why? g. What will be the competitive market input price ratio, Why? h. Explain what exchange efficiency is, and why we would need to demonstrate it holds if we had heterogenous consumers with different preferences. V Suppose we have a representative consumer with a utility function U(x, y) = x02y 0.8, industry x with a production function x = f(kxlx) = (kxls) 0.25, and industry y with a production function y = f(ky, ly) = ky + 41. Total capital and labor endowments are described by the constraints lx + y = 1;ky + ky = 1. a. Find the RTS for industries x and y. b. Find the equation governing the PPF (Hint: Technical efficiency). c. Using your answer from part (b), find the rate of product transformation (RPT). d. Find the representative consumer's Marginal Rate of Substitution. e. Find the efficient x and y. f. What will be the competitive market output price ratio, ? Why? g. What will be the competitive market input price ratio, Why? h. Explain what exchange efficiency is, and why we would need to demonstrate it holds if we had heterogenous consumers with different preferences. V