Question One (Efcient Production Set) (a) What is the efcient production set? Explain using a diagram. (b) If the production function for two products are: Y = SKO-VLO-3 X = EKG-SLO-4 If K =12 and I = 6 derive an expression for the Efcient production set and illustrate it in a diagram. Question Two In a competitive economy, the marginal cost of producing X is MCX: 20 + 59X. The marginal cost of producing Y is MCYZ 10 + quy. Prices are pg; 2 5, and py: 5. What linear relationship describes the proportion in which the goods should be produced? Question Three - Challenge Question - Not for marking but try it before tutorial class. (Competitive General Equilibrium with Production) An economy has the following characteristics: (i) Two goods (X & Y) which are produced using the following production function: X = 2Kx0-5Lx0-5 where Kx and LX are the quantities of inputs assigned to producing quantity X of good X. Y = 7Kv0-5Lv0-5 where Kv and Lv are the quantities of inputs assigned to producing quantity Y of good Y. (ii) Two inputs (K & L) (iii) Two identical consumers (A & B) with a. Utility function for consumer i : U = Xi0-5Yi0-5 i = A,B. b. Each has an endowment of 10 units of L and 4 units of K Denote pX and pv as the prices of goods X and Y, and w and r as the prices of labor and capital. Assume two price taking firms - one producing good X and the other producing good Y. Answer the following questions about this economy. (a) State the Lagrangian for the consumer choice problem in this economy. (b) Derive the aggregate demand equations for goods X and Y. (c) The input demand equations for the inputs are as follows: = L, = K, 1523:, K233 x2w x2r J"7w y7r Using these demand equations (and other things) write down the prot equations for both rms. (d) Derive the supply equations for Y and X. (Hint: recall that supply equals marginal cost in a competitive economy) (e) Write down the conditions for competitive equilibrium. (t) Solve for the competitive equilibrium relative prices