Question 1 is an open question. For questions 2 and 3 select one alternative and provide a short motivation, without motivation, you will receive zero points. 1. Consider the following production function: /(K, L) = L + K2/3. (a) [4 points] Find the marginal product of labor and capital and the marginal rate of technical substitution, and state if the returns to capital and labor are increasing, decreasing or constant. (b) [3 points] Graph the isoquant of the production function for Q = 20 in our reference space L x K, with L on the horizontal axis. (c) [7 points] How can we determine the combination of inputs that minimizes the costs to produce Q = 20 in the long-run? Suppose pz = 1 and py = 1/2, determine the levels of L and K of the above mentioned combination. (d) [5 points] State whether the function exhibits constant, increasing or decreasing returns to scale. 2. [7 points] Consider the following production function: Q(K, L) = 12/3 13/3. This production function exhibits constant return to scale. Hint: in case you choose true, you should prove that this is the case for any A and (L, K); if you choose false then you can rely on a counterexample. A. True B. False 3. [7 points] Consider a production target Q. For any given production function Q(L, K), the combinations of inputs that minimize the cost to produce such target in the short- and long-run always coincide. A. True B. False