Problem 2 You've been given the following production function: Q = 50L 2L2 + 15K 0.5K2 Let's assume this is a perfectly competitive market, so you have no control over the market price price for wages (w = 5), rental rate (7" = 8), and the price for the produced good (p = 9). (a) Calculate the returns to scale and explain what would happen with a 5% increase in capital (K) and labor (L). Just give an approximate amount. (b) Assume we are in the short-run and labor (L) is xed at 10 units. What is the optimal amount of capital we need? (c) What is the prot in the short-run? (d) What is the marginal rate of technical substitution (M RTS)? Assume we are now in the long-run, and no input is xed. (e) What is the optimal combination of capital and labor? You do not have to numerically solve. Just nd one as a function of the other (ie - K in terms of L or L in terms of K)