1. Write down the firm's profit function2. Write down the firm's marginal product of labour (MPL), marginal product of capital (MPK), and the marginal rate of technical substitution (MRTS)3. Does the firm exhibit a diminishing marginal product of capital? Prove it4. Find the firm's demand functions for labour and capital5. Say the central bank decides to increase interest rate, causing r to go up. What effect will this have on the firm's use of L and K? What effect will it have on output (Y) and profits?6. Do you think the predictions above would be accurate if applied to the real world (say the Uk economy today)? Which, if any, do you think might be inaccurate? And why? Explain it two/three sentences at most

2. Cemre owns a firm that uses labour (L) and capital (K) to sell widgets (Y), according to the following production function: Y = F(L, K) = In(L) + In(K) Cemre buys her factors and sells her output in perfectly competitive markets. The market prices for L, K and Y are w, r and p, respectively