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. a. Write down the firm's profit function. [10% ] b. Write down the firm's marginal product of labour (MPL), marginal product of capital (MPK) and marginal rate of technical substitution (MRTS). [15%] c. Does the firm exhibit a diminishing marginal product of capital? Prove it. [10% ] d. Find the firm's demand functions for labour and capital. [30%] e. Say the central bank decides to increase interest rates, 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? [15%] f. 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 in two or three sentences at the most. [20%]