Consider a firm with the following production function: (, ) = ^0.5^0.5. The price of labour (L) is GHS 4 per unit while the price of capital (K) is 5 per unit. For parts (a) - (e) assume that this firm has 16 units of capital it cannot change in the short-run a) In ordinary language, explain what it means to say this production function exhibits diminishing marginal returns. b) Show that this production function exhibits diminishing marginal returns c) If the price of output is GHS 10 per unit, how many units of labour should the firm employ to maximize profit? d) At this quantity of labour (from part (a)), what quantity of output will the firm produce and how much profit will the firm make? e) Derive the firm's short-run total cost function. f) Derive the firm's marginal and average cost functions. g) What is the total cost of producing 100 units of output? For the rest of this question, assume that the firm is now free to choose any level of capital and labour. h) How many units of capital and labour will it choose to minimize the cost of producing 100 units of output? i) What is the total cost of producing the 100 units? Compare this with your answer in part e) and explain the difference or similarity