5. Consider a firm with the following production function, which uses capital, K, and labor, L: f (K. L) = min {4K, _) . The price of capital is $100 and the price of labor is $50. a) What are the returns-to-scale properties of the firm's production technology? Prove your answer. b) What input combination should be the firm use to produce O units of output? C) What is the firm's total cost of production as a function of the amount of output, Q? d) What is its marginal and average cost of production? e) Suppose the price of labor falls to $25. What input combination should the firm use now to produce O units of output? What is its total, marginal, and average cost of production? f) Suppose that in the short run, the firm's capital stock is fixed at 10 units. Describe the firm's optimal input combination as a function of Q g) Derive the firm's short-run total, variable, and fixed cost functions. h) Derive the firm's short-run marginal, average, average variable, and average fixed cost functions