Questions 3 and 4 refer to a profit-maximizing price-taking firm in both its input and output markets. The firm produces a single output Q according to the production function Q = f(L, K) = 100 + 30 x In L + 20 x In K Question 3 In the initial situation, labour is paid an hourly wage rate w = $6.00 and the hourly rental cost of capital is r = $10.00. The firm sells its product at a price P = $4.00 per unit of output Q. Which of the following is true? A. The Hessian determinant evaluated at the profit-maximizing input combination (L, K) is 0. 375 B. The profit-maximizing input combination is (L, K) = (8,20) C. The marginal physical product of labour is 30 D. The most profitable output level is Q = 100 E. The value of the marginal physical product of labour is 120 Question 4 Inflation engenders a situation where all the prices have doubled. As a result, w = $12. 00, r = $20.00, and P = $8.00 What is the profit-maximizing input combination in this new situation? A. (L, K) = (20,8) B. A corner solution C. (L, K) = (8,20) D. Prices are too high for the firm to be profitable E. Inflation distorts relative prices