The question

5. (15 points) In this set of problems, we explore a firm's short-run choice of how much labor to combine with a given amount of capital to employ in order to maximize profits. Suppose that this firm's profits, or total revenues minus total costs, are given by the profit function n = py - Wix1 - W2x2. In particular, consider a firm that produces output y by employing labor inputs in the amount x, and capital inputs in the amount x2 according to the production function y = f(x1, x2) = X12. Suppose that the price per unit of output is p = 10, the wage paid to each unit of labor is w, = 3, the price per unit of capital is w2 = 3, and capital inputs are fixed in the short- run at X2 = 6. 1. Solve for the quantity of labor x, that this firm should employ in order to maximize profit in the short run. Solve for the quantity of output y that the firm produces at this profit-maximizing quantity of labor. ii. Illustrate the isoprofit curve and this firm's short-run production function in the diagram