Mathematica Problem 2 Use Mathematica to solve the following problems: A firm produces output Q using labor, L, and capital, K. Its production function is: .6 .4 Q = 10 L K 1. Plot the production function in 3 dimensions with Q on the vertical axis. Set the range on L from 0 to 15 and the range on K from 0 to 1000. 2. Hold K constant at 800, and graph the MP and AP of labor. Set the range on L from 0 to 15. 3. Hold L constant at 6 and graph the MP and AP of capital. Set the range on K from 0 to 1000. 4. Suppose the wage, W, equals 10 and the price of capital, r, equals .05, graph the equal-cost curves for total costs, TC, of \$50, \$100, and \$200. 5. Graph the equal-product curves for output equal to 225, 425, 625. 6. For Q = 425, W = 10, r = .05, and TC = \$100, graph the equal-product and equal cost-curves on the same diagram. What is the cost-minimizing combination of capital and labor that should be used to produce 425 units of Q? 7. If W = 10 and r = .05, TC = 10 L + .05 K. Solve for TC in terms of Q (Hint: use the least cost rule) and graph the TC curve. Q should be on the horizontal axis. Limit the range of Q to 600. 8. Graph the MC and AC curves for W = 10 and r = .05. Limit the range of Q to 600. 9. Suppose this is a monopoly firm. It faces the following demand curve: P = 1 - .0009 Q where P is the price of its output. Graph the demand and marginal revenue, MR, curve for this firm. 10. Add the MC and AC curve to your diagram in 9 and determine the profit maximizing output for the firm. What are the monopoly profits? 11. Determine the price and output if this were a competitive industry. 12. Determine the deadweight loss of the monopoly.