Numerical Questions Ch11 (solutions)

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ECO 2144 Chapter 11. December 6, 2023 1 of 6 Question 1 At the current level of output a firm’s marginal cost equal 16 and marginal revenue equals 10. The firm (a) Is producing the profit-maximizing amount. (b) Should produce more. (c) Should produce less. (d) There is not enough information Solution: Answer b is the correct one Question 2 If the inverse demand curve a monopoly faces is p = 100 − 2 Q , and MC is constant at 16, then maximum profit (a) Equals 1,218. (b) Equals 336. (c) Equals 882. (d) Cannot be determined solely from the information provided Solution: In this case, the marginal revenue equation is MR = 100 − 4 Q . The monopolist maximizes profit if 100 − 4 Q = 16. This means that 4 Q = 84, or Q = 21, and P = 100 − 2(21) = 58. To calculate the profit, note that if the marginal cost is constant, then ı = Q ( p − MC ). Thus, ı = 21(58 − 16) = 882. Question 3 If the inverse demand curve a monopoly faces is p = 100 − 2 Q , and MC is constant at 16, then the deadweight loss from monopoly equals Solution: Here, the easiest approach is to illustrate this graphically, as shown below. Notice that under perfect competition, p = MC: Using this condition, we can clearly see that Q = 42 : To calculate the deadweight loss, one should calculate the area of the yellow triangle shown below: (42 − 21) × (58 − 16) 2 = 441.

ECO 2144 Chapter 11. December 6, 2023 2 of 6 Question 4 The inverse demand curve a monopoly faces is p = 100 − 2 Q . The firm’s cost curve is C ( Q ) = 20 + 6 Q . (a) What is the profit-maximizing solution? Solution: In this case, the marginal revenue function is MR = 100 − 4 Q; and the MC = 6. We know that the monopolist maximizes profits when MC = MR: Thus, 6 = 100 − 4 Q . Therefore, Q = 23 : 5 and p = 100 − 2(23 : 5) = 53 : (b) What is the firm’s economic profit? Solution: To calculate profits we have to use the cost function ı = p × Q − C ( Q ). In this case, ı = 53 × 23 : 5 − 20 − 6 × 23 : 5 = 1084 : 5. (c) How does your answer change if C ( Q ) = 100 + 6 Q ? Solution: he maximization problem is not altered because the marginal cost remains the same. What changes is the fixed cost, which goes from 20 to 100. This means that the profits will be reduced by 80, which implies that the new profits are ı = 1004 : 5. Question 5 If a monopoly’s inverse demand curve is p = 12 − 2 Q and its cost function is C ( Q ) =

ECO 2144 Chapter 11. December 6, 2023 3 of 6 24 + 2 Q + 0 : 5 Q 2 (a) What Q ∗ maximizes the monopoly’s profit (or minimizes its loss)? Solution: In this case, the marginal revenue function is MR = 12 − 4 Q; and the MC = 2+ Q . We know that the monopolist maximizes profits when MC = MR: Thus, 2 + Q = 12 − 4 Q . Therefore, Q = 2. (b) What is the profit-maximazing price? Solution: p = 12 − 2(2) = 8 : (c) What is the profit? Solution: To calculate profits we have to use the cost function ı = p × Q − C ( Q ). In this case, ı = 8 × 2 − (24 + 2 × 2 + 0 : 5 × 2 2 ) = − 14. (d) Would the monopoly operate or shut down? Solution: We have to compare the scenario in which the monopolist shuts down to the one in which it maximizes profits. In the former, ı = − 24. So, it makes more sense to keep operating. Question 6 Imagine that Gillette has a monopoly in the market for razor blades in Mexico. The inverse market demand curve for blades in Mexico is p ( Q ) = 968 − 20 Q , where p is the price of blades in cents and Q is annual demand for blades expressed in millions. Gillette has two plants in which it can produce blades for the Mexican market: one in Los Angeles and one in Mexico City. In its L.A. plant, Gillette can produce any quantity of blades it wants at a marginal cost of 8 cents per blade. Letting Q 1 and MC 1 denote the output and marginal cost at the L.A. plant, we have MC 1 ( Q 1 ) = 8. The Mexican plant has a marginal cost function given by MC 2 ( Q 2 ) = 1 + 0 : 5 Q 2 . (a) Find Gillette’s profit-maximizing price and quantity of output for the Mexican market overall. How will Gillette allocate production between its Mexican plant and its U.S. plant? Solution:

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