pp_M2practice_ans

In short, π < 0 → firms exit → Supply curve decreases → P increases → π ↑ . Firms continue to exit until π = 0 . 2. Suppose that the long-run average cost for BC Company, a firm in a perfectly competitive market, is LRAC = 200 − 4 q + 0 . 05 q 2 . (a) What is the output at which LRAC attains its minimum? (b) What is the value of LRAC and LRMC at this output level? (c) If all firms in this market are identical, what is the long-run equilibrium price? (a) We find the minimum of LRAC by finding the q for which the slope (first derivative) is equal to zero: dLRAC dq = − 4 + 0 . 1 q = 0 ⇒ q ∗ = 40 Alternatively, we can use the fact that LRMC = LRAC at the minimum of the LRAC . But we then need to find LRMC first, which means we need to find the total cost. LRAC = TC q → TC = LRAC × q = 200 q − 4 q 2 + 0 . 05 q 3 LRMC = dTC dq = 200 − 8 q + 0 . 15 q 2 We can now find the q for which LRAC achieves its minimum by setting: LRMC = LRAC 200 − 8 q + 0 . 15 q 2 = 200 − 4 q + 0 . 05 q 2 0 . 1 q 2 − 4 q = 0 q (0 . 1 q − 4) = 0 Which means that either q = 0 or q = 40 . Because q = 0 is not a meaningful result, the LRAC is minimized when q = 40 , as we found above. (b) We replace the above level of output in the LRAC. LRAC ( q ∗ ) = 200 − 4 q ∗ + 0 . 05 q ∗ 2 = $120 Recall that when LRAC achieves its minimum (at q ∗ ), LRMC = LRAC . Therefore, we have LRAC ( q ∗ ) = LRMC ( q ∗ ) = $120 3

(a) P MC = 500 100 = 5 (b) L = P − MC P = 400 500 = 0 . 8 The Lerner index ranges between 0 and 1, so 0.8 is a high degree of market power. (c) L = − 1 η 0 . 8 = − 1 η η = − 1 0 . 8 → η = − 1 . 25 We expect an elastic demand because the monopolist would not be maximizing profit if it were on the inelastic portion of demand. 7. A pharmaceutical company holds a patent for a drug and faces the following inverse demand: p = 50 − 3 Q . The marginal cost of the pharmaceutical company is constant at $5. (a) What is the profit-maximizing level of output and price for the pharmaceutical company? (1 points) Profit-maximization requires: MR = MC 50 − 6 Q = 5 → Q = 45 / 6 = 7 . 5 → P = 50 − 3 Q = 27 . 5 (b) Suppose now that the market for this particular drug becomes a competitive market with the same demand curve. As in class, assume that the supply curve is the same as the marginal cost of the monopoly. What would be the competitive market equilibrium price and quantity? In perfect competition Inverse Demand equals inverse supply (MC) 50 − 3 Q = 5 → Q = 15 → P = 50 − 3 Q = 5 (c) On a graph: • Draw the pharmaceutical company’s demand, marginal revenue, and marginal cost. • Show the optimal quantity and price for the monopolist calculated in (a) and label it e M . • Show the equilibrium quantity and price if the market was perfectly competitive calcu- lated in (b) and label it e C . • Calculate the deadweight loss caused by the monopoly and label it DWL on the graph. 6