Suppose the inverse demand for the patented drug Zuker, a drug that helps reduce

Question

Suppose the inverse demand for the patented drug Zuker, a drug that helps reduce sugar cravings among children, is P = 4 - Q/20 so that MR = 4 - Q/10. Willy Wonka, Inc., the manufacturer of Zuker, has the cost function C = 100 + 8.4Q - 5/4 Q^2 + 1/30 Q^3 such that MC = 8.4 - 5/2Q + Q^2/10. Answer the following questions: Calculate Willy Wonka, Inc.'s profit-maximizing output. Calculate Willy Wonka, Inc.'s profit from selling Zuker. Calculate Willy Wonka, Inc.'s Lerner Index when selling at the profit-maximizing output.

Explanation / Answer

Equilibrium at MR=MC

4-Q/10 = 8.4 - 5/2Q+Q^2/10

Q^2/10- 5Q/2 + Q/10 = -4.4

Q^2 - 25Q + Q = -44

Q^2 - 24Q + 44 = 0

Q^2 - (22+2)Q + 44 =0

Q(Q-22) -2 (Q-22) = 0

Q=2, 22

At Q=2 the firm will be in loss of 104

At Q = 22

P = 4-22/20 =2.9

Profits = TR(P*Q)-TC = (4*22-22*22/20) - (100+8.4*22-5*22*22/4+22*22*22/30) = 29.067

L = (P-MC)/P

= (2.9 - (8.4-5*22/2+22*22/10))/2.9) =0.37931

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