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 - 5/2 Q + Q62/10. 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

Equate MC and MR for profit-maximizing output. Q will be 22.

Cost will be 100+8.4*22 - 5/4 * 222 + 223/30 = 34.7

Profit = PQ - Cost

= 2.9 * 22 - 34.7

= 29.

c. Lerner Index = (P-MC)/MC

MC = 1.8 by substituting Q=22 in MC equation.

(2.9-1.8)/1.8 = 0.6.

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