The following equation represents the weekly demand that a local theater faces.

Question

The following equation represents the weekly demand that a local theater faces. Qd = 2000 - 25 P + 2 A, where P represents price and A is the number of weekly advertisements. Presently the theater advertises 125 times per week. Assuming this is the only theater in town, and its marginal cost, MC, is equal to zero, a. Determine the profit maximizing ticket price for the theater. b. What is the price elasticity of its demand at this price? c. What is the elasticity of its demand with respect to advertising? d. Now suppose the theater increases the number of its ads to 250. Should the theater increase its price following this ad campaign? Explain.

Explanation / Answer

Profit maximizing condition for a monopolist since its the only theater in town is nothing but MR = MC
where MC = 0
Q = 2000 + 250 - 25P
Q = 2250 - 25 P

R (q) = p . Q
= p (2250 - 25P)

dR/dp = MR= 2250 - 25P = 0
P = 2250 / 25 = 90

0 = P [ 1- 1/e] e = 1

increasing advertisements increases quantity of tickets by double the amount so e > 1 where quantity effect dominates

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