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

(a) Qd = 2000 - 25P + (2 x 125) = 2000 - 25P + 250 = 2250 - 25P

25P = 2250 - Qd

P = 90 - 0.04Qd

A monopolist maximizes profit by equating marginal revenue (MR) with MC.

Total revenue (TR) = P x Qd = 90Qd - 0.04Qd2

MR = dTR/dQd = 90 - 0.08Qd

Equating with MC (= 0),

90 - 0.08Qd = 0

0.08Qd = 90

Qd = 1125

P = 90 - (0.04 x 1125) = 90 - 45 = 45

(b) Price elasticity of demand = (dQd/dP) x (P/Qd) = - 25 x (45 / 1125) = - 1

(c) Advertising elasticity = (dQd/dA) x (A/Qd) = 2 x (125 / 1125) = 0.22

(d) Absolute value of price elasticity of demand is equal to 1, so demand is unitary elastic and an increase will price will not change its total revenue. Therefore, the firm may or may not increase its price, irrespective of increase in number of advertisings.

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