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

Qd = 2000 - 25 P + 2A

If A = 125, then Qd = 2000 - 25 P + 2*125
Qd = 2000 - 25 P + 250
Q = 2250 – 25P [Use Qd =Q]
25P = 2250 - Q
P = (2250 – Q)/25
TR = P*Q = (2250Q – Q2)/25
MR = dTR/dQ = (2250 – 2Q)/25

a. Since it’s a monopolist, its profit maximizing output will meet the condition –

MR = MC
(2250 – 2Q)/25 = 0
2Q = 2250
Q = 1125
P = (2250 – 1125)/25 = $45 per unit

b.

Price elasticity of demand= dQ/DP * P/Q
= - 25 * 45/1125
= -1

c.

elasticity of demand with respect to advertising= dQ/dA * A/Q
= 2 * 125/1125
0.22

d. The elasticity of its demand with respect to advertising is less than 1 which means that when advertising increases by 1%, then quantity demanded changes by 0.22%. Increasing price would further reduce the demand for the product.

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