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 = 2,000 – 25P+2A
Qd=2,000 – 25P +2(125)
Qd=2,250 – 25P
P = 2,250/25 – (1/25)Q
=90 – 1/25Q
TR = 90Q – 1/25Q^2
dR/dQ = 90 – 2/25Q
MC= 0
Equilibrium condition MR=MC
90 – 2/25Q =0
Q = 90*25 /2
= 1,125
P = 90 – 1/25(1125)
=90 -45
= 45
b)   Elasticity of demand = dQ/dp*P/Q
Dq/dP = - 25
Ed = -25*45/1125
=1
c)   Ed w.r,.t Advertisement
=2*45/1125
=0.08

d)   Theatre should not increase the price since the elasticity of demand with respect to advertisement is less than unity.

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