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

Q = 2000 - 25P +2(125) ;

P = 90 - 0.04Q ( demand curve equation ) ;

MR equation is 90 - 0.08Q ;

for profit max. equating MR anc MC ; hence 90 - 0.08Q = 0 ;

Q= 1125 ;

corresponding price = 90-(0.04)(1125) = 45 ;

MR = p( 1+ 1/e) ; hence e = -1( elasticity) ;

C) answer = (dQ/dA )/( Q/A) = 2/(1125/125) = 0.222

if the number of advertisement increases then he should increase his price ;

Q = 2000 - 25P +2(250) ;

P= 100 - 0.04Q ;

new profit max Q = 100 / 0.08= 1250 ; P = 50 ;

hence increase price by 5 units

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.