In: Economics
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.
Q=2000-25P+2A
Q=2000-25P+2(125)
Q=2250-25P
P=90-0.04Q
Total Revenue=P X Q
We can derive marginal revenue by doing the derivative of total revenue.
Given that marginal cost is equal to zero.
a) Profit is maximized when MR=MC
90-0.08Q=0
Q=1125
P=90-0.04Q=90-0.04(1125)=90-45=45
So, the profit-maximizing ticket price for theatre is 45.
b) We know that MR=P(1+1/e)
Therefore, e=-1.
So, the price elasticity of its demand at this price is -1.
c) We can calculate elasticity of its demand with respect to advertising as follows:
So, elasticity of its demand with respect to advertising is 0.22.
d) Now, number of advertisement increases to 250.
Q=2000-25P+2A
Q=2000-25P+2(250)
Q=2500-25P
P=100-0.04Q
Profit will be maximized when MR=MC
100-0.08Q=0
Q=1250
P=100-0.04Q=100-0.04(1250)=100-50=50
So, new profit-maximizing price is 50, so, price should increase by 5 units (50-45) when theater increases the number of its ads to 250.