Cinema Theater has estimated the following demand functions for its movies: Dayt

Question

Cinema Theater has estimated the following demand functions for its movies:

Daytime demand, QD = 400 - 50 PD Nighttime demand, QN = 200 - 20 PN The marginal cost of serving another customer is $5 and its fixed costs are $100.

a. If the theater uses third degree price discrimination, what price will it charge for daytime tickets? How many will be sold?

b. If the theater uses third degree price discrimination, what price will it charge for nighttime tickets? How many will be sold?

c. What is the profit associated with using third degree price discrimination?

d. If the theater does not use price discrimination and charges the same price to all customers, what is that price and how many tickets will be sold?

e. What happens to profit when the theater does not engage in third degree price discrimination? How much does it rise or fall?

Explanation / Answer

Daytime demand, QD = 400 - 50 PD Nighttime demand, QN = 200 - 20 PN The marginal cost of serving another customer is $5 and its fixed costs are $100.

a. If the theater uses third degree price discrimination, what price will it charge for daytime tickets? How many will be sold?

P = 8 - 0.02*Q

TR = 8Q - 0.02Q^2 ;

MR = 8 - 0.04Q

MR = MC = 5

8 -0.04Q = 5

Q = 75

P = $6.5

b. If the theater uses third degree price discrimination, what price will it charge for nighttime tickets? How many will be sold?

P = 10 - 0.05 Q ;

TR = 10Q - 0.05Q^2 ;

MR = 10 - 0.1 Q ;

MR = MC = 5

10 -0.1Q = 5

Q = 50

P = $7.5

c. What is the profit associated with using third degree price discrimination?

Profit = (75*6.5 - 5*75 - 100) + (50*7.5 - 5*50 ) = $137.5

d. If the theater does not use price discrimination and charges the same price to all customers, what is that price and how many tickets will be sold?

average = (6.5+7.5)/2 = $7

Qd = 50 and Qn = 60 ..total = 110 tickets

Profit = 110*7 - 5*110 -100 = $120

e. What happens to profit when the theater does not engage in third degree price discrimination? How much does it rise or fall?

Fall

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