# Calculating the profits with & without price discrimination

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?

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#### Solution Preview

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

Day time demand=QD=400-50 PD

QD=400-50PD

50PD=400-QD

Or

PD=8-0.02QD

Total Revenue in daytime=TRD=PD*QD=(8-0.02QD)*Qd=8QD-0.02QD^2

Marginal Revenue in daytime=MRD=d(TRD)/d(QD)=8-0.04QD

Marginal Cost in daytime=MCD=$5

In case of third degree discrimination, Cinema Theater will maximize its profits by charging daytime tickets such that

MRD=MCD ...

#### Solution Summary

Solution describes the steps to calculate optimal price and sale levels with and without third degree price discrimination. It also calculate the profits in each case.