Question

A movie theater faces the following demand curves: Seniors: Ps = 27-Q Adults: Pa = 33 - Q The theater has a fixed cost of 50, and a constant marginal cost of 1 per ticket. a) If the movie theater uses segmenting, calculate the ticket prices charged to adults and seniors. b) How much profit does the movie theater earn from segmenting? c) Illustrate the profit maximizing choices on both inverse demand functions along with CS and profit. d) Suppose the theater is legally prevented from using price discrimination. Calculate and illustrate the aggregate inverse demand. What price will they charge per ticket? How much profit will they earn? e) Find the total consumer surplus without price discrimination and illustrate it on the aggregate inverse demand. Under which scenario are the consumers better off?

Answer 1

Since prices are asked for separately, I have assumed that this movie theatre follows a monopoly pricing:

Prices charged to senior is 14 and prices charged to adult is 17

Total profits earned from segmenting is 425

Cs of seniors is denoted by shaded triangle ABC on the left graph. CS of adults is shown by shaded triangle A'B'C' in the right graph. Profit maximizing choice for seniors is at Q=13 and of adults is at Q=16. Total profits from seniors is shown by rectangle BCED in left graph. Profits from adults is shown by rectangle B'C'E'D' in right graph.

Consumer surplus in senior market: Area of triangle ABC: 0.5*13*(27-14)= 84.5

Consumer surplus in adult market: Area of triangle A'B'C': 0.5*16*(33-17)= 128

Total CS from both markets: 128+84.5= 212.5

Since market cannot be segmented, price is chosen over aggregate quantity demanded i.e. Qa plus Qs.

total quantiy demanded then is 29 with a price of 15.5 and profit of 420.5

Total consumer surplus is area of shaded region ABC, which is:

0.5*29*(30-15.5)= 210.25

Therefore, comparing the 2 CS, consumers are relatively better off when market is segmented, i.e. under differential pricing for seniors and adults