Question

A movie theater faces the following hourly inverse demand curves:

Seniors: PS = 88 - Q
Adults: PA = 94 - Q
The theater has a fixed cost of $40, and a constant marginal cost of $2 per ticket.
a) If the movie theater uses segmenting, calculate the ticket prices charged to adults and seniors.

Answer 1

Price for Seniors $ 45

Price for Adults $ 46

Step-by-step explanation:

As the theater uses segmenting it will solve to maximize profit on each segment:

PS = 88- Q

Total Revenue = price x quantity = (88 - Q) Q = -Q^2 + 88Q

Marginal Revenue = 88-2Q

Marginal Revenue = Marginal Cost --> point to maximize profit

88 - 2Q = 2

(88 - 2) / 2 = Q

43 = Q

P = 88 - 43 = 45

For Adults:

Revenue (94 - Q)*Q = 94Q - Q^2

Marginal Revenue = 94 - 2Q

Marginal Revenue = Marginal Cost --> point to maximize profit

(94 - 2)Q = 2

Q = 46

P = 94 - 46 = 46