Problem 9. Suppose that at the only movie theater in New Brunswick, the costs of

Question

Problem 9. Suppose that at the only movie theater in New Brunswick, the costs of operation consist of a fixed cost of 1000S, and a payment to a movie distributor of 18 per person that sees the movie. Suppose, however, that the theater owner knows that there are two types of customers, students and professors. The inverse demand function for the students is given by Ps 11-0.1q, and the inverse demand function for the professors is given by PP = 21-0.5q a. Assuming that the theater owner can ask for student ID to differentiate between students and professor, can price discriminate between the two, what is the theater's profit maximization problem? b. What are the profit maximizing prices for students and professors? What can you say about elasticity of demand and price for students and professors?

Explanation / Answer

(a) With price discrimination, profit is maximized when

Marginal revenue for students (MRs) = Marginal cost, and

Marginal revenue for professors (MRp) = Marginal cost

(b) Marginal cost (MC) = $1

For students,

Ps = 11 - 0.1qs

Toal revenue (TRs) = Ps x qs = 11qs - 0.1qs2

MRs = dTRs / dqs = 11 - 0.2qs

Equating MRs with MC,

11 - 0.2qs = 1

0.2qs = 10

qs = 50

Ps = 11 - (0.1 x 50) = 11 - 5 = $6

For professors,

Pp = 21 - 0.5qp

Total revenue (TRp) = Pp x qp = 21qp - 0.5qp2

MRp = dTRp / dqp = 21 - qp

Equating MRp with MC,

21 - qp = 1

qp = 20

Pp = 21 - (0.5 x 20) = 21 - 10 = $11

Elasticity of demand (E) = (dq / dP) x (P/ q)

For students,

Ps = 11 - 0.1qs

0.1qs = 11 - Ps

qs = 110 - 10Ps

Elasticity = (dqs / dPs) x (Ps / qs) = - 10 x (6 / 50) = - 1.2

For professors,

Pp = 21 - 0.5qp

0.5qp = 21 - Pp

qp = 42 - 2Pp

Elasticity = (dqp / dPp) x (Pp / qp) = - 2 x (11 / 20) = - 1.1

Since absolute value of elasticity is higher for students, demand is more elastic for students and less elastic for professors. Therefore lower price is charged from students and higher price is charged from professors (Ps < Pp).

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