The Joffrey Ballet has hired you to assist in setting ticket prices. The ballet

Question

The Joffrey Ballet has hired you to assist in setting ticket prices. The ballet company recognizes that there are two distinct demand curves for ballet tickets. One demand curve applies to students, while the other is for everyone else. The two demand curves are: PS = 25 - 0.0025QS and PE = 30 - 0.01QE; where PS is the student price, and PE is the price for everyone else. The marginal cost is $20 and the total cost is 20Q. Hint: Whenever inverse demand is P = a - bQ, marginal revenue is MR = a - 2bQ.

a. What is the total profit that would be collected if the company decides not to price discriminate?

b. If the ballet company decides to price discriminate, what are the profit-maximizing price and quantity levels in each sub-market? Calculate total profits in each sub-market. How does the total across the two sub-markets compare to the total profit from part (a)?

c. What is the elasticity of demand at the quantities calculated in (b) for each market? Verify that the monopolist is charging a higher markup to the group of consumers that is less elastic.

Explanation / Answer

a) When there are no price discrimination, same price is charged from the two groups using the marginal cost. Find the single demand function

PS = 25 - 0.0025QS gives QS = 10000 - 400PS

and PE = 30 - 0.01QE gives QE = 3000 - 100PE

Combinded demand Q = 13000 - 500P

Inverse demand P = 26 - 0.002Q

MC = 20

Find the market quantity and market price

MR = 26 - 0.004Q and MC = 20

26 - 0.004Q = 20

Q* = 1500 and P* = 26 - 0.002*1500 = 23

Single price is $23

QS = 10000 - 400*23 = 800 and QE = 3000 - 100*23 = 700

Profits = TR - TC = 1500*23 - 20*1500 = $4500

b) Price discrimination has two seperate prices and quantities

MR1 = MC MR2 = MC

25 - 0.005QS = 20 30 - 0.02QE = 20

QS = 1000 QE = 500

PS = 25 - 0.0025*1000 = 22.5

PE = 30 - 0.01*500 = 25

Total profit = 22.5*1000 + 25*500 - 1500*20 = 5000

See that price discrimination increases profits

c) Elasticity = P/(MC - P)

ed for students = 22.5/(20 - 22.5) = -9

ed for everyone = 25/(20 - 25) = -5

See that student have elastic demand because demand elasticity value is relatively higher. Hence the price charged to students is lower at 22.5. Markup from students = (P - MC)/MC = (22.5 - 20)/20 = 12.5% and for everone else =  (25- 20)/20 = 25%. Hence monopolist is charging a higher markup to the group of consumers that is less elastic.

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