Problem 8. Suppose that RU Shuttles is a monopolist in providing transportation
ID: 1125705 • Letter: P
Question
Problem 8. Suppose that RU Shuttles is a monopolist in providing transportation services between New Brunswick and Newark Campuses. During the daytime (from 06.00 a.m. to 06.00 p.m.) the demand for transportation services is Q 100- P, where Q is the quantity demanded (the number of passengers) and P is the price for transportation services. The demand at night (from 06.00 p.m. to 06.00 a.m.) is ON = 50-P. The marginal cost of transportation is 20s. a. Suppose that RU Shuttles applies third degree price discrimination and charges different prices during the daytime and at night. What are the optimum prices? b. Assume that price discrimination is forbidden by the law, and RU Shuttles charges a uniform price for all passengers. What is the optimum price? c. Which case is better for society? (HINT: Social welfare=consumer surplus+ profits)Explanation / Answer
a) Use respective marginal revenue functions and marginal cost
DaY: MR1 = 100 - 2Q and Night MR2 = 50 - 2Q
Profit maximizing price and quantity
100 - 2Qd = 20 and 50 - 2Qn = 20
Qd* = 40 and Qn* = 15
Pd* = 100 - 40 = $60 and Pn* = 50 - 15 = $35
These are the optimum prices
b) For uniform price, single demand function is Q = 150 - 2P or P = 75 - 0.5Q. Marginal revenue is MR = 75 - Q
This gives MR = MC
75 - Q = 20
Q* = 55 and price P* = 75 - 0.5*55 = 47.50
This is the optimum price
c) Single price monopolist case
CS + Profits = 0.5*(75 - 47.50)*55 + (47.50 - 20)*55 = 2268.75
Price discriminating monopolist
CS + Profits = 0.5*(100 - 60)*40 + 0.5*(50 - 35)*15 + (60 - 20)*40 + (50 - 35)*15 = 2737.50
Price discrimination is better for society because socital surplus is relatively higher.