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MGEB01 Practice Question Set 5
Question 1
A monopolist sells a good in two markets, and he is only capable of doing simple per-unit
pricing in each market. The inverse demand curve in the two markets are p1 = 100 − Q1,
p2 = 100− 2Q2 respectively. The firm’s total cost is (Q1 +Q2)2.
Q1a.
Suppose that the monopolist can charge different prices in each market, what is the objec-
tive function of the monopolist?
Q1b.
What is the profit-maximizing quantities Q1, Q2 in the two markets? Hint: The
marginal cost is MC(Q) = 2(Q1 + Q2), and the marginal revenues are MR1(Q) =
100− 2Q1,MR2(Q) = 100− 4Q2 (double slope, same intercept).
Q1c.
What are the profit-maximizing prices p1, p2 in the two markets?
Q1d.
Suppose that the monopolist have to charge the same price in each market. In this case,
you need to find the total demand first. What is it? (hint: sum up the individual market
demands Q1, Q2 to get Q))
1
Q1e.
What is the objective function for part d (in terms of Q)?
Q1f.
Plot the objective function (with Q being the horizontal axis).
Q1g.
Find out the profit-maximizing quantity Q and the profit-maximizing price P .
Question 2
A monopolist airliner hires you as a manager. They have business travellers and tourists
as two types of customers, whose inverse demands are P = 100 − x and P = 80 − x
respectively. The monopolist as your boss is not very happy with the idea of reducing the
price of business-class tickets, and is thinking about reducing the quality of the economy-
class ticket instead. For simplicity, assume that there is no cost.
Q2a.
Suppose that the economy class ticket can be reduced to have a quality of x = 50. Find out
the lump-sum price of economy class ticket PE that can extract the maximum consumer
surplus from tourists.
Q2b.
Given PE, find out the maximum price that of the business-class ticket PB that can be
charged without making the business travellers going for the economy-class tickets.
Q2c.
Suppose that the profit is just PB + PE. By comparing the profits from reducing business-
class ticket price versus reducing economy-class quality to x = 50, what would you recom-
mend to your monopolist boss?