Introductory Microeconomics: Problem Set 4
- Suppose that a monopoly can produce any level of output it wishes at a constant
marginal (and average) cost of £5 per unit. Assume that the monopolist sells its
good in two markets which are separated by some distance. The demand curves in the two markets are
given by Q1 = 55 - P1 and
Q2 = 70 - 2P2.
- If the monopolist can maintain the separation between the two markets, what level of
output should be produced and what price should be charged in each? Calculate total
profits and consumer surplus in this situation.
- How would your answer to (a) change if it only costs consumers £5 to transport goods
between the two markets? Would consumers be happy about this change?
- How would your answer change if transportation costs were zero?
- There are two firms in an industry, producing identical goods. One of the firms
acts as a price leader. The leader knows that, in equilibrium, the follower firm will
always choose the same price that she has chosen. The market demand for the good
supplied by the two firms is given by
Q = q1 + q2 = 34 - P, where
Q is total industry output, q1 is the leader's and
q2 the follower's output respectively, and P is the market
- The follower's production costs are given by
TC2 = 0.25q22.
Show that the follower firm will produce output according to
q2 = 2P, where P is the price chosen by the leader.
- The leader's production costs are given by
TC1 = 20q1.
Knowing that she faces the residual demand curve given by
q1 = 34 - P - q2, what price will she choose
to maximise her own profit?
- What would the maximum profits each could earn in equilibrium? Does the result surprise you?
- A publisher pays the author of a book a royalty of 15% of the total revenue. Demand for the
book is q = 200 - 5p and the production cost is
c(q) = 10 + 2q + q2.
Think of the publisher as having a monopoly in the market for this book.
- Find the average and marginal cost of production.
- Write down the expression for profits and find the optimal quantity of books sold from the
publisher's perspective, given that the publisher is a monopolist who maximises profits.
- How many books would the author like to sell?