Introductory Microeconomics: Problem Set 4

  1. 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.

    1. 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.
    2. 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?
    3. How would your answer change if transportation costs were zero?

  2. 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 price.

    1. 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.
    2. 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?
    3. What would the maximum profits each could earn in equilibrium? Does the result surprise you?

  3. 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.

    1. Find the average and marginal cost of production.
    2. 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.
    3. How many books would the author like to sell?