Introductory Microeconomics: Week 6 Problem Set

Firm conduct under imperfect competition.
  1. A monopolist faces a demand curve q = 200 - p/2, where p is price and q is quantity. Its costs are given by C(q) = 4q + q2.

    1. What is the maximum profit the monopolist can make?
    2. What is the maximum revenue the government can earn by imposing a per unit tax on the monopolist?
    3. If the firm is a profit maximiser, by how much are its profits reduced by the imposition of such a tax?

  2. Consider two social media firms, which are both considering a controversial policy such as banning/rehabilitating a controversial figure like Donald Trump, or blocking/allowing all tracking of user activity. Use a simple game theoretic model to analyse their interaction. (Simple means two players, playing just once, each with two possible actions, taken simultaneously.) Is the situation more like the prisoner's dilemma or the crop choice games discussed in lecture?

  3. Consider a monopolist that wishes to price discriminate by means of a "block pricing" scheme: buyers must pay p1 for purchases up to amount q1, then benefit from a lower price p2 for any further purchases. (Let the consumer's total, freely chosen purchases be denoted "q2"). The firm's customers are identical and have inverse demand functions P = 90 - Q. The firm has costs MC = AC = 20.

    1. If charging a single price for all purchases (by a single customer), what price should the firm charge to maximise profits? (Would your answer be different for a larger market of many identical such customers?)
    2. Illustrate in a diagram how the firm's new block pricing scheme can be used to increase profits earned.
    3. What are the optimal choices of p1, q1, and p2 to maximise profits earned from an individual consumer?

  4. The libraries of two colleges demand subscriptions to a publisher's academic journals. The publisher's marginal costs of providing online access are zero. The journals in question are Horrible History, Execrable Economics, and Awful Accounting. The two colleges are willing to pay the following amounts for each journal.

    HHEEAA
    Pembroke2,0001,1001,400
    College X1,8001002,100

    1. The publisher cannot price discriminate, but can choose either to sell individual subscriptions to each journal or, alternatively, to bundle all three together and sell a package subscription. Which strategy will maximise profits in this case?
    2. Suggest a different set of willingness to pay values for College X that would change your answer to part (a).

  5. A firm's customer has demand function of q = 80 - p. The firm's MC = AC = 10. The firm charges the customer a fixed membership fee of £1,000 and a price p = £20.

    1. Is the firm maximising profits? If not, how could it do better?
    2. Suppose a second customer enters the market. This customer's inverse demand is q = 50 - p. The firm cannot discriminate, i.e. must treat the two customers identically. Do your answers to part (a) change?

  6. Suppose that a wholesale market for fresh vegetables has a demand curve given by qD = 90 - 3p and a supply curve given by qS = 6p, where is p the price in £s per tonne and q is the quantity of vegetables.
    1. Assuming that the market is perfectly competitive,
      1. What are the equilibrium values of price and quantity? Draw and fully label an appropriate diagram illustrating the equilibrium (with price on the vertical axis).
      2. Suppose the government imposed a minimum price of £14 per tonne. Now what are the equilibrium values of price and quantity?
    2. Now a supermarket takes over all wholesale business, so the the market for vegetables is a monopsony. The supermarket will sell them on to the same customers; assume that the consumer market for supermarket vegetables is still competitive.
      1. What are the equilibrium values of price and quantity? Draw and fully label an appropriate diagram illustrating the equilibrium.
      2. Calculate the deadweight loss associated with the monopsony and explain why it arises.

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