Introductory Microeconomics: Problem Set Week 5

  1. Consider a perfectly competitive industry with 24 producers, each with the same cost function C(y) = 16 + 4y2. Market demand is given by Y = 150 - 2p.

    1. Calculate the supply function for each firm, market supply, and the equilibrium price in the market, p*.
    2. In the long run, firms can leave the industry, or new ones (with the same cost functions given above) can enter. In the long-run equilibrium, what is the price, the output of each firm, and the number of firms?

  2. 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?

  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. Consider a market supplied by two firms. The market inverse demand curve is p = 72 - 3y, where y = y1 + y2 is the combined output of the two firms. The firms have identical constant returns to scale production technologies with constant marginal costs of 12.

    1. Assuming Cournot competition, derive the equilibrium output, price, and profits for each firm.
    2. Verify the Cournot mark-up equation.
    3. Calculate and interpret the HHI index for this industry.
    4. Suppose that Firm 1 invents a new production process which cuts its marginal cost in half. Repeat the calculations from parts (a) and (c) and compare the results with your earlier findings.

  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. Suppose that a single firm takes over all wholesale vegetable dealing, becoming a monopsonist. Customers (vegetable retailers, that is) remain the same, continue to compete with one another as before, and have the same demand curve.
      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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