Notes

Easterbrook and Fishel (1991) is a thorough coverage of the economic structure of corporate law. Manne (1965) is a crucial first paper on mergers and the market for corporate control. Hart (1995) contains a useful discussion of voting structure in public companies. Lucas (1983) is an excellent introduction to weighted majority games and voting power. Teall (2007) contains a useful discussion and analysis of voting power and corporate governance issues. The link between concentration and welfare seems to be well known in the literature (see, for example, Shy 1996), but seems to have had little influence on the design of actual competition policies. Hylton (2003, Chapter 3) and Spulber (1989, Chapter 19) also analyse optimal enforcement and deterrence of anti-trust violations.

Exercises

  • 1. Suppose that victims cannot take any care to avoid accidents, and suppose that there are two firms who are potential injurers, each of whom can take care. The following table describes the levels of care, costs of care, and expected damages.
  • 1

Levels of care

Costs of care

Expected damage to victim

Total social costs

Firm 1

Firm 2

Firm 1

Firm 2

None

None

0

0

30

None

Care

0

4

24

Care

None

6

0

20

Care

Care

6

4

12

(a) Compute the total social costs for each combination of levels of care. What is the efficient outcome here?

Consider the following strict liability rule: irrespective of the level of care taken by each firm, if there is an accident, firm 1 will be liable for a pre-specified fraction s1 of the victim's losses, and firm 2 will be liable for a pre-specified fraction s2 of the victim's losses, with s1 + s2 = 1.

  • (b) Suppose that the firms cannot collude amongst themselves. Write down the payoff matrix for the strategic game between firms 1 and 2. Does the strict liability rule outlined above induce both firms to behave efficiently? In other words, is the efficient outcome a Nash equilibrium?
  • (c) Is {None, None} a Nash equilibrium? If so, under what conditions? If not, why not?
  • (d) Is {Care, None} a Nash equilibrium? If so, under what conditions? If not, why not?
  • (e) Is {None, Care} a Nash equilibrium? If so, under what conditions? If not, why not?
  • (f) Does your answer in part (b) change if the firms can collude amongst themselves and jointly choose their levels of (for example, if the firms were to merge to form a single firm)? Explain.

Now consider the following negligence rule: the court first sets due standards of care, z1 and z2 for firms 1 and 2, and applies these due standards as follows: [1]

2. Consider the four-player weighted majority game:

  • (a) In which coalition is player 1 pivotal?
  • (b) Find the voting power of player 1, using the Shapley-Shubik index.
  • (c) Repeat questions (a) and (b) for players 2, 3 and 4.
  • 3. Price controls are a common form of regulation. Suppose there is a single firm

that produces a single good, Q. The ordinary demand curve for this good is:

where P is the price of the good and x is the quantity demanded. Suppose that

marginal costs of production are constant and equal to c = 0.

  • (a) What is the efficient price and quantity? How much profit does the firm earn if it charges this price?
  • (b) If the firm acts as a monopolist and chooses a single price to maximise its profits, what price would it select? What would its profits be in such a situation? What quantity would it produce? Who is harmed if the firm is allowed to act as an unregulated monopolist, and how much are they harmed?

Now suppose you are advising the government on the design of a system of consumer protection laws to regulate prices. A firm is said to be a price gouger if it sets its price above its marginal cost. Let p be the (exogenous) probability that a price gouging firm will be prosecuted and found guilty by a court and punished.

  • (c) Given p, design a system of fines that induces the firm to choose the efficient price and quantity. For example, you may recommend that the government should fine the firm according to the quantity it produces, the price it charges, its level of profits, revenue, or some combination of these variables (or none of them). The choice is up to you. You may assume that the firm is a risk-neutral expected profit maximiser. Carefully explain why your system of fines is optimal. Does your optimal fine depend on p? If your optimal fine is implemented and the firm correctly perceives p, will the firm ever price gouge?
  • (d) Now suppose that the firm's marginal costs are constant and equal to %, but that the government mistakenly believes that the firm's marginal costs are zero. If the government implements the scheme of fines you designed in question 1, what are the welfare consequences?
  • (e) Now suppose that the firm's marginal costs are constant and equal to 0 (and the government knows this), but that the government does not know that the true demand curve is actually:

If the government implements the scheme of fines you found in question 1,

what are the welfare consequences?

(f) What can you conclude about the ability of governments to implement efficient price-gouging laws? Briefly discuss, with reference to your answers above.

  • [1] If a firm meets its due standard of care, it is not liable to pay any damages to the victim. • If firm 1 is the only firm which does not meet its due standard ofcare, it will be held liable for the total amount of the victim's damages. Similarly, if firm 2 is the only firm which does not meet its duestandard of care, it will be held liable for the total amount of the victim'sdamages. • If both firms 1 and 2 do not meet their due standards of care, theywill both be held liable for some pre-specified portion of the victim'sdamages, with firm 1 paying a fraction s1 of the victim's damages, andfirm 2 paying a fraction s2 of the victim's damages, where again we have s1 + s2 = 1. (g) Suppose that the due standards of care are set at the efficient levels foreach firm. Repeat parts (b) to (f) above.
 
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