# Notes

- 1 Introduction
- 1. Hirshleifer (1982) sets out a similar set of propositions.
- 2. See Demsetz (1969), p. 1.
- 3. This analytical distinction is due to Buchanan and Stubblebine (1962).
- 2 Courts, Legal Rules, and Markets
- 1. See, for example, Benson (1990) for a book-length treatment. Friedman (1994) also discusses some historical examples.
- 2. The role of private property rights in enhancing the efficiency of resource allocation is further explored in Chapter 7.
- 3. This term was coined by Joskow and Noll (1981). See also Peltzman (1989).
- 4. Schelling (1978, page 121) and Brennan and Buchanan (1985, chapter 1) contain discussions of this role of rules within broader contexts.
- 5. The results of the analysis still go through if instead of depending directly on X, x depended on some
*function*of*X,*say*f(X),*where*f*is strictly increasing. For example, fX) could be the average choice of x rather than the aggregate of the individual x/s. - 6. These examples are due to Holcombe (1983).
- 7. The statement of this result is due to Young (1996).
- 3 The Coase Theorem
- 1. The role of this simplifying assumption - that individuals 'consume' money - is meant to reflect the fact that money represents purchasing power over all other goods in the economy.

*du _{F}*(Q,

*M*

_{F})

_{n}.

*d*(Q,

*M*

_{F})

_{n}

2. This means that we have * ^{F} - >* 0 and

*0 .*

^{F F}<*dQ dQ*^{2}

*du-* (Q, *M _{F})* 9

^{2}u

*-*(Q,

*M*-) .

3. This means that we have * ^{F F} >* 0 and

^{F}_{2}

*0 .*

^{F}<*dM _{F} dM_{F}*

- 4. This means that we have:
^{dVg(Q}'^{Mr}) < 0 and^{d Vr(Q}'^{Mr}) < 0. The analy- - 9Q 9Q
^{2}

sis would go through, with appropriate modifications, if the production of *Q *was assumed to generate a *positive* externality.

*dv _{R}(Q*,

*M*(Q,

_{R}) „ , d^{2}v_{R}*M*

_{R})

_{A}

5. This means that we have: ^{r r} > 0 and ^{r} 2 ^{R} < 0.

*dM _{R}* 9MR

6. It is important to note that there may also be cases in which optimality does not require tangency of indifference curves. This can happen, for example, if the indifference curves are straight lines.

- 7. See Boadway and Bruce (1991), p. 68.
- 8. Hurwicz (1995) attempted to show that quasi-linearity is not only a sufficient condition, but is also a
*necessary*condition. In other words, Hurwicz attempted to show that if preferences are not quasilinear, then the contract curve could not be a horizontal line. However, in an important recent paper, Chipman and Tian (2011) show that a much wider set of preferences yield a horizontal contract curve. In other words, quasi-linear preferences are not necessary for the invariance version of the Coase Theorem. - 9. This is the example developed by Aivazian and Callen (1981).
- 4 Accident Law and Markets, Part I: The Unilateral Care Model
- 1. The level of care chosen by the monopolist is analogous here to the choice of quality. Since we have assumed that marginal consumption benefits u'(Q) are independent of the level care, this results in the monopolist choosing the efficient level of care. Under a different set of assumptions about the interaction between care and marginal benefits, this result would not, in general, hold. In this more general case, the monopolist may choose an inefficiently high or low level of care.
- 2. These results are illustrated for the case of CO
_{2}abatement in McKibbin and Wilcoxen (2002) chapter 5. - 8 Contract Law and Markets
- 1.
*Hadley & Anor*v.*Baxendale & Ors*[1854] England and Wales High Court (Exchequer Court), J70. - 9 Crime, Punishment and Deterrence - Markets for Illegal Activities and the Economics of Public Law Enforcement
- 1. The analysis follows Becker, Murphy and Grossman (2006). A series of exercises in Bergstrom and Varian (2009) pp. 299-300, also considers a similar model.
- 10 Topics in Corporate Law and Competition Law
- 1. See Grossman and Hart (1980), p. 46.
- 2.
*f*(and indeed all power indices that we compute) have the property that^{ss}

ЕФ = 1.

3. Note that this is not quite the same thing as *i* being critical. Player *i* can be critical and turn a winning coalition into a losing one, but that does not mean that other players in the coalition are also critical. A minimal winning coalition is one in which *all* members are critical.

- 11 Litigation, Settlement and the Market for Lawyers
- 1. This approach is due to Rubinstein, Safra and Thomson (1992). It is also discussed in Osborne and Rubinstein (1994), page 302, and Muthoo (1999), chapter 2.
- 2. See, for example, Baye et al (2005), Propositions 3 and 5.
- 3. This result was first stated by Plott (1987).
- 4. Excellent overviews of recent research are provided in Garfinkel and Skaperdas (1996) and Anderton and Carter (2009).