Econ 522 Economics of Law Dan Quint Spring 2012 Lecture 3

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 Efficiency: “all available Kaldor-Hicks improvements made”  roughly, maximizing total value, or total surplus, or total payoffs, to everyone in society…  …where everything is translated into dollars, so we’re able to add/compare across people  Means that…  each scarce resource is owned by whoever values it most  goods are produced whenever their value is greater than their cost  and so on Last week, we defined efficiency

 Externalities  People make choices based on private cost and private benefit  Efficiency is based on social cost and social benefit  When social cost > private cost, negative externality  people will do something more than efficient amount  When social benefit > private benefit, positive externality  people will do something less than efficient amount  Barriers to trade, taxes  Monopoly/private information And we discussed some forces that lead to inefficiency

 Posner: yes – ex-ante, we would all have agreed to efficient laws  Analogy to lottery ticket with highest expected value  Example for asymmetric situations (landlords and tenants)  Cooter & Ulen: yes – if we want to adjust the distribution of wealth, better to do it through tax system  Several reasons taxes better than legal system for redistributing wealth And we asked: Should efficiency be the normative goal of the law?

1.Taxes can target “rich” and “poor” more precisely than the legal system can 2.Distributional effects of legal changes are harder to predict 3.Lawyers are more expensive than accountants 4.More narrowly-targeted taxes cause greater distortion than broad-based taxes Four reasons the tax system is a better way to redistribute wealth than the legal system

6 Two goods: beer (x), pizza (y) One consumer, with $60 and utility u(x,y) = x 0.5 y 0.5 a. Given prices p for beer and q for pizza, calculate demand. (x,y) = (30/p, 30/q) Beer and pizza are produced at $1 per unit, and perfectly competitive markets So without any taxes, p = q = $1 b. Calculate demand, and utility, with no tax. (x,y) = (30, 30)u(x,y) = = 30 c. Calculate demand and utility with $0.50 tax on beer. (x,y) = (20, 30)u(x,y) = =  d. How much revenue does $0.50 tax on beer raise? 20 X $0.50 = $10 e. Calculate demand and utility with $0.20 tax on both goods. (x,y) = (25, 25)u(x,y) = = 25 f. How much revenue does $0.20 tax on both goods raise? 25 X $ X $0.20 = $10 g. Which is the better way to raise revenue? To make this last point, an example

 Aside from maximizing efficiency, what are other plausible normative goals for a legal system?  When would you expect these goals to be in conflict with efficiency? Discussion question

Let’s first dispense with the straw man. I’ve never heard of an economist who believes that every efficient policy is good, and I’ve heard of very few who believe that every inefficient policy is bad. It’s true that most economists do seem to believe that any good policy analysis should start by considering efficiency. That doesn’t mean it should end there. I think economists are right to emphasize efficiency, and I think so for (at least) two reasons. First, emphasizing efficiency forces us to concentrate on the most important problems. Second, emphasizing efficiency forces us to be honest about our goals. – Steven Landsburg A nice blog post about why policy evaluation should at least start with efficiency…

Politician: Here’s my program to make the health care system work better by subsidizing health care for the poor. Economist: Your program costs a billion dollars and delivers half a billion dollars worth of benefits. That’s inefficient. Politician: So what? Economist: Well, the “so what” is that maybe you could take that billion dollars and deliver a full billion dollars worth of benefits instead if you spent it a little differently. Why not just hand the cash out to poor people? Politician: Because I don’t want to help all poor people. I only want to help sick poor people – and this is the only way I can think of to do that. Economist: Ah. So your goal here is not to make the health care system work better at all. Instead it’s to transfer resources to sick poor people. Politician: I guess so. Economist: That’s fine. Now we can have a healthy debate about whether that’s what we want to do. “Emphasizing efficiency forces us to be honest about our goals”

 We’ve seen two arguments in favor  Posner: it’s what we all would have agreed on ex-ante  C&U: if you want to redistribute, it’s better to do it through taxes  But there are definitely some problems with efficiency  Distribution matters; not everything is monetizable; people might care about procedural fairness  My take  In this class, we’ll mostly focus on the positive questions  But in the background, I think of efficiency as a “pretty good”, but definitely imperfect, measure of “goodness” Summing up… is efficiency a good goal for the law?

11  I don’t have many “absolute beliefs” about economics  Some people do  I hope that doesn’t make things too confusing Before we move on, a quick digression…

12  I don’t have many “absolute beliefs” about economics  Some people do  I hope that doesn’t make things too confusing  Relatedly, if I don’t see economics as a set of rules to memorize, how do I know what I know?  I need to see a model, or an example, that demonstrates it Before we move on, a quick digression…

13  introduce some basic game theory  begin property law Rest of today:

14 Some basic game theory

15  Today, we focus on static games  Also known as simultaneous-move games  A static game is completely described by three things:  Who the players are  What actions are available to each player  What payoff each player will get, as a function of  his own action, and  the actions of the other players  Any complete description of these three things fully characterizes a static game A brief introduction to game theory

16  (Story)  Players: player 1 and player 2  Two actions available to each player: rat on the other, or keep mum  Payoffs:  u 1 (mum, mum) = -1  u 1 (rat, mum) = 0  u 1 (mum, rat) = -10  u 1 (rat,rat) = -5  Same for player 2 A classic example: the Prisoner’s Dilemma

17 In two-player games with finite actions, one way to present game is payoff matrix -1, -1-10, 0 0, -10-5, -5 MumRat Mum Rat Player 2’s Action Player 1’s Action Player 1’s PayoffPlayer 2’s Payoff Always Player 1

18  We solve a game by looking for a Nash equilibrium  Nash equilibrium is a strategy profile (an action for each player) such that:  No player can improve his payoff by switching to a different action…  …given what his opponent/opponents are doing Nash Equilibrium

19  If any player can improve his payoff by changing his action, given his opponents’ actions, then it is not a Nash equilibrium  Is (Mum, Mum) an equilibrium?  No, if player 2 is playing Mum player 1 gains by deviating A strategy profile is a Nash Equilibrium if no player can gain by deviating -1, -1-10, 0 0, -10-5, -5 MumRat Mum Rat Player 2’s Action Player 1’s Action

20  My best response to a particular play by the other player is whichever action(s) give me the highest payoff  To find Nash Equilibria…  Circle payoff from player 1’s best response to each action by his opponent  Circle payoff from player 2’s best response to each action  Any box with both payoffs circled is an equilibrium  Because each player is playing a best-response to his opponent’s action…  …so neither one can improve by changing his strategy In two-player games, we find Nash equilibria by highlighting best responses -1, -1-10, 0 0, -10-5, -5 MumRat Mum Rat Player 2’s Action Player 1’s Action

21  Another classic: Battle of the Sexes  (Story)  Circle player 1’s best responses  Circle player 2’s best responses  We find two equilibria: (ballgame, ballgame) and (opera, opera)  Game theory usually doesn’t have that much to say about which equilibrium will get played when there are more than one Some games will have more than one equilibrium 6, 30, 0 3, 6 Baseball GameOpera Baseball Game Opera Player 2’s Action Player 1’s Action

22  Growth model  (Story)  Circle player 1’s best responses  Circle player 2’s best responses  Two equilibria: (invest, invest) and (consume, consume)  Some papers explain differences in growth across countries by saying some are in “good” equilibrium and some are in “bad” one Sometimes, there will be a “good” and a “bad” equilibrium 2, 20, 1 1, 01, 1 InvestConsume Invest Consume Player 2’s Action Player 1’s Action

23  Scissors, Paper, Rock for $1  Look for Nash Equilibria by circling best responses  No square with both payoffs circled  No equilibrium where each player plays a single action  In this class, we’ll focus on games with a pure-strategy Nash equilibrium Some games don’t have any equilibrium where players only play one action 0, 01, -1 -1, 10, 0 ScissorsPaper Scissors Paper Player 2’s Action Player 1’s Action -1, 1 1, -1 Rock 1, -1-1, 1 Rock 0, 0

24  Now on to… That’s a very quick introduction to static games

25 Property Law

26 To begin, a story

27  We already saw one reason  Tragedy of Commons – overuse of land is held in common  For another example, imagine two neighboring farmers  Each has two choices: farm his own land, or steal crops from his neighbor  Stealing is less efficient than planting my own crops  Have to carry the crops from your land to mine  Might drop some along the way  Have to steal at night  move slower  If I steal your crops, I avoid the effort of planting and watering Why do we need property law in the first place?

28  Suppose that planting and watering costs 5, the crops either farmer could grow are worth 15, and stealing costs 3  With no legal system, the game has the following payoffs:  We look for equilibrium  Like Prisoner’s Dilemma  both farmers stealing is the only equilibrium  but that outcome is Pareto-dominated by both farmers farming Why do we need property law in the first place? 10, 10-5, 12 12, -50, 0 FarmSteal Farm Steal Player 2 Player 1

29  Suppose there were lots of farmers facing this same problem  They come up with an idea:  Institute some property rights  And some type of government that would punish people who steal  Setting up the system would cost something  Suppose it imposes a cost c on everyone who plays by the rules So how do we fix the problem?

30 So how do we fix the problem? 10 – c, 10 – c-5 – c, 12 – P 12 – P, -5 – c-P, -P FarmSteal Farm Steal Player 2 Player 1 10, 10-5, 12 12, -50, 0 FarmSteal Farm Steal Player 2 Player 1 MODIFIED GAMEORIGINAL GAME  If P is big, and c is not too big, then 12 – P < 10 – c  In that case, (Farm, Farm) is an equilibrium  Payoffs are (10 – c, 10 – c), instead of (0, 0) from before

31  Anarchy is inefficient  I spend time and effort stealing from you  You spend time and effort defending your property from thieves  Instead of doing productive work  Establishing property rights, and a legal process for when they’re violated, is one way around the problem So the idea here…

32  Cooter and Ulen: property is “A bundle of legal rights over resources that the owner is free to exercise and whose exercise is protected from interference by others”  Property rights are not absolute  Appendix to ch. 4 discusses different conceptions of property rights  Any system has to answer four fundamental questions:  What things can be privately owned?  What can (and can’t) an owner do with his property?  How are property rights established?  What remedies are given when property rights are violated? Overview of Property Law

33  BUT… Answers to many of these seem obvious source:

34  Take a look at Coase, “The Problem of Social Cost”  See you Wednesday Wednesday: Coase