Econ 522 Economics of Law

Econ 522Economics of Law Dan Quint Fall 2011 Lecture 3

HW1 is online (due 11:59 p.m. Thurs Sept 22)Also lecture notes – try View  Notes Page

Monday, we defined efficiency • Efficiency: “make all available Kaldor-Hicks improvements” • roughly, maximizing total value, or total surplus, or total payoffs, to everyone in society… • …where everything is translated into dollars, so we can 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

And we discussed some forces that lead to inefficiency • 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 asked: Should efficiency be the normative goal of the law? • 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

Discussion question • 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?

A nice blog post about why policy evaluation should at least start with efficiency… 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 http://www.thebigquestions.com/2010/08/30/efficiency-experts

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

To make this last point, an example Two goods: beer (x), pizza (y) One consumer, with $60 and utility u(x,y) = x0.5 y0.5 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) = 300.5 300.5 = 30 c. Calculate demand and utility with $0.50 tax on beer. (x,y) = (20, 30) u(x,y) = 200.5 300.5 = 6000.5» 24.49 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) = 250.5 250.5 = 25 f. How much revenue does $0.20 tax on both goods raise? 25 X $0.20 + 25 X $0.20 = $10 g. Which is the better way to raise revenue? 8

Summing up… is efficiency a good goal for the law? • 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”

Before we move on, a quick digression… • 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… • 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 11

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

Some basicgame theory

A brief introduction to game theory • Today, we focus on static games • Also known as simultaneous-move games • A static game is completely described by three things: • Who the playersare • 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 classic example: the Prisoner’s Dilemma • (Story) • Players: player 1 and player 2 • Two actions available to each player: rat on the other, or keep mum • Payoffs: • u1(mum, mum) = -1 • u1(rat, mum) = 0 • u1(mum, rat) = -10 • u1(rat,rat) = -5 • Same for player 2

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

Nash Equilibrium • 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… • …givenwhat his opponent/opponents are doing

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

In two-player games, we find Nash equilibria by highlighting best responses • 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’sbest response to each action by his opponent • Circle payoff from player 2’sbest response to each action • Any box with both payoffscircled is an equilibrium • Because each player is playinga best-response to his opponent’s action… • …so neither one can improve by changing his strategy Player 2’s Action Mum Rat -1, -1 -10, 0 Mum Player 1’s Action 0, -10 -5, -5 Rat

Some games will have more than one equilibrium • Another classic: Battle of the Sexes • (Story) • Circle player 1’sbest responses • Circle player 2’sbest 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 Player 2’s Action Baseball Game Opera 6, 3 0, 0 BaseballGame Player 1’s Action 0, 0 3, 6 Opera

Sometimes, there will be a “good” and a “bad” equilibrium • Growth model • (Story) • Circle player 1’sbest responses • Circle player 2’sbest 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 Player 2’s Action Invest Consume 2, 2 0, 1 Invest Player 1’s Action 1, 0 1, 1 Consume

Some games don’t have any equilibrium where players only play one action • 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-strategyNash equilibrium Player 2’s Action Scissors Paper Rock 0, 0 1, -1 -1, 1 Scissors -1, 1 0, 0 1, -1 Player 1’s Action Paper 1, -1 -1, 1 0, 0 Rock

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

Property Law

To begin, a story

Why do we need property law in the first place? • 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 26

Why do we need property law in the first place? • 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 Player 2 Farm Steal 10, 10 -5, 12 Farm Player 1 12, -5 0, 0 Steal

So how do we fix the problem? • 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? ORIGINAL GAME MODIFIED GAME Player 2 Player 2 Farm Steal Farm Steal 10, 10 -5, 12 10 – c, 10 – c -5 – c, 12 – P Farm Farm Player 1 Player 1 12, -5 0, 0 12 – P, -5 – c -P, -P Steal Steal • 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

So the idea here… • 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

Overview of Property Law • 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?

Answers to many of these seem obvious • BUT… source: http://www.msnbc.msn.com/id/21088150/

Monday: Coase • Please see me if you’re not yet registered • Take a look at Coase, “The Problem of Social Cost” • Have a good weekend

Econ 522 Economics of Law