Econ 522 Economics of Law

Econ 522Economics of Law Dan Quint Spring 2010 Lecture 3

Lecture notes are onlineView  Notes Page to see slide and my notes

Monday, we talked about efficiency • Efficiency: “no available Kaldor-Hicks improvements” • roughly, maximizing total value, or total surplus, or total payoffs, to everyone in society • but translating everything into dollars, so we can add/compare across people • Should efficiency be the normative goal of the law? • Posner: yes, we would all have agreed to efficient laws ex-ante • analogy to lottery ticket with highest expected value • for asymmetric situations…

Example: why everyone might want efficient laws even with asymmetries • Two possible laws: landlords pay heat, tenants pay heat • If tenants pay heat, it costs $50 a month • If landlords pay heat, tenants will run heater all day – costs $100 a month, makes tenants $10 happier • Suppose currently, tenants pay heat, tenants get value $650 from apartment (with heat), landlord faces costs of $400, rent is $500 • Switch to landlords paying heat: tenants costs go down $50, landlord costs go up $100, suppose rent goes up $75 • Both sides are worse off with switch to inefficient law! Tenants pay heat Landlords pay heat Tenants payoff 650 – 500 – 50 = 100 660 – 575 = 85 Landlords payoff 500 – 400 = 100 575 – 100 – 400 = 75

But there are problems with efficiency as a normative goal • Ignores distribution of wealth • Doesn’t consider procedural fairness • Auctioning off last seats for this class • Value is equated with willingness to pay • I need a heart transplant, someone else is willing to pay more to use heart as decoration

Cooter and Ulen gave a more pragmatic defense of efficiency as goal of law • If we’re worried about distribution of wealth… • it’s better to have legal system achieve efficiency, • and handle distribution through tax system • Multiple reasons why tax system is a better way to redistribute wealth • Redistribution through laws would be like “narrowly-targeted taxes” on particular activities… • …but narrow taxes are worse than broad taxes

To make this last point, an example(The question I distributed Monday) 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? 6

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 8

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

Dominant Strategies • In the Prisoner’s Dilemma, one player’s best action is the same, regardless of what his opponent does • This is called a dominant strategy • Regardless of what he thinks 2 will do, 1 would rather play Rat Player 2’s Action Mum Rat -1, -1 -10, 0 Mum Player 1’s Action 0, -10 -5, -5 Rat

Nash Equilibrium • In most games, players won’t have a single move that’s always best • 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

Why do we need property law at all? • In a sense, same question as, why do we prefer organized society of any sort to anarchy? • Suppose there are two neighboring farmers • Each can either 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? • 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… • http://www.msnbc.msn.com/id/21088150/

One early, “classic” property law case • Pierson v. Post (NY Supreme Court, 1805) • Post organized a fox hunt, was chasing a fox • Pierson appeared “out of nowhere,” killed the fox, took it • Post sued to get the fox back • Lower court sided with Post; Pierson appealed to NY Sup Ct • Both were wealthy, pursued the case on principle or out of spite • Question: when do you own an animal?

Pierson v. Post • Court ruled for Pierson (the one who killed the fox) • “If the first seeing, starting, or pursuing such animals… should afford the basis of actions against others for intercepting and killing them, it would prove a fertile source of quarrels and litigation” • (Also: just because an action is “uncourteous or unkind” does not make it illegal) • Dissenting opinion: a fox is a “wild and noxious beast,” and killing foxes is “meritorious and of public benefit” • Post should own the fox, in order to encourage fox hunting

Same tradeoff we saw earlier: Pierson gets the fox • simpler rule (finders keepers) • easier to implement • fewer disputes Post gets the fox • more efficient incentives • (stronger incentive to pursue animals that may be hard to catch) • Just like Fast Fish/Loose Fish vs Iron Holds The Whale • Fast Fish/Loose Fish is the simpler rule, leads to fewer disputes • Iron Holds the Whale is more complicated, but is necessary with whales where hunting them the old-fashioned way is too dangerous

Monday: Coase • Please see me if you’re not yet registered • Take a look at Coase and Demsetz papers • Have a good weekend

Econ 522 Economics of Law