Econ 522 Economics of Law Dan Quint Fall 2010 Lecture 3

HW1 is online (due 5 p.m. Sept 24) Also lecture notes – try View  Notes Page

 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  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 Monday, we talked about efficiency

 20 fishermen  Catch 260 – H fish per hour of fishing  Get disutility of 8 fish per hour  What would be the efficient amount to fish?  Each fisherman gets utility h(260 – H) – 8h  Total fish caught = H(260 – H), total disutility cost = 8H  Efficiency: maximize H(260 – H) – 8H = 252H – H 2  Derivative = 252 – 2H = 0, so H = 126  So efficiency requires 126 total man-hours of fishing per week  If everyone fishes same amount, that’s 126/20 = 6.3 hours/day  H = 126, so people catch 260 – 126 = 134 fish/hour  Each person’s utility is 6.3 (134) – 6.3 (8) = – 50.4 = fish/day I completely mangled the example about fishing (externalities causing inefficiency)

 20 fishermen  Catch 260 – H fish per hour of fishing  Get disutility of 8 fish per hour  What will people choose to do on their own?  Each fisherman gets utility h(260 – H) – 8h  Maximize private gain = h(260 – H) – 8h = h(260 – H – h) – 8h = 252h – Hh – h 2  Derivative = 252 – H – 2h = 0, so h = 252 – H – h = 252 – H  So everyone fishes the same amount, so H = 20h, and h = 252 – 20h or 21h = 252 or h = 12  So everyone fishes 12 hours/day  H = 240, so people catch 260 – 240 = 20 fish/hour  Each person’s utility is 12 (20) – 12 (8) = 240 – 96 = 144 fish/day I completely mangled the example about fishing (externalities causing inefficiency)

 20 fishermen  Catch 260 – H fish per hour of fishing  Get disutility of 8 fish per hour  So…  Efficient level of fishing is 6.3 hours/day for each person, giving everyone utility of fish/day  But acting in their own interest, everyone fishes 12 hours/day, giving everyone utility of 144 fish/day  The point: since fishing imposes a negative externality, people naturally do it “too much” (more than the efficient amount) I completely mangled the example about fishing (externalities causing inefficiency)

Hours fishing, per day, per fisherman Total fish caught “Maximum sustainable yield” Efficient level of fishing “Equilibrium” fishing level H (260 – H)

 Posner: yes – ex-ante, we would all have agreed to efficient laws  Analogy to lottery ticket with highest expected value  We saw an example for asymmetric situations (landlords and tenants) Next, we asked: Should efficiency be the normative goal of the law?

 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 But there are problems with efficiency as a normative goal

“The central question [in this book]… is a simple one: what set of rules and institutions maximize the size of the pie? What legal rules are economically efficient? There are at least three reasons why that is the question we ask. The first is that while economic efficiency… is not the only thing that matters to human beings, it is something that matters quite a lot to most human beings. The second reason is that there is evidence that considerable parts of the legal system we live in can be explained as tools to generate efficient outcomes… It is a lot easier to make sense out of a tool if you know what it is designed to do. A final reason is that figuring out what rules lead to… efficient outcomes is one of the things economists know how to do – and when you have a hammer, everything looks like a nail.” - Friedman, Law’s Order, p. 312 Friedman has his own take on why we should study efficiency

 Cooter and Ulen (textbook ch. 1)  Efficiency should not necessarily be the goal of society  But efficiency should be the goal of the legal system  If redistribution is desirable, it’s better to make the legal system efficient, and address distribution through taxes  Cooter and Ulen offer four reasons why the tax system is a better way to redistribute wealth than the legal system Cooter and Ulen give a more pragmatic defense of efficiency as a goal for 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

12 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 (The question I distributed Monday)

 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” So, summing up… is efficiency a good goal for the law?

14  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…

15  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…

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

17 Some basic game theory

18  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

19  (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

20 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

21  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 Dominant Strategies (skipped this in lecture) -1, -1-10, 0 0, -10-5, -5 MumRat Mum Rat Player 2’s Action Player 1’s Action

22  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…  …given what his opponent/opponents are doing Nash Equilibrium

23  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

24  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

25  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

26  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

27  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

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

29 Property Law

30  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 at all?

31  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? 10, 10-5, 12 12, -50, 0 FarmSteal Farm Steal Player 2 Player 1

32  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?

33 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

34  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…

35  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

36  BUT…  Answers to many of these seem obvious

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

38 (I doubt we’ll get to…)

39  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? One early, “classic” property law case

40  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 Pierson v. Post

41 Pierson gets the fox  simpler rule (finders keepers)  easier to implement  fewer disputes Same tradeoff we saw earlier: 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