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### Chapter Thirty-Three

Law and Economics

Effects of Laws

- Property right assignments affect
- asset, income and wealth distributions;
- e.g. nationalized vs. privately owned industry.

Effects of Laws

- Property right assignments affect
- asset, income and wealth distributions;
- e.g. nationalized vs. privately owned industry.
- resource allocations;
- e.g. the tragedy of the commons
- e.g. patents encourage research.

Effects of Laws

- Punishments affect
- incentives for illegal behavior;
- e.g. high speeding fines can reduce the amount of speeding.

Effects of Laws

- Punishments affect
- incentives for illegal behavior;
- e.g. high speeding fines can reduce the amount of speeding.
- asset, income and wealth distributions;
- e.g. jail time results in lost income.

Crime and Punishment

- x is the quantity of an illegal activity produced by an individual.
- C(x) is the production cost.
- B(x) is the benefit.
- Gain is B(x) - C(x).
- What is the rational choice of x?

Crime and Punishment

First-order condition is

Notice that marginal costs matter more than

do total costs.

Crime and Punishment

- Detection of a criminal is uncertain.
- e is police effort.
- (e) is detection probability; (e) = 0 if e = 0 (e) as e .

Crime and Punishment

- Given e, the criminal’s problem is

Crime and Punishment

- Given e, the criminal’s problem is
- First-order condition is

Crime and Punishment

- Given e, the criminal’s problem is
- First-order condition is
- Low e low (e) low marg. cost.
- High e high (e) high marg. cost.

Crime and Punishment

- Higher fines and larger police effort both raise marginal production costs of illegal activity.
- Which is better for society -- higher fines, or more police effort?

Crime and Punishment

- Higher fines and larger police effort both raise marginal production costs of illegal activity.
- Which is better for society -- higher fines, or more police effort?
- Police effort consumes resources; higher fines do not.
- Better to fine heavily.

Liability Law

- An injurer, IN, and a victim, V.
- x is effort by IN to avoid injuring V.
- cIN(x) is IN’s cost of effort x; cIN(x) as x .
- L(x) is V’s loss when IN’s effort is x; L(x) as x .

Liability Law

- Society wishes to minimize total cost; i.e.

Liability Law

- Society wishes to minimize total cost; i.e.
- Social optimality requires
- I.e. IN’s private marginal cost of effort equals marginal benefit of her extra effort.

Liability Law

- Liability rules:
- no liability rule
- strict liability rule
- negligence rule.
- Which is best?

Liability Law

- No Liability Rule:
- IN faces only private cost, cIN(x).
- Hence chooses effort level
- No liability results in suboptimal low care level and excessive injury.

Liability Law

- Full Liability Rule:
- IN faces private cost and V’s costs, cIN(x) + L(x).
- Hence chooses the socially optimal effort level where

Liability Law

- Negligence Rule: IN is liable for V’s loss if and only if care effort level , a legally determined effort level.

Liability Law

- Negligence Rule: IN is liable for V’s loss if and only if care effort level , a legally determined effort level.
- What if the court sets , the socially optimal effort level?

Liability Law

- So full liability for IN; hence she chooses

Liability Law

- So full liability for IN; hence she chooses
- And no liability for IN; hence she chooses

Liability Law

- So full liability for IN; hence she chooses
- And no liability for IN; hence she chooses
- I.e. the negligence rule is socially optimal when

Liability Law

- Both full liability and negligence rules are socially optimal, but
- full liability fully insures V always, and
- the negligence rule fully insures V only if IN’s care effort level .

Liability Law

- Both full liability and negligence rules are socially optimal, but
- full liability fully insures V always, and
- the negligence rule fully insures V only if IN’s care effort level .
- Victims prefer full liability; injurers prefer the negligence rule.

Bilateral Accidents

- V and IN can each exert effort to avoid a loss.
- cV(xV) and cIN(xIN).
- Loss is L(xV,xIN).
- Society wishes to

Bilateral Accidents

- Society wishes to
- Social optimality requires V’s MC of effort = MB of his effort IN’s MC of effort = MB of her effort.
- I.e.

Bilateral Accidents

- No Liability: Both V and IN face only their private effort costs, not the full social costs of their actions.

Bilateral Accidents

- No Liability: Both V and IN face only their private effort costs, not the full social costs of their actions.
- Hence V and IN both provide too little effort.
- No liability is socially suboptimal.

Bilateral Accidents

- Full Liability: V is fully compensated for all injury costs.

Bilateral Accidents

- Full Liability: V is fully compensated for all injury costs.
- Hence V chooses
- Full liability is socially suboptimal in bilateral accidents.

Bilateral Accidents

- Strict Division of Losses: IN must pay a fixed fraction, f, of loss caused.
- IN minimizes
- IN chooses effort satisfying

Bilateral Accidents

- IN chooses effort satisfying
- Optimality requires
- Since f < 1, IN chooses less than the optimal effort level;

Bilateral Accidents

- IN chooses effort satisfying
- Optimality requires
- Since f < 1, IN chooses less than the optimal effort level;
- Strict division of losses is a socially suboptimal liability rule.

Bilateral Accidents

- Negligence Rule: IN is fully liable for loss only if her effort level , a legally determined effort level.
- Social optimality requires V and IN to choose effort levels

and

, where

and

Bilateral Accidents

- Suppose V chooses
- Then IN is fully liable and wishes to
- I.e. IN chooses

Bilateral Accidents

- Now suppose IN chooses
- Then V wishes to
- I.e. V chooses

Bilateral Accidents

- Now suppose IN chooses
- Then V wishes to
- I.e. V chooses
- The Nash equilibrium of the negligence rule game is the socially optimal outcome.

Bilateral Accidents

- Strict Liability with Defense of Contributory Negligence Rule: IN is fully liable unless V’s care level is less than a specified level

Bilateral Accidents

- IN is fully liable unless V’s care level is less than a specified level
- If society chooses and V chooses , then IN is fully liable, so her best reply is

Bilateral Accidents

- IN is fully liable unless V’s care level is less than a specified level
- If society chooses and V chooses , then IN is fully liable, so her best reply is
- If IN chooses , then V’s best reply is

Bilateral Accidents

- IN is fully liable unless V’s care level is less than a specified level
- If society chooses and V chooses , then IN is fully liable, so her best reply is
- If IN chooses , then V’s best reply is
- I.e. the rule causes a socially optimal Nash equilibrium.

Bilateral Accidents

- Notes:
- socially optimal liability rules do not generally fully compensate the victim.
- socially optimal accident deterrence is distinct from optimal accident compensation.

Treble Damages & Antitrust Law

- The Sherman and Clayton Acts allow an agent damaged by price-fixing to sue and recover treble damages.
- How does such a penalty affect the behavior of a price-fixing cartel?

Treble Damages & Antitrust Law

- Assume firms collude to form a cartel with a constant marginal production cost,
- Market demand is

Treble Damages & Antitrust Law

- Assume firms collude to form a cartel with a constant marginal production cost,
- Market demand is
- Cartel’s goal is

Treble Damages & Antitrust Law

- Assume firms collude to form a cartel with a constant marginal production cost,
- Market demand is
- Cartel’s goal is
- Solution is

Treble Damages & Antitrust Law

- Suppose fixing price at results in damages to a victim V.
- V’s probability of winning suit against the cartel is
- If V wins, the cartel must pay

Treble Damages & Antitrust Law

- Suppose fixing price at results in damages to a victim V.
- V’s probability of winning suit against the cartel is
- If V wins, the cartel must pay
- Cartel’s problem is now

Treble Damages & Antitrust Law

- Cartel’s problem is now
- Solution is not generally the same as for the original problem
- So generally cartel behavior is affected by the penalty.

Treble Damages & Antitrust Law

- Special case -- suppose is the cartel’s profit. The cartel’s goal is

Treble Damages & Antitrust Law

- Special case -- suppose is the cartel’s profit. The cartel’s goal is
- Maximizing after-penalty profit requires maximizing before-penalty profit.

Treble Damages & Antitrust Law

- Special case -- suppose is the cartel’s profit. The cartel’s goal is
- Maximizing after-penalty profit requires maximizing before-penalty profit.
- The cartel’s behavior is unaffected by the penalty.

Treble Damages & Antitrust Law

- What if consumers can seek to be damaged?

Treble Damages & Antitrust Law

- What if consumers can seek to be damaged?
- Suppose consumer utility is quasi-linear;
- Consumer can win damages
- So consumer’s goal is

Treble Damages & Antitrust Law

- Consumer’s goal is
- I.e.

Treble Damages & Antitrust Law

- Consumer’s goal is
- I.e.

Treble Damages & Antitrust Law

- Consumer’s goal is
- Since consumer’s action depends upon the effective price, rewrite the cartel’s problem as

Treble Damages & Antitrust Law

- Consumer’s goal is
- Since consumer’s action depends upon the effective price, rewrite the cartel’s problem as
- Solution is the sameas the original problem;

Treble Damages & Antitrust Law

- Solution is the same as the original problem;
- is the price paid by buyers. Then

Treble Damages & Antitrust Law

- Solution is the same as the original problem;
- is the price paid by buyers. Then
- So

Treble Damages & Antitrust Law

- The cartel’s price , the price set in the absence of damage penalties.
- But the effective price to both consumers and the cartel is the same as in the no damages case.

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