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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.

- asset, income and wealth distributions;

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.

- asset, income and wealth distributions;

Effects of Laws

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

- incentives for illegal behavior;

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.

- incentives for illegal behavior;

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

B(x)

C(x), higher, but

same MC

C(x), low MC

No change to illegal activity level.

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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