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Chapter Thirty-Three Law and Economics

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Effects of Laws u Property right assignments affect –asset, income and wealth distributions; v e.g. nationalized vs. privately owned industry.

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

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Effects of Laws u Punishments affect –incentives for illegal behavior; v e.g. high speeding fines can reduce the amount of speeding.

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

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

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Crime and Punishment First-order condition is Notice that marginal costs matter more than do total costs.

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Crime and Punishment B(x) C(x), low MC

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Crime and Punishment B(x) C(x), low MC C(x), higher, but same MC No change to illegal activity level.

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Crime and Punishment B(x) C(x), low MC

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Crime and Punishment B(x) C(x), low MC C(x), high MC Higher marginal costs deter crime.

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Crime and Punishment u Detection of a criminal is uncertain. u e is police effort. u (e) is detection probability; (e) = 0 if e = 0 (e) as e .

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Crime and Punishment u Given e, the criminal’s problem is

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Crime and Punishment u Given e, the criminal’s problem is u First-order condition is

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

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Crime and Punishment B(x) Higher police effort deters crime.

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

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

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

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Liability Law u Society wishes to minimize total cost; i.e.

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

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Liability Law u Liability rules: –no liability rule –strict liability rule –negligence rule. u Which is best?

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

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

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

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

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Liability Law u So full liability for IN; hence she chooses

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Liability Law u So full liability for IN; hence she chooses u And no liability for IN; hence she chooses

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

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

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

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Bilateral Accidents u V and IN can each exert effort to avoid a loss. u c V (x V ) and c IN (x IN ). u Loss is L(x V,x IN ). u Society wishes to

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

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

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

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Bilateral Accidents u Full Liability: V is fully compensated for all injury costs.

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

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

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

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

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

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Bilateral Accidents u Suppose V chooses u Then IN is fully liable and wishes to u I.e. IN chooses

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Bilateral Accidents u Now suppose IN chooses u Then V wishes to u I.e. V chooses

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

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

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

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

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

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

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

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Treble Damages & Antitrust Law u Assume firms collude to form a cartel with a constant marginal production cost, u Market demand is

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Treble Damages & Antitrust Law u Assume firms collude to form a cartel with a constant marginal production cost, u Market demand is u Cartel’s goal is

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Treble Damages & Antitrust Law u Assume firms collude to form a cartel with a constant marginal production cost, u Market demand is u Cartel’s goal is u Solution is

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Treble Damages & Antitrust Law u Suppose fixing price at results in damages to a victim V. u V’s probability of winning suit against the cartel is u If V wins, the cartel must pay

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

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Treble Damages & Antitrust Law u Cartel’s problem is now u Solution is not generally the same as for the original problem u So generally cartel behavior is affected by the penalty.

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Treble Damages & Antitrust Law u Special case -- suppose is the cartel’s profit. The cartel’s goal is

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Treble Damages & Antitrust Law u Special case -- suppose is the cartel’s profit. The cartel’s goal is u Maximizing after-penalty profit requires maximizing before-penalty profit.

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Treble Damages & Antitrust Law u Special case -- suppose is the cartel’s profit. The cartel’s goal is u Maximizing after-penalty profit requires maximizing before-penalty profit. u The cartel’s behavior is unaffected by the penalty.

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Treble Damages & Antitrust Law u What if consumers can seek to be damaged?

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

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Treble Damages & Antitrust Law u Consumer’s goal is u I.e.

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Treble Damages & Antitrust Law u Consumer’s goal is u I.e.

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Treble Damages & Antitrust Law u Consumer’s goal is u Since consumer’s action depends upon the effective price, rewrite the cartel’s problem as

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Treble Damages & Antitrust Law u Consumer’s goal is u Since consumer’s action depends upon the effective price, rewrite the cartel’s problem as u Solution is the same as the original problem;

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Treble Damages & Antitrust Law u Solution is the same as the original problem; u is the price paid by buyers. Then

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Treble Damages & Antitrust Law u Solution is the same as the original problem; u is the price paid by buyers. Then u So

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Treble Damages & Antitrust Law u The cartel’s price, the price set in the absence of damage penalties. u But the effective price to both consumers and the cartel is the same as in the no damages case.

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