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Question from Past Microeconomics Qualifying ExamEdit

Fall 2000 - Section II, Question two, George Mason University Consider a simple model of torts. A risk-neutral "defendant" is in a position to exert care,  c , so as to avoid damaging a risk-neutral "plaintiff." The damages to the plaintiff are  D(c) . Obviously,  D'(c)<0 , since exerting care decreases the damage done. For simplicity assume that:

  • (i) the function  D(c) is known by all parties in advance of any action, and
  • (ii) the level of care  c is observable by all parties.

After the defendant chooses  c , the plantiff suffers damages  D(C) and can file a lawsuit to recover those damages. In order to pursue the suit, the plaintiff spends  f on lawyer's fees. The probability of winning the case is  p(f) where  p'(f)>0 , since better legal preparation confers a higher chance of winning, and  p''(f)<0 , since there are decreasing returns to legal preparation. If she loses, she has to pay  f and does not recover anything. If the plaintiff wins the case, then she recovers  D(c) but has to pay taxes  t on the compensation, so she wins  D(c)(1-t) net of taxes. (The plaintiff does not directly recover legal fees,  f , if she wins.)

  • a. Characterize the plaintiff's optimal expenditure on legal fees. Clearly label the plaintiff's choices, objective, and constrains. Explain the meaning of any relevant first-order conditions. (Hint: Risk-neutrality means that you don't need to use a utility function, so you can restrict attention to the money involved).
  • b. Suppose the government increases the tax rate  t Determine the effect that this has on how much the plaintiff spends on legal fees. (Use comparative statistics if you can).
  • c. Briefly model and comment on the effect of a tax increase on the care  c exerted by potential defendants.

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