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, , so as to avoid damaging a risk-neutral "plaintiff." The damages to the plaintiff are . Obviously, , since exerting care decreases the damage done. For simplicity assume that:
- (i) the function is known by all parties in advance of any action, and
- (ii) the level of care is observable by all parties.
After the defendant chooses , the plantiff suffers damages and can file a lawsuit to recover those damages. In order to pursue the suit, the plaintiff spends on lawyer's fees. The probability of winning the case is where , since better legal preparation confers a higher chance of winning, and , since there are decreasing returns to legal preparation. If she loses, she has to pay and does not recover anything. If the plaintiff wins the case, then she recovers but has to pay taxes on the compensation, so she wins net of taxes. (The plaintiff does not directly recover legal fees, , 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 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 exerted by potential defendants.