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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.