A woman plans to divorce her philandering husband. If she can prove he cheated on her, she will receive a $500,000 cash settlement. If she cannot, her settlement will be $250,000. Her lawyer offers to take the case and presents her with the following payment options: a $100,000 flat fee, or 1/3 of the settlement. He promises to hire a private detective (at a cost of $25,000) to prove infidelity, at the lawyer's own expense, but the client is not sure whether to trust the lawyer. If hired, the detective will be certain to provide proof of adultery.
a. Suppose the woman agrees to the flat-fee plan. What can the woman expect to receive if the lawyer hires a detective? What if he doesn't? What can the lawyer expect to receive in either case? Explain the associated principal - agent problem. Who is the principal? Who is the agent?
b. Determine the rewards to both the woman and the lawyer of hiring a detective under the settlement plan whereby the woman must pay 1/3 of her settlement to the lawyer. What happens to the principal - agent problem if the woman chooses this plan?