Sarah's demand for routine medical visits is q = 10 - 0.2p when ...

[leo leo]

Sarah's demand for routine medical visits is q = 10 - 0.2p when she is healthy and q = 20 - 0.2p when she is sick. Medical visits cost 50 each if Sarah has no medical insurance. She is sick 20 of the time. Sarah is considering two different insurance plans. One offers free medical visits; the other plan costs less up front but requires that Sarah pay 5 per medical visit. Compare the two plans in terms of the trade-off between risk and moral hazard.
 
  What will be an ideal response?

Question 2

Sam hires an attorney to present a court case. If Sam wins the case, he will receive some money. This payoff is a function of the attorney's hours and which judge is assigned the case that day. Judge A is very understanding toward people in Sam's position, but judge B is very harsh toward people like Sam. Is it possible for Sam to get the attorney to deliver the optimal amount of effort and make the attorney bear all of the risk?
 
  What will be an ideal response?

[dawsa925]

Answer to Question 1

At 50 per visit, Sarah makes no visits when she is healthy and 10 visits when she is sick. Under the first plan, she makes 10 visits when she is healthy and 20 visits when she is sick. Thus, Sarah will make 10 more visits with the first insurance plan. Under the second plan, Sarah makes 9 visits when she is healthy and 19 visits when she is sick. The moral hazard is greater (by one visit) under the first plan. Under the first plan, Sarah's risk is zero. She pays only the up-front premium regardless of her health. Under the second plan she will make (0.8  9 ) + (0.2  19 ) = 11 visits at 5 each. Her risk, as measured by the variance of her expenditures, is (0.8  100 ) + (0.2  1600 ) = 400. Thus, the second plan is riskier for her but generates less of a moral hazard on her part.

Answer to Question 2

Yes. If Sam accepts a fixed payment from the attorney and lets the attorney keep the proceeds, if any, from the case, the attorney bears all of the risk. Since the attorney will enjoy the full marginal benefit of her effort, she puts in the optimal level of effort.