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.

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 nine 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.