Question

1. Bob does not have insurance. When Bob is sick his income is IS=$0. When Bob is healthy his income is IH=$40,000. Bob’s probability of getting sick is p=0.25.

a.) What is Bob’s expected income without insurance?

b.) Plot Bob’s IS, IH, and E[I] in the “Utility-Income” space and in the “IS-IH” space. Label all aspects of the graphs, including the coordinates of all important points.

c.) What is the slope of Bob’s Zero-Profit Line?

2. Assume Bob is offered an insurance contract (A) that will give him an income if IS A=$10,000 if he gets sick, and an income of IH A=$30,000 if he stays healthy. Bob’s probability of getting sick is still p=0.25.

a.) What is Bob’s expected income with this insurance contract?

b.) Redraw your graphs from the question #1. Add to the new graphs the appropriate dots to capture IS A and IH A under contract A.

c.) Given what you know about Bob from question #1, is contract A full or partial? How do you know?

d.) Given what you know about Bob from question #1, is contract A fair or unfair? How do you know?

Answer 1

Solution-1)

a) Bob’s expected income without insurance: 40,000 (1-0.25) = 40,000 * 0.75 = 30,000

b) Enclosed Graph-1

c) As depicted on graph the slope changes with P. It has a flatter slope for sicker person with higher P.

Solution-2)

a) When sick = ($10,000 * 0.25) = $2,500

When healthy = ($30,000 * 0.75) = $ 22,500

b) Enclosed Graph-2

c) It was partial contract because it included some and not contained all terms of agreement for their contract. For example, Bob had no insurance coverage

d) The contract seems to be unfair. The reason is that the some rights have been curtailed such as insurance coverage

GRAPH-1 GRAPH-2 Actual MPR Actual MPR Medication gap Medication gap 0 50 100 150 200 250 300 350 100 150 200 250 300 350