Adverse Selection, numerical example. In the Shire, every hobbit has an income o

Question

Adverse Selection, numerical example. In the Shire, every hobbit has an income of 10 each year and a utility function represented by U (I) = I 0.05I2. Hobbits occasionally get sick, and when they do, they go to the hospital and are made immediately better. A hospital visit costs 8. There are three types of hobbits and each has a different probability of getting sick (types cannot be changed):

d.) A private health plan, Green Cross, is set up. After the 1st year of operation, Green Cross finds they have lost money. Why? They commission a study to discover the probability that a member of Green Cross gets sick. What is the probability? They fix a new actuarial fair premium based on their study. What is the new rate?

e.) Who joins the plan in the 2nd year? Why? Is the plan sustainable?

f.) What will the eventual equilibrium be? Who will buy insurance and how much will it cost under the sustainable plan?

g.) Would an individual mandate to buy insurance make the hobbits better or worse off relative to a world with no individual mandate?

Explanation / Answer

Marginal analysis is an important decision-making tool in the business world. Marginal analysis allows business owners to measure the additional benefits of one production activity versus its costs. This analysis can help an owner understand whether an activity is profitable and thus make a decision based on that information.

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