7 economics

Mark wants to maximize his expected utility. His preferences are represented by the utility function U(y) = y 1 2 where y is a monetary payoff. Mark is offered the following bet on the toss of a coin by Amanda; If the coin comes up tails Amanda pays Mark 1, 000 If the coin comes up heads Mark pays Amanda 1, 000 Mark's initial capital is 10, 000 which he retains in its entirety if he does not take the bet. 1. What is Mark's expected utility if he accepts the bet? 2. Will he accept the bet? Explain your answer. 3. Is Mark risk averse, risk neutral or risk loving? Explain your answer.

Amanda offers Mark an alternative bet whereby if the coin comes up tails Amanda gives him 10, 000 but if the coin comes up heads Mark gives Amanda his entire 10, 000. 4. Show that Mark does not accept this bet. Amanda offers Mark yet another alternative bet whereby Mark still loses his entire 10, 000 if the coin comes up heads, but if the coin comes up tails Amanda pays him50, 000. 5. Does Mark accept this new alternative? Explain your answer. 6. Given that Mark loses his entire10, 000 if the coin comes up heads, what is the smallest amount that Amanda has to pay Mark in the event of tails in order to persuade him to take the bet?

The local government wants to hire a manager to undertake a public project. If the project fails, it will lose 20, 000. If it succeeds, the project will earn 100, 000. The manager can choose to "work" or to "shirk". If she shirks, the project will fail for sure. If she works, the project will succeed half of the times but will still fail half of the times. Measured in monetary terms, the manager's utility is 10, 000 lower if she works than if she shirks. In addition, the manager could earn 10, 000 in another job (where she would shirk). Assume further that both parties are risk neutral. 1. Describe the dynamic game using the extensive form representation. 2. Which is the compensation scheme that maximizes government's utility? Which is the expected wage of the manager in any equilibrium of the game? 3. Do you think the solution will change with a risk-averse manager? 4. Assume that the government prefers to sell the project to the manager. What should be the fee paid to the government?

Discuss the trade-off between insurance and incentives in the presence of moral hazard when the agent is risk-averse. Do you think it is true that a risk-neutral principal should pay more to hire a risk-averse agent than a risk neutral agent? Explain your answer.

Consider the market for health insurance. Suppose that the market is comprised of 4 groups of people of differing risk categories. There are a large and equal number of people in each group, but insurers cannot tell which group a person belongs to (i.e. this is a situation of asymmetric information). Each group faces a risk of requiring medical treatment of value $10,000. Suppose that the willingness to pay of people in each group is as follows: Risk 0.2 0.4 0.6 0.8 willingness to pay 2,500 5,200 6,800 8,500 Actuarially fair premium Risk Premium a. Complete the table of actuarially fair insurance premiums that could be charged to each group separately by an insurance company large enough to diversify the risks. How do these compare to the willingness to pay? b. Suppose now that the risk category is private information. What is the average riskiness of a person seeking insurance? What premium would an insurance company have to charge to break even? c. Will all the agents participate at this price? If not what would be the composition of risks facing the insurer? Would the premium found above be sufficient to cover the risks taken by the insurer? d. Continue with this logic. What will be the price of insurance in the equilibrium and which groups will participate? e. Is this an efficient outcome?

Are the following statements true or false? a. An insurance company must be concerned about the possibility that someone will buy fire insurance on a building and then set fire to it. This is an example of moral hazard. b. A life insurance company must be concerned about the possibility that the people who buy life insurance may tend to be less healthy than those who do not. This is an example of adverse selection. c. In a market where there is separating equilibrium, different types of agents make different choices of actions. d. Moral hazard refers to the effect of an insurance policy on the incentives of individuals to exercise care. e. Adverse selection refers to how the magnitude of the insurance premium affects the types of individuals that buy insurance.

b) Assume an actuarial fair insurance is charged, and that each type is risk neutral and hence only values health care spending at its expected cost to the health plan

What will happen if the health plan offers to insure the full population at the actuarially fair premium and consumers are allowed to not buy insurance? What will be the market equilibrium if only full insurance is allowed.

c) Now assume that consumers are risk averse, and are willing to pay 50% more than the expected value of their expected health insurance cost as the premium. Calculate the willingness to pay for insurance for each of these three types of consumers.

What happens in this scenario if a health plan attempts to offer insurance at an actuarially fair premium? What is the equilibrium.

d) Now assume that in addition to having risk averse consumers, there are administrative costs equal to 20% of the expected costs. (This is a typical rate for small plans in the US.) In this scenario, the health plan is not willing to offer actuarially fair insurance, but instead will add these costs onto the premium offer. Note that this administrative cost/profit does not affect the value of the insurance to consumers, only affects premiums.

What happens in this scenario with risk averse consumers? What is the equilibrium.

e) Continuing to assume administrative costs, how much of a penalty (or tax) on those not buying insurance will the government have to charge in order to make all three of the risk averse groups willing to buy insurance and result in an equilibrium in which everyone is insured?

f) Comment on how this problem is related to the uninsurance problem in the US?

The faculty at the Smith School have started sharing their business contacts with the administration and students to help in recruiting efforts. The hope is that these business contacts will provide job leads for students, potential students for the school and possibly donations to the school. The new dean of the Office of Career Management (OCM) surveyed MBA students, undergraduates, and administration officials to determine how much value they place on these faculty contacts. These three groups represents all the members of the Smith School who receive any value from these contacts. The survey revealed that full-time MBA students (as a whole) valued the senior faculty contacts at $100 each and the junior faculty contacts at $50 each. Senior faculty contacts are often higher up in an organization and thus potentially more valuable to students and administrators. The undergraduate students (as a whole) valued both junior and senior faculty contacts at $50 each. Finally, administrators (as a whole) valued senior faculty contacts at $50 each and junior faculty contacts at $30 each. The total number of senior faculty contacts available is 100. The total number of junior faculty contacts available is 50. The Smith School plans to make these contacts available to students and administrators at no charge.

a. Draw a demand curve combining the demand curves of each of the three sets of consumers for all 150 contacts.

b. Faculty claim that the opportunity cost of providing this contact information is $160 per contact. If faculty are paid $160 to provide these contacts, how many contacts should the Smith School purchase? N

c. Suppose the administration asks for contributions from students who make use of the contacts in order to raise the money paid to faculty. Will enough money be collected to generate the optimal number of contacts? Explain.

d. The companies that comprise the faculty contacts also value the distribution of their employee names to students. In the past this form of networking has been beneficial in finding the best new employees. These companies place a value of $50 on the distribution of each senior and junior faculty contact. Will the Smith School change the number of contacts it purchases given this new information? Explain.

e. If the companies offered to contribute $25 per contact distributed by the Smith School, would this change your answer to part d? Explain.