4 Tackle the following.

Two players: The employee (Raquel) and the employer (Vera). Raquel has to choose whether to pursue training that costs 1, 000 to herself or not. Vera has to decide whether to pay a fixed wage of 10, 000 to Raquel or share the revenues of the enterprise 50:50 with Raquel. The output is positively affected by both training and revenue sharing. Indeed, with no training and a fixed wage total output is 20, 000, while if either training or profit sharing is implemented the output rises to 22, 000. If both training and revenue sharing are implemented the output is 25, 000. 1. Construct the pay-off matrix 2. Is there any equilibrium in dominant strategies? 3. Can you find the solution of the game with Iterated Elimination of Dominated Strategies? 4. Is there any Nash equilibrium?

Firms Alpha and Beta serve the same market. They have constant average costs of 2 per unit. The firms can choose either a high price (10) or a low price (5) for their output. When both firms set a high price, total demand = 10,000 units which is split evenly between the two firms. When both set a low price, total demand is 18,000, which is again split evenly. If one firm sets a low price and the second a high price, the low priced firm sells 15,000 units, the high priced firm only 2,000 units. Analyze the pricing decisions of the two firms as a non-co-operative game. 1. In the normal from representation, construct the pay-off matrix, where the elements of each cell of the matrix are the two firms' profits. 2. Derive the equilibrium set of strategies. 3. Explain why this is an example of the prisoners' dilemma game.

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.