PLCY 289 First Test Spring 2006

Please answer all questions in a blue book. Use graphs and equations whenever possible. Points will only be given if answers are accompanied by appropriate explanations. The test is given under the guidelines of the UNC Honor Code. You have 2 hours and may use a calculator.

Part I: Explain whether each of the following statements is true, false, or uncertain. The amount of credit you receive will entirely depend on your explanation. [approximately 90 minutes]

  1. Legal trading of food stamps is more efficient and should therefore be permitted.
  2. To induce a minimum amount of consumption of a public good P*, a block grant with maintenance of effort is cheaper than a matching grant with maintenance of effort.
  3. The ‘tax back rule’ in a welfare program reduces the incentive for beneficiaries to work. Reducing this rate will thus increase the number of hours worked among the beneficiary population.
  4. The household production model of economic behavior predicts that the elasticity of labor supply with respect to own wage will be higher for men than for women.
  5. In the market for insurance with two different types (high risk and low risk), a policy that caters only to the high risk may also be purchased by the low risk types, leading to a ‘pooling’ equilibrium.
  6. An upward sloping demand curve for leisure is consistent with utility maximizing behavior only if leisure is an inferior good.

Part II: Long problem [approximately 30 minutes]

  1. Suppose an agent has the utility function U = [(w)1/2 - e], where e can assume the level 0 or 1, and the agent’s reservation utility is 3. The principal is risk neutral. Denote the agent’s wage conditional on output as WL if output is 0 and WH if output is 100. Only the agent observes effort; there is only one principal but many agents. The table below shows the outputs.
  2. Does the principal prefer high effort or low effort?
  3. Suppose the principal prefers high effort, what are the incentive compatibility and individual rationality constraints? Explain in complete sentences the meaning of each of these constraints.
  4. What is the optimal contract under low and high effort, and what is the agent’s (expected) utility in each case?
  5. Suppose the principal prefers high effort but now effort is fully observable. What is the optimal contract and what is the agent’s utility? Explain why the answer to (c) is different from (d).
  6. Suppose that high effort is preferred and effort is not observed, but now there are many principals competing for one agent. Explain how this will affect your answer in (c). Will the agent’s utility be higher or lower now?

Effort

/

Probability of Output

0 / 100 / Total
Low (e = 0) / 0.3 / 0.7 / 1
High (e = 1) / 0.1 / 0.9 / 1