To test your understanding of the model in section 16.2 consider the following reparameterization. The reservation utility level of the agent is
only 3. A high level of effort gives a = 3, while a low level gives a = 0. (Thus, if we can contract contingent on the level of effort, we would have
to pay $9 for a low level of effort and $36 for high.) A high level of effort gives no sale with probability .2, a $100 sale with probability .4, and a $400 sale with probability .4. For a low level of effort, the three probabilities are .4, .4, and .2.
(a) What is the optimal way to induce the agent to put in a low level of effort, if you can contract contingent on the size of the sale (only)?
(b) What is the optimal way to induce the agent to put in a high level of effort?
(c) What is the optimal contract (if you are a risk neutral principal) to offer this agent?