When solving the agency problem example in Notes 3-5a, one subtle, but important feature of the basic setup is that neither the employer, P, nor the worker, A, have any initial wealth. This problem asks you to consider what might happen if A had some initial wealth.

1. Suppose a decision-maker is considering playing a lottery that pays either $11 or $21, with the probability of each being 50%, and the decision-maker has an initial wealth of $0. Assuming the decision-makers utility function is U(w) = (w), what is the risk premium associated with this lottery?

2. Now suppose the decision-maker has the same utility function, and is considering the same lottery. But, the decision-maker has an initial wealth of $8. What is the risk premium associated with this lottery?

Hint: When considering the effects of wealth, think of the lottery in terms of the final wealth position. That is, when calculating the decision-makers utility, think about the decision-makers total wealth, which includes both the outcome of the lottery and the initial wealth of $8.

3. Compare your answers to parts a and b. What does that comparison tell you about the effects of initial wealth on the risk premium? Why does that change occur?