1. (7) The Economics of Uncertainty (Chapter 6) John is a salesperson. He is currently paid on a commission basis. In bad years he makes $22,500 a year; in good years, he makes $62,500 a year. The probability of a bad year is 0.4. The probability of a good year is 0.6. a) (1) What is his expected income? John is risk averse. His utility function is u = y , where u is utility and y is income. b) (1) What expected utility does he receive from his commission income? () (1) What is his certainty-equivalent income, ie. what certain income would give him the same expected utility as he receives from his commission income? Because his company operates nationally and has a large salesforce, it knows its total revenue from sales with certainty. His company is considering paying its salespeople by salary rather than by commission. d) (2) Assume that all salespeople are the same and that a salesperson cannot affect their sales by increasing sales effort. Show that both the salespeople and the company are better off if the company pays its salespeople a salary of $45,000 a year rather than under the current commission arrangement. The salary contract is therefore more efficient. Why? e) (1) Now modify d) so that a salesperson's sales depend on his effort, which the company cannot observe. What moral hazard effect may arise when payment is by salary rather than by commission? f) (1) Now modify c) so that some people are more talented at sales than others. What adverse selection effect may arise when payment is made by salary rather than by commission? When the moral hazard effect and the adverse selection effect are taken into account, the commission contract may be more efficient than the salary contract