You work for the State Department of Labor and have been given the task of evaluating a state job-training program. In order to conduct the analysis, suppose that the typical client for the program has the following utility function of income I:
Where α > 0, 0 < β < 1.
a. Sketch the typical client’s utility function and explain the person’s attitude toward risk.
b. Suppose that you must evaluate a proposed government job-training program that would have an unpredictable effect on the typical client’s income, which is u = (I + α)β currently $20,000 per year. The program will leave the person’s annual income unchanged with probability 0.3, or it will increase his income by $10,000 with probability 0.7. Calculate the benefit of the program to the typical client, assuming that α = $5,000 and β = 0.5.