Al works as a sales clerk at a department store for a fixed salary of $2,500 per month
He is offered a job as a salesperson at a car dealership in which there is a 50 percent chance that he will make $5,000 a month and a 50 percent chance that he will make only $1,000 a month. The figure above Al's utility of wealth curve: a) What is Al's expected income from the offered job? b) What is Al's expected utility from the offered job? c) Will Al accept the offer? Why or why not? d) What is the minimum fixed salary for which Al will continue to work for the department store and not accept the dealership's offer?
a) The probability that Al will make $5,000 a month is 0.5, and the probability that he'll make $1,000 a month is also 0.5. Therefore Al's expected income is $5,000 × 0.5 + $1,000 × 0.5 = $3,000 per month.
b) Al's utility of wealth curve shows that if he makes $5,000 a month, his utility is 100, and if he makes $1,000 a month, his utility is 40. Therefore Al's expected utility is 100 × 0.5 + 40 × 0.5 = 70.
c) Al chooses the job that maximizes his expected utility. Al's utility of wealth curve shows that if he stays at the current job and makes $2,500 a month with certainty, his utility is 80. If Al accepts the car dealership's offer, his expected utility (calculated in part (b)) is 70. So Al will not accept the dealership's offer.
d) Al will continue to work for the department store and not accept the dealership's offer if his fixed salary gives him a greater utility than that expected from the offered job, 70. As Al's utility of wealth curve shows, his utility is 70 if his risk free income is $2,000 a month. So Al will stay at the current job if his fixed salary is greater than $2,000 a month.
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