16.9 Compensating wage differentials for risk An individual receives utility from daily income (y), given by U y 100y % 1 2 y2 :

16.9 Compensating wage differentials for risk An individual receives utility from daily income (y), given by Uð yÞ ¼ 100y % 1 2

y2

:

The only source of income is earnings. Hence y ¼ wl, where w is the hourly wage and l is hours worked per day. The individual knows of a job that pays $5 per hour for a certain 8-hour day. What wage must be offered for a construction job where hours of work are random—with a mean of 8 hours and a standard deviation of 6 hours—to get the individual to accept this more

‘‘risky’’ job? Hint: This problem makes use of the statistical identity Eðx2

Þ ¼ Var x þ Eðx2

Þ: