22.4 An individual receives utility from daily income (Y), given by U(Y) = 100F- -^ Y 2

.

The only source of income is earnings. Hence, Y = 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 E(X 2

) =

where E means "expected value."