People like to earn money, but they don't like to work outdoors in the summer, due to the high heat. Suppose that the utility function is \(U(w,x)=w^{1/2}-0.5h\) , where w is the wage and h is a measure of the number of very hot days.
a. What is the marginal utility of the measure of very hot days, h?
b. Suppose that Sacramento has h=3 and San Francisco has h=1. If people can earn w=10 in San Francisco, then how much must someone earn in Sacramento in order to consider working in Sacramento, all else the same?