1) Construction workers in the town of Cortland, NY have Cobb-Douglas utility for labor and consumption U(L,C)= (20-L)C and MRS= (C)/(20-L) where L is the number of hours of labor supplied in a day andC is the dollar amount of consumption goods purchased with wage income (p_c=$1).R= 20-L is the number of hours of leisure that the worker has during the day.

a) Derive the labor supply function for workers in Cortland.

b) Draw the labor supply curve on a graph withon the horizontal axis andon the vertical axis.

2) Pete has a wealth of$1,000 . Pete just bought a new car, but he is a reckless driver. So tomorrow when he drives to work for the first time, there is a75%chance that he will have an accident and only a25% chance that he will not. If he has an accident, he will have to pay$600 in damages and repairs. Suppose Pete's utility of wealth,is given by the function: u(w)= sqrt(w)

a) What is the expected value of Pete's wealth tomorrow?

b) What is his expected utility?

c)How much would Pete be willing to pay to avoid the possible loss of income?

Suppose Pete could buy car insurance.

e) What is the maximum premium that the insurance company can charge to get Pete to buy this policy?

f)What is the insurance company's expected profit if it charges the maximum premium that Pete is willing to pay?

Pete decides to become a more a careful driver so that his chances of an accident fall to

g) What happens to the premium that the insurance company can charge?

h) What happens to the company's expected profit?