1. Consider a firm. With probability 0.5, it will generate high revenue $10000, and with the remaining probability, it will generate low revenue $2000. The only cost is labor, and it only hires one worker. Suppose that the labor's utility is u(w)=sqrt(w) where w is the wage. a) Consider a profit-sharing contract between the firm and the labor. The wage rate is 20% the of the revenue. What is the expected value of this contract? What is the expected utility of this contract? b) An alternative contract is a fixed wage contract. The firm pays a fixed wage rate of regardless of the revenue. What is the fixed wage that makes the labor indifferent between profit-sharing and fixed contracts? c) Suppose the firm is risk neutral, i.e., only cares about expected profit. What is the optimal contract to offer? What is the economic intuition behind this result? d) We assume that the firm is risk neutral. Why do you think this isa reasonable assumption