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After graduation, Bates College students are either hired by investment banks and earn wage wB. =400 or hired by nonprofits and earn wage yX=0. Let p denote the probability that a student is hired by a nonprofit. Bates College students have the utility function: u(c)=c where c is consumption and is a number such that 01. An insurer offers students wage insurance contracts of the following form: students pay insurance premium regardless of which job they get (i.e., they pay the premium in either state of the world) and receive insurance benefit b=400 only if they end up working at a nonprofit. Bates College requires that any wage insurance sold to their students pays b=400. To start assume, that there is only one student at Bates College named Peter. Peter's probability of working at a nonprofit is given by pR=0.8 and his is given by R=0.5. 1. What is Peter's expected utility without wage insurance? 2. Suppose that there is a monopoly in the wage insurance market. Specifically, there is only one insurance provider and no other insurers can enter the market. In this case, what is the equilibrium ? 3. For the remainder of this question, assume that the wage insurance market is perfectly competitive. In this case, what is the equilibrium ? 4. Explain in words why this must be the equilibrium . ( 23 sentences)