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Question 5: Wage insurance After graduation, Bates College students are either hired by investment banks and earn wage wB =400 or hired by nonprofits and earn wage wN=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? For the remainder of this question, assume that the wage insurance market is perfectly competitive. 2. Now, suppose that there are two students at Bates College, Peter (same as above) and Kathy. Kathy's probability of working at a nonprofit is given by pS=0.2 and her is given by S=0.5. There is asymmetric information: students know their own types but insurers do not. Bates College still requires that b=400. Characterize the equilibrium in the wage insurance market. Specifically, in equilibrium, who purchases insurance and what prices do they pay? Succinctly walk through each step of your analysis. 3. Now, suppose there are two students at Bates College, Peter (same as above) and Jenny. Jenny's probability of working at a nonprofit is given by pS=0.2 and her is given by aS= 0.25. There is asymmetric information: students know their own types but insurers do not. Bates College still requires that b=400. Characterize the equilibrium in the wage insurance market. Specifically, in equilibrium, who purchases insurance and what prices do they pay? Succinctly walk through each step of your analysis. 4. Now, suppose there are two students at Bates College, Peter (same as above) and Martha. Martha's probability of working at a nonprofit is given by pS=0.2 and her is given by S. There is asymmetric information: students know their own types but insurers do not. Bates College still requires that b=400. For what values of S will the equilibrium in the wage insurance market be associated with deadweight loss? Succinctly show your work