please answer ALL nine parts of this question if you show full work and are neat i will be sure to leave a thumbs up. please answer as soon as possible. thank you so much! Please be very clear and label the answers!

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 eam wage gX=0. Let p denote the probability that a student is hired by a tooprofit. Bates College students have the utility function: u(c)=ca where c is consumption and is a number such that 01. An insurer offers students wage insurance contracts of the following form: students pay inrurance premhum rogardiess of which job they get (i.e., they pay the preminum in either state of the world) and receive insurance benefit b=400 enly if they end up working at a noenprofit. Bates College requires that any wage insurance sold to their students pays b=400. To start ascume, that there is colly one student at Bates College named Peter. Peter's probability of working at a nonptofit is given by pR=0,8 and his a is given by aR=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 enier the market. In this case, what is the equibibrium ? 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 . (2-3 sentences) 5. Now, suppose that there are two students at Bates College, Peter (same as above) and Kathy. Kathy's probability of working at a nomprofit is given by 0S=0.2 and her a is given by aS=0.5. There is asymmetric informadion: students lenow their own types but insurers do not. Bates College still requires that b=400. Characterize the equilibrium in the wage insurance market. Specifieally, in equilibrium, who purchases insurace and what prices do they pay? Succinctly walk through each step of your analysis. 6. Now, suppose there are two students at Bates College, Peter (sane as above) and Jenny. Jenny's probability of working at a nonprofit is given by pS=0.2 and her a 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. 7. 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 a is given by oS : There is asymmetric informution: 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? Succinetly show your work. 8. Explain in words why there is deadweight loss for the values of aS that you answered above. (2-3 sentences) 9. Fxplain in words why the amount of deadweight loss depends on the aS parameter. (2-3 sentences) |