Reference no: EM133575347

Case Study: Suppose individuals have a utility function given by ??(??) = square root ??. All individuals havethe same utility function but have different probabilities of having an accident. Assumegroup 1 individuals start with a wealth of $100 and face a .5 probability of having anaccident. Assume group 2 individuals start with a wealth of $100 and face a .2probability of having an accident. If an accident occurs both groups will lose $36.Suppose there were very few high-risk individuals in the economy but the insurancecompany was totally unaware that the high risk population existed. Assume also thatthere is only one insurance company (so no competition and thus the insurancecompany offers a full-insurance coverage contract to the low risk individuals andcharges premiums to low risk consumers that extract their full willingness to pay forthis contract).

Question a) What would the premium be to the low risk consumer?

Question b) How much would the insurance company make on each low-risk consumer?

Question c) How much would the insurance company lose on each high-risk consumer?

Question d) Show, using the diagram that we utilized in class (where the horizontal axisis wealth in the non-accident state and the vertical axis is wealth in the accident state)the iso-expected utility curve for the low and high risk person through the contractpurchased by the low risk consumers. Include the EL line we used in class to showthat the insurance company makes money on a low risk consumer.