2) Consider the following game. There is a population of people all with an initial wealth of $ 10,001}. Each person faces a potential loss of $ 5,303. The population is made up of ?5% of people of type 1 and 25% of people of type 2. Individuals of type 1 have a probability of loss of 20% while those of type 2 have a probability of loss of 10%. We assume that all individuals have identical 1'v'on Neumann Morgenstern2 type preferences represented by the following utility function : U[x} = lnx. a) What is the expectation of wealth for type 1 individuals? [2 points) b) What is the expectation of wealth for type 2 individuals? {2 points) c) What is the maximum price that a Type I consumer would pay for full insurance? (2 points) d) What is the maximum price that a Type 2 consumer would be willing to pay for full insurance? (2 points) Imagine an insurance company that cannot distinguish between the two types of consumers but who knows the probabilities of having a type 1 client and those of having a type 2 client. e) Suppose that this company decides to offer an insurance product whose price, actuarially fair3 in expiration, is equivalent to the average loss in this population. What is the price of this insurance? Will the Type 2 consumer agree to buy this insurance? [2 points) f} Now imagine that an insurance company offers insurance at a price equivalent to the actuarially fair price for type 1 individuals + an additional amount equivalent to 20% of the cost of risk for these individuals in order to cover their management costs and the firm's profit margin. What is the price of this insurance? [2 points} 8) Would Type 1 and Type 2 individuals