purchase this insurance? h) Suppose that the management costs of this insurance company are fixed and that it plans to increase its profits by offering a second product which consists in insuring 20% of the loss at a price of $ 110. Would Type 2 individuals buy this insurance? (2 points} D) Would Type 1 individuals prefer this second product to the first product offering full insurance but at a higher unit price? (2 points) Consider the following game. There is a population of people all with an initial wealth of $ 1U,DDD. Each person faces a potential loss of $ 5,UUU. The population is made up of 25% of people of type 1 and 25% of people of type 2. Individuals of type I have a probability of loss of 2% while those of type 2 have a probability of loss of 10%. We assume that all individuals have identical Von Neurnann MorgensternZ type preferences represented by the following utility function : V(x} = Inx. 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 1 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