Let us work through a numerical example of the asymmetric information insurance model discussed in class. I could not make this work with nice numbers - so this will require some numerical equation solving. You can use any software you are familiar with for that (and google will also solve equations). The important part are the equations, not the precise numbers. So let us keep it to 2 decimal places. There are two strictly risk averse expected utility maximizing consumers who have iden- tical 'Bernoulli' utility for consumption, which is given by u(c) = c. Both consumers have an identical wealth endowment of $1, and face an identical loss of $0.5. However, they differ in their probability of the loss occurring. The good type has a probability of loss of 0.1. The bad type has a probability of loss of 0.4. Suppose half the consumers are bad type. We will suppose a competitive insurance market(s) (zero expected profits.) 1. Assuming consumer type is known by firms, what are the two optimal insurance pre- miums offered? nd how much insurance does each type buy? 2. Now suppose that firms offer insurance at the 'actuarially fair' (zero expected profit) premium for an average consumer of unknown type. show that the bad type would "overinsure" (i.e. buy more insurance than the loss) while the good type underinsures. 3. The choice of insurance amount in the previous question would 'give away' the con- sumer's type. So now let us consider the case where firms offer only one particular contract (i.e. they offer a point/allocation to consumers, who can accept it or not. They do not offer a premium that results in a budget line.) In equilibrium this con- tract must be zero expected profits and it must be acceptable to both consumer types. In this example no such contract can exist because the good type would never accept any contract that provides insurance at the average odds. Demonstrate/verify this fact. (Note: this does not necessarily involve a complicated numerical answer. There is a 'simple' approach to answer this that does not need a calculator either.) 4. It appears that a separating set of contracts is possible in this setting: The good consumers will be offered and accept some amount of insurance at an actuarially fair total price for them. The bad consumers will be fully insured at the actuarially fair total price for them. As well, any pooling contract would never attract both types. Detemine the two optimal insurance contracts that are offered in equilibirum. (This one will require numerical solution techniques.)