2. Adverse Selection Consider the market for coffee machines. There are 200 risk-neutral buyers and 160 risk-neutral sellers. Each buyer wants to buy at most one coffee machine; each seller owns exactly one coffee machine. There are two types of coffee machines: high quality and low quality machines. High quality machines have a failure probability of 0.2, whereas the low quality machines have a failure probability of 0.75. The utility that a buyer derives from a coffee machine without failure amounts to 400 (measured in monetary terms). If the coffee machine has a failure the utility of the buyer decreases - by the amount of the repair costs to 200. Assume that 25% of the coffee machines are of high quality. Each seller has a reservation price of 300 for a high quality machine and a reservation price of 240 for a low quality machine. a) Derive a buyer's maximum willingness to pay for a high quality and a low quality coffee machine. Suppose that sellers know the quality of their machines, whereas the buyers can- not distinguish between high and low quality machines (asymmetric informati- on). b) Derive aggregate supply and aggregate demand as a function of the market price. c) Characterize the market outcome. Comment briefly on its efficiency. d) How large may the failure probability of the low quality machines maximally be, so that there is just no partial market breakdown? 2. Adverse Selection Consider the market for coffee machines. There are 200 risk-neutral buyers and 160 risk-neutral sellers. Each buyer wants to buy at most one coffee machine; each seller owns exactly one coffee machine. There are two types of coffee machines: high quality and low quality machines. High quality machines have a failure probability of 0.2, whereas the low quality machines have a failure probability of 0.75. The utility that a buyer derives from a coffee machine without failure amounts to 400 (measured in monetary terms). If the coffee machine has a failure the utility of the buyer decreases - by the amount of the repair costs to 200. Assume that 25% of the coffee machines are of high quality. Each seller has a reservation price of 300 for a high quality machine and a reservation price of 240 for a low quality machine. a) Derive a buyer's maximum willingness to pay for a high quality and a low quality coffee machine. Suppose that sellers know the quality of their machines, whereas the buyers can- not distinguish between high and low quality machines (asymmetric informati- on). b) Derive aggregate supply and aggregate demand as a function of the market price. c) Characterize the market outcome. Comment briefly on its efficiency. d) How large may the failure probability of the low quality machines maximally be, so that there is just no partial market breakdown