Analytical Problems

1. An individual has a health insurance plan with a deductible of $1200 and a coinsurance rate of 50%. Their demand curve is Q=20-(P/10), and the equilibrium market price of medical care is $100 per unit. What quantity of medical care would the individual choose to consume?

2. Suppose that consumers are all risk neutral and so they do not purchase health insurance. The equilibrium price of a doctor visit is $30, the supply of doctor visits is perfectly elastic, and the aggregate demand for doctor visits is given by Q=200-5*P. Calculate the effect that universal perfect health insurance (that is, coinsurance rate=0) would have on social welfare, measured as the sum of consumer surplus plus producer surplus.

3. Consider a version of the Akerlof model in which neither buyers nor sellers observe car quality (though somehow – please suspend your disbelief – both buyers and sellers enjoy higher utility from higher quality cars). For this question, please assume that both buyers and sellers recognize that neither can observe car quality.

Sellers’ utility function is given by US=M+Σxi and buyers’ utility is given by

UB=M+Σ2xi where M is the level of consumption of non-car goods and xi is the quality level of car, and there is a uniform distribution of quality of the cars held by sellers, xi~U[0,20].

In this market, is there is a price, p, at which all cars will sell? If not, prove there is no such price. If so, calculate what prices will work.

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