17.10 The used car supply in Metropolis consists of 10,000 cars. The value of these cars ranges from

$5,000 to $15,000, with exactly one car being worth each dollar amount between these two figures. Used car owners are always willing to sell their cars for what they are worth. Demanders of used cars in Metropolis have no way of telling the value of a particular car. Their demand depends on the average value of cars in the market (P
) and on the price of the cars themselves (P) according to the equation Q
1.5 P
P.

a. If demanders base their estimate of P
on the entire used car market, what will its value be and what will be the equilibrium price of used cars?

b. In the equilibrium described in part (a), what will be the average value of used cars actually traded in the market?

c. If demanders revise their estimate of P
on the basis of the average value of cars actually traded, what will be the new equilibrium price of used cars? What is the average value of cars traded now?

d. Is there a market equilibrium in this situation at which the actual value of P
is consistent with supply-demand equilibrium at a positive price and quantity?