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 \((\bar{P})\) and on the
price of the cars themselves \((P)\) according to the equation $$Q=1.5
\bar{P}-P$$
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 \(\bar{P}\) 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 \(\bar{P}\) is consistent with supply-demand equilibrium at a positive price
and quantity?