Consider the market for used cars. Each car on the market has a quality, denoted q, which can take any number between 0 and 10, with equal probability. In other words, q follows a uniform distribution on the interval [0,10]. Sellers of used cars know the value of the car, and the lowest price that a seller will accept for a car of quality q is P = a*q. Potential buyers do not know the value of any given car, but do know the distribution of q. A buyer’s maximum willingness to pay for a car of quality q is P = b*q.
Under what condition will this market not unravel (i.e. will there not be market failure)?