The market for used cars is shown in the above figure. Buyers ...

[jwb375]

The market for used cars is shown in the above figure. Ten percent (10%) of all cars are lemons. A mechanic is offering to inspect a car for sale and certify that a car is not a lemon. If car sellers are risk neutral, what is the highest price that a car seller would pay for such a service? Who would buy this service?

[shailee]

Lemon owners would not buy this service because they know that their cars would not pass the inspection. Sellers of good cars would receive $1,900 for their cars if this service did not exist, and $2,000 for their cars with this service. Thus, each owner of a good car would pay no more than $100 for this service. All good car sellers would buy this service since not being certified signals that a car is a lemon.

[jwb375]

Thank you!

[shailee]

Always glad to help...

[debasdf]

The market for used cars is shown in the above figure. Buyers cannot tell whether any given car is a lemon. For all cars offered for sale to be sold, the percent of all cars that are lemons is θ. What happens to θ if car buyers incur a $100 transaction cost when buying a used car?

[Juro]

The sellers of good cars have a reservation price of $1,800. Setting $1,800 equal to the expected value of a car yields 1800 = (θ ∗ 1,000) + ((1 - θ) ∗ 2,000) = 2,000 - (θ ∗ 1,000). So, θ = 20%. If a $100 transaction cost is incurred then set 1800 = (θ ∗ 1,000) + ((1 - θ) ∗ 2,000) - 100. This yields θ equals 10%. If buyers incur a transaction cost, their net expected value of a car purchase declines. The probability of a car being a lemon must decline to keep the price above the reservation price of sellers of good cars.