The market for used cars is shown in the above figure. Buyers cannot t

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?

ANSWER

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.