Question

Suppose that in Burnt Church, Pennsylvania, the quality distribution of the 1000 used cars on the market is such that the number of used cars of value less than V is V/2. Original owners must sell their used cars. Original owners know what their car is worth, but buyers can't determine a car's quality until they buy it. An owner can either take their car to an appraiser and pay the appraiser $100 to appraise the car (accurately and credibly), or they can sell the car unappraised. In equilibrium, car owners will have their cars appraised if and only if the car's value is at least:

(a) $100
(b) $500
(c) $300
(d) $200
(e) $400

Answer 1

In the given market scenario with imperfect information, car owners will decide to pay for an appraisal if and only if it adds more value to the car than the cost of the appraisal. Given the distribution function and the cost of the appraisal, car owners will appraise their cars if their value is at least $200.

Step-by-step explanation:

In the scenario provided for Burnt Church, Pennsylvania, we are dealing with a market with imperfect information, where original owners know their car's value, but buyers cannot determine it until after the purchase. This situation creates a dilemma for the owners regarding whether to pay for an appraisal or to sell their cars unappraised. The equilibrium is the point where it is advantageous for the owner to pay for an appraisal because the expected increase in the selling price due to the appraisal exceeds the appraisal fee. Given the distribution function V/2 for the number of cars valued less than V, owners would only have their cars appraised if the value of the appraisal ($100) is lower than the expected increase in the car's selling price that would result from being appraised. In such markets, higher prices can signal higher quality to consumers.In markets with imperfect information, the price often acts as a signal of quality. This situation can lead to a separation of the market into two segments: cars that are appraised and those that are not. If getting a car appraised adds more than $100 in perceived value (the cost of the appraisal) to the buyer, then it is a beneficial investment for the seller. Thus, sellers will opt to appraise cars that can fetch a higher price post-appraisal. In this context, marking the value of V at which appraisals are sought is key to understanding the market dynamics.Conclusion Given the details provided, the correct answer to when an owner will have their car appraised is when the car's value is at least $200 (answer choice d). This is because the appraisal adds enough value to make the investment worthwhile for cars valued at or above this price.