Question

Think of the market in 2014 for a specific kind of used car, say a 2011 Citrus. Suppose that these cars have proved to be either largely trouble free and reliable ("peach") or have had many things go wrong ("lemon"). Suppose that each owner of a peach Citrus values it at $12,500; he is willing to sell it for a price at least higher than this but not for a lower price. Similarly, each owner of a lemon Citrus values it at $3,000. Suppose that potential buyers are willing to pay up to $18,000 for a peach Citrus and $8,000 for a lemon Citrus. The quality of the car is private information to the owner and the buyer only knows that peaches are a fraction f of used Citruses and lemons the remaining fraction (1 − f).Almost all cars depreciate over time, and so it is with the Citrus. Every month that passes, all sellers of Citruses — regardless of type — are willing to accept $400 less than they were the month before. Also, with every passing month, buyers are maximally willing to pay $3,000 less for a peach than they were the previous month and $800 less for a lemon.Assume f = 0.8, and this fraction never changes.

a) Will there be a market for peach now (month 0)? Explain briefly.

b) After two months (month 2), what will be the minimum price a seller will accept for (i) a peach and (ii) a lemon? What will be the maximum price a buyer is willing to pay for (iii) a peach and (iv) a lemon? Show your calculations.

c) Will there be a market for peach in month 2? Explain briefly

Answer 1