danryan.us

New solution based on excellent in-class comments 27 September 2012. Strong point made that unless the car was more useful to the buyer than the $4000 then it would an almost trivial problem: the existence of any risk at all that the car is a lemon would make me not buy it.

I think we can take this into account and still present a simple and elegant solution. Let us simply recognize that the motivation to do the exchange (that is, buy the car), suggests that the value TO THE BUYER is at least $4000 and almost certainly at least $4000 plus a little bit more. This based on the idea that the market exchange happens when the exchange is somehow mutually beneficial.

1. If I am willing to buy this car in good working condition for $4000 then we can assume the value to me of having this car in good working condition is at least $4000. One way to write this is $V = 4000 + x\quad where\quad x\ge 0$.
2. As usual, we use the accounting principle of figuring out what all of our assets and liabilities are at a specific moment in time.
3. This will yield the following possible outcomes situations (we ignore the "impossible" situations such as the car is a known lemon but I buy it anyway)

There are, as you probably have discovered, different ways of thinking about this problem. Let's try to find the simplest one.

The main thing we want to determine is how much it would make sense to pay a mechanic to eliminate the uncertainty about buying a lemon.