Statistical Abstract of The Problem
Suppose we can use some number, to index the quality of used cars, where is uniformly distributed over the interval . The average quality of a used car which could be supplied to the market is therefore 1/2. There are a large number of buyers looking for cars who are prepared to pay their reservation price of for a car that is of quality . There are also a large number of sellers who are prepared to sell a car of quality for the price . If quality were observable, the price of used cars would therefore be somewhere between and, and the cars would be sold and everyone would be perfectly happy. If the quality of cars is not observable by the buyers, then it seems reasonable for them to estimate the quality of a car offered to market using the average quality of all cars.
Based on this estimation, the willingness to pay for any given car will therefore be, where is the average quality of all the cars. Now, assume that the equilibrium price in the market is some price, where . At this price, all the owners of cars with quality less than will want to offer their cars for sale. Since again, quality is uniformly distributed over the interval from 0 to this, the average quality of the cars offered for sale at will be worth only . We know however that for an expected quality worth, buyers will only be willing to pay . Therefore we can conclude that no cars will be sold at . Because is any arbitrary positive price, it is shown that no cars will be sold at any positive price at all. The market for used cars collapses when there is asymmetric information.
Read more about this topic: The Market For Lemons
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