Consider a market for used cars. Buyers are willing to pay up to $1,000 for a good car and $400 for a lemon. Sellers are willing to accept at least $750 for a good car and $300 for a lemon. If buyers offer a price equal to the average of their willingness to pay, what is the deadweight loss (DWL) in this market?

(Hint: Suppose my value for a pen is $10 but your value is $13. In this case, if the pen remains with me, the DWL = $3)

Question

Consider a market for used cars. Buyers are willing to pay up to $1,000 for a good car and $400 for a lemon. Sellers are willing to accept at least $750 for a good car and $300 for a lemon. If buyers offer a price equal to the average of their willingness to pay, what is the deadweight loss (DWL) in this market?

(Hint: Suppose my value for a pen is $10 but your value is $13. In this case, if the pen remains with me, the DWL = $3)

BlackTom AI · Accepted Answer

We start by identifying the price that will be offered in this market. The instruction says buyers offer a price equal to the average of their willingness to pay. The buyers’ willingness to pay (WTP) for a good car is 1000 and for a lemon is 400. The average of these two buyer WTP values is (1000 + 400) / 2 = 700. So the price P that will be offered is 700.

Next, compare this price to the sellers’ minimum acceptable prices:
- For a good car, sellers require at least 750. Since 700 < 750, a good car will not be traded at this price.
- For a lemon, sellers require at least 300. Since 700 > 300, a lemon would be willing to sell at this price philosophically, but we must also check whether buyers are willing to buy at this price. Buyers are only willing to pay up to 400 for a lemon, and the offered price is 700, which exceeds the buyers’ WTP. Therefore, a lemon will not be traded either.

Thus, with a price of 700, no trades occur in the market for either type of car, so the market is in a no-trade equilibrium.

Now consider what the efficient (fully informed) outcome would be if trades could occur at prices that maximize total surplus:
- A lemon trades if the price lies between 300 (seller’s minimum) and 400 (buyer’s maximum). The surplus from such a trade would be 400 − 300 = 100 per lemon.
- A good car trades if the price lies between 750 (seller’s minimum) and 1000 (buyer’s maximum). The surplus from such a trade would be 1000 − 750 = 250 per good car.

Since the actual price of 700 lies between neither of these ranges, the lemon trade and the good-car trade are both blocked in the current setup. In the efficient outcome, at least the lemon would trade (there is a potential surplus of 100 per lemon).

Deadweight loss (DWL) is the loss of total surplus due to the absence of trades that would have been profitable in the efficient outcome. The only potentially realizable trade at the efficient price is the lemon trade, with a per-unit surplus of 100. Since no lemons trade here, the DWL would be the forgone surplus of 100 per lemon (assuming one lemon in the market). If there were multiple lemons, we would multiply by the quantity traded in the efficient outcome and keep in mind there is only one lemon unit described in this setup.

In the context of this question, the correct assessment is that the DWL from the no-trade outcome, given the price 700, corresponds to the forgone surplus from the lemon trade, which is 100. Therefore, the deadweight loss is 100 (per lemon in this simplified one-unit illustration).

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