Why is there a deadweight loss in this lemons market?

Question

Is there a deadweight loss in this used car market and why?

On the plums side we can make a pareto improvement by exchanging information and matching 200 buyers and sellers who will gain from trade.

On the lemons side, we can't say for certain that it is inefficient. Lemons are being exchanged at the expected value of a car (50% of cars are plums and 50% are lemons) which is 12k. This becomes the maximum WTP of an ignorant buyer, so the exchange is not inefficient, there are equity issues but not efficiency issues. A Pareto improvement is not possible because any gain that buyers make when given information (they will keep their money in their pockets) is a loss to sellers. (Is this correct? the sale of 600 lemons is Pareto efficient but why can you not return to this point once you're off equilibrium without making sellers worse off?)

So is the deadweight loss the 400k on each side, or just the 400k in the plums market, or is it something else - 2 million on the right hand side for example because the true WTP is 16k? What do you think?

Answer 1

You can calculate the total social surplus (= CS + PS) in this equilibrium and compare it to the social surplus in the efficient allocation of cars.

Equilibrium allocation

The equilibrium (under asymmetric information) has price equal to $12000$. Thus, in the lemon's market, \begin{align} CS_L&=(8000-12000)\times1000=-4000000\\ PS_L&=\frac12\times(12000-2000)\times1000=5000000. \end{align} Total social surplus in the lemon's market is \begin{equation} TS_L=CS_L+PS_L=1000000. \end{equation} In the plum's market, \begin{align} CS_P&=(16000-12000)\times400=1600000\\ PS_P&=\frac12\times(12000-4000)\times400=1600000. \end{align} Total social surplus in the lemon's market is \begin{equation} TS_P=CS_P+PS_P=3200000. \end{equation} Joint surplus from the two markets: \begin{equation} TS=TS_L+TS_P=4200000. \end{equation}

Efficient allocation

Efficiency occurs when lemons are priced at $8000$ and plums at $16000$. Note that in both markets, since demand is perfectly elastic, consumer surplus is zero at the efficient allocation. So total surplus is the same as producer surplus. \begin{align} TS_L^*&=\frac12\times(8000-2000)\times600=1800000\\ TS_P^*&=\frac12\times(16000-4000)\times600=3600000\\ TS^*&=TS_L^*+TS_P^*=5400000. \end{align}

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The gap between $TS^*$ and $TS$ is the DWL. The inefficiency arises from the fact that, in equilibrium (with asymm info), some cars are in the wrong hands: the last 400 lemons sold and the potential 200 plums that were unsold.