# Why does having a single market price maximize quantity traded?

From what I have heard, the exchange of goods defined by the intersection of supply and demand generally maximize quantity traded, although this doesn't apply in cases of monopolies, imperfect information etc. I am trying to understand why this is true, and came across what appears to be a counter example:

There are 4 people in a market for eggs, 2 buyers and 2 sellers. The buyers are each willing to pay up to \$10 and \$3 for 1 egg each. The sellers are willing to sell an egg each at \$9 and \$2. The most productively efficient trades are when one egg is bought for some price between \$9 and \$10 and another is bought for some price between \$2 and \$3. What happens according to supply and demand is that one egg is traded for a price between \$3 and \$9.

The fact that there is one price seems, in this case, to reduce the total traded quantity. What am I missing?

• The question is not entirely clear. By "maximize productive efficiency" do you mean that everyone maximized their individual profits? What a single equilibrium market price does is create a Pareto efficient equilibrium. The notions of Pareto efficiency and equilibrium are a bit more complicated than maximal achieveable profit, I recommend reading about these notions. – Giskard Oct 24 '15 at 6:26
• Changed productive efficiency to quantity traded. – InquisitivePerson Oct 24 '15 at 16:23

In the example you gave buyer 1 (reservation price 10) and seller 1 (reservation price 9) have a collective surplus of \$1, and buyer 2 (reservation price 3) and seller 2 (reservation price 2) have a collective surplus of \$1, meaning both pairs 'feel' they gained \$1 by trading. But in the competitive equilibrium, buyer 1 and seller 2 have a collective surplus of \$ 8. If they give buyer 2 and seller 1 one dollars each, everyone would still be more happy than in the other situation. So the second sale is in some way inefficient.