In the last lecture we demonstrated that there was no way to efficiently provide public goods, whether via a market or any other institution.  Now we turn to private goods.

We start with a very simple example: bilateral trade.  A seller holds an object that is valued by a potential buyer.  We want to know how to bring about efficient trade:   the seller sells the object to the buyer if, and only if, the buyer’s willingness to pay exceeds the seller’s.

We first analyze the problem using the Vickrey-Clarke-Groves Mechanism.  We see that the VCG mechanism, while efficient, is not feasible because it would require a payment scheme which results in a deficit:  the buyer pays less than the seller should receive.

Then, following the lines of the public goods problem from the previous lecture we show that in fact there is no mechanism for efficient trade. This is the dominant strategy version of the Myerson-Satterthwaite theorem. In fact, we show that the best mechanism among all dominant-strategy incentive compatible and budget balanced mechanisms (i.e. the second-best mechanism) takes a very simple form.  There is a price fixed in advance and the buyer and seller simply announce whether they are willing to trade at that price.

We see the first emergence of something like a market as the solution to the optimal design of a trading institution. We also see that markets are not automatically efficient even when there are no externalities, and goods are private.  There is a basic friction due to information and incentives that constrains the market.

Next we consider the effects of competition.  Our instincts tell us that if there are more buyers and more sellers, the inefficiency will be reduced.  By a series of arguments I show the first sense in which this is true.  There exists a mechanism which effectively makes sellers compete with one another to sell and buyers compete with one another to buy.  And this mechanism improves upon the fixed price mechanism because it enables the traders themselves to determine the most efficient price.  I call this the price discovery mechanism (it is really just a double auction.)

Finally, in one of the best moments of the class, what was previously some random plots of values and costs on the screen coalescees into supply and demand curves and we see how this price discovery mechanism is just another way of seeing a competitive market.  This is the second look at how markets emerge from an analytical framework that did not presuppose the existence of markets at the beginning.

Here are the notes.