We have spent most of the course using the tools of dominant-strategy mechanism design to understand efficient institutions and second-best tradeoffs.  These topics have a normative flavor:  they describe the limits of what could be achieved if institutions were designed with efficiency as the goal.

But most economic activity is regulated not by efficieny-motivated planners but by self-interested agents.  This adds an additional friction which potentially moves us even further from the first-best.  Self-interested mechanism designers will probably introduce new distortions into their mechanisms because as they try to tilt the distribution of surplus their way.

In this lecture we use the model of an auction to see the simplest version of this.  We consider the problem of designing an auction for two bidders with the goal of maximizing revenue rather than efficiency.  We do not have the tools necessary to do the full-blown optimal auction problem but we can get intuition by studying a narrower problem:  find an optimal reserve price in an English auction.

With a diagram we can see the tradeoffs arising from adjusting the reserve price above the efficient level.  The seller loses because sometimes the good will go unsold but in return he gains from receiving a higher price when the good is sold.  The size and shape of the regions where these gains and losses occur suggest that it should be profitable to raise the reserve price above cost.

Without solving explicitly for the optimal reserve price we can give a pretty compelling, albeit not 100% formal, argument that this is indeed the case.  At the efficient reserve price (equal to the cost of selling) total surplus is maximized.  A graph of total expected surplus as a function of the reserve price should be locally flat at the efficient point. (We are implicitly assuming differentiability of total expected surplus which holds if the distribution of bidder values is nice.) Buyers’ utility is unambigously declining when the reserve price increases.  Since total surplus is by definition the sum of buyers’ utility and seller profit, it follows that seller profit is locally increasing as the reserve price is raised above the efficient level.

Thus, while we know that in principle this allocation problem can be solved efficiently, when the allocation is controlled by a profit maximizer, there is a new source of inefficiency.  The natural next question is whether competition among profit-maximizing sellers will mitigate this.

Here are the slides.