There is a stockpile of bottled water over here and a bunch of thirsty people over there. What should be done?

Before you can answer that question you first have to figure out what is possible. Don’t think yet about what institution or economic system you are going to use to bring about the outcome, first just ask what is feasible in principle.

There are two choices to make.  First,  which consumers will get water bottles (the allocation). And second, how much money will be transferred from the consumers to the suppliers (the transfers).

The welfare associated with any choice can be summarized by a pair of numbers: the total utility or surplus of consumers and the surplus of producers. You can plot the set of all such pairs that can be generated by some choice of allocation and transfers on a graph where consumer surplus is on one axis and producer surplus is on the other.

We are really interested in the Pareto efficient choices: the ones on the frontier of the feasible set. In our problem the frontier is a line with slope negative 1. Here’s how you achieve these points. First you allocate all of the water bottles to those consumers who value them the most. This achieves the maximum total surplus. Then you specify transfers in order to distribute this surplus in various ways between suppliers and consumers. As you vary the transfers you move along the frontier swapping  producer for consumer surplus dollar for dollar.

Now that you have the feasible set you ask yourself what your social welfare function is. That is, how do you compare different points on the graph? You are essentially saying how you evaluate tradeoffs which reduce the utility of one individual and raise the utility of another. Once you have settled on a standard you choose the best point from the frontier according to that standard.

Then you start asking what economic system you can use to achieve it.

The price system is one. But the price system has a big problem. When water bottles are allocated by setting a price the two dimensions in your graph collapse into one. For example, if you want to achieve the surplus maximizing allocation with a price you are forced to accept one particular division of that surplus. There is a market clearing price p and every consumer who gets a bottle of water pays p to a supplier.

Another way of saying this is that market clearing prices correspond to one single point on your frontier. Is it the point you wanted before you started considering the price system as a mechanism? That would be quite an accident. And barring such a coincidence you are now left asking what else could be done within the confines of the price system?

You can choose a price different from the market clearing price. As you vary the price you do two things. First, you worsen the allocation and as a result total surplus goes down.  So you move inside the old frontier. That’s bad. Second, you change the division of surplus. This traces out a new frontier giving you more than one choice. That’s good.

Now you can consult your social welfare function again and ask which point on the price-system-generated frontier do you like the best. Will it be the point corresponding to market-clearing prices? Of course it depends on your social welfare function but again it would be quite a coincidence.

For example it could be that market-clearing prices are very high and give almost all surplus to producers and leave consumers with close to zero surplus. If your social welfare function has diminishing marginal rate of substitution of one individual’s utility for another (whether they are consumers or producers, it doesn’t really matter) you will prefer a more interior point which would be achieved by setting prices below market-clearing levels. You are essentially willing to reduce total surplus by a bit (due to misallocation) in order to achieve a better distribution.

Thus, my response to Erik Brynjolffson, who writes in the comments to my post on price gouging:

Producers also are people, just like consumers, and we’d like to see their utility increased, ceteris paribus. Thus, even if production decisions don’t change, I don’t follow your argument that we should put zero weight on producer surplus.

is that nowhen did I say that we should do that and it’s not part of the argument. Instead the argument is that as long as you don’t think we should always be indifferent to arbitrarily reducing the surplus of one party in favor of another (again regardless of who is a consumer or a supplier) then your optimal price will not be the market-clearing price.

Let me emphasize that this is a very special problem because the quantity of water bottles was given, we don’t have to worry about incentives to produce. Another effect of the price system is to provide those incentives. And when supply is elastic, distorting prices reduces welfare for another reason:  the quantity is distorted. The point I am making applies in the special cases when this distortion is small.  For example when supply lines are cut in a natural disaster.

Other commenters, like Tyler Cowen, argue that supply cannot be considered perfectly inelastic even in rare, unexpected natural disasters. That’s true, but this is not a limiting argument. It doesn’t require perfectly inelastic supply. The tradeoff is still there with highly, but not perfectly, inelastic supply.