Thursday, November 4, 2010

Understanding Excess Supply (The Non-Algebraic Version)

I have just taught the theory of the supply curve at the principles level for the umpteenth time, and my conscience is in open rebellion. This business with the horizontal demand curve and setting supply equal to marginal costs is simply rubbish; it denies some of the most important, and obvious, facts about how capitalism actually works.

At the level of an individual firm, the theory obscures what ought to be the starting point for analysis—that in a capitalist economy the normal state of affairs is that firms set production at a level that requires them to chase consumers any way they can, and that the usual result is that some offerings go unsold. Across the entire economy the level of activity is nearly always demand-constrained, not supply-constrained.

Consider the relationship between buyers and sellers at the level of individual enterprises. From observers like Alec Nove and Janos Kornai, we have come to recognize that the prevalence of buyers’ markets is what distinguishes capitalism; in the state-managed systems of pre-1989 socialism, the seller was king. This suggests that excess supply is the most likely state of affairs, excess demand the least likely. An exact equality between demand and supply at the market-determined price is essentially impossible.

Of course, demand is not determinant. It is best represented as a subjective frequency distribution, to which sellers would adjust their production plans. Suppose, to keep things simple, this is a normal distribution. (I don’t think this assumption changes anything important.) Suppose also that marginal costs are symmetric around the mean of expected demand—that the increase of MC for one unit more is equal to its decrease for one unit less. This equalizes the direct financial cost of over- and underproduction, another convenience for our analysis. (If MC increases at an increasing rate, incidentally, this would be a reason for a bias toward underproduction, and therefore excess demand, ceteris paribus; so it’s not the answer we’re looking for.) Now let the seller maximize profit by making an ex ante decision about how much to supply for this uncertain demand.

What we would expect to see is an equal incidence of ex post excess demand and excess supply. But this is not how it is.

Let’s add a couple of new elements: first, suppose that consumers are not utility maximizers, gathering all information about product quality, prices and suppliers costlessly and then making the optimal purchase, but satisficers. They have benchmark price and quality points, and they select the first seller who meets them. Second, consider a sequential model where, in each period, consumers begin their search with the seller they transacted with in the previous period, so, if the seller continues to meet the buyers’ price and quality points, the customer is still theirs. This fits with the literature in marketing, which stresses that a sale should always be seen as the opening to future sales and therefore worth a much greater investment than it would justify from a myopic perspective.

This new element has the effect of biasing the seller’s choice of a production level: it is more expensive to lose out on a sale than to produce or stock an extra item for which there is no ex post demand. Producers in general set their output to the right of the mean of expected demand, and excess supply is the norm.

This is not quite eureka. It works for the special case of constant variable costs, but there is more work to do to incorporate upward-sloping MC and the effect that raising the selling price (due to being further out on the MC curve) has on the proportion of consumers (whose price benchmarks are also stochastic) who will continue to satisfice. What we get, in the end, is a case for generalized excess supply that depends on the relationship between the parameters governing the two forms of uncertainty—the size of the market (the number of desired purchases) and the market share for any single firm (the proportion of buyers who regard a particular selling price as acceptable)—as well as the seller’s marginal cost structure. For further complication one can also relax the assumption that buyers always return if their satisficing conditions are met; this probability could also be governed by a parameter. (Note that one useful result of this model is that it relaxes the so-called law of one price in a way that is consistent with real-world data.)

Such a model would provide microfoundations for demand-constrained macroeconomics. Working this out is of less interest to me, but it should be clear that there is a certain amount of equilibrium slack in such a system. What would the dynamics look like, however? Would chronic excess-suppliers of this sort respond differently to aggregate demand shocks, compared to the Walrasian firms that populate existing general equilibrium models?

During the next two years economists (at least those in the US) will be freed from having to think about policy and can shift their attention to the theoretical foundations of their discipline.

12 comments:

john c. halasz said...

I'm not getting the bit about rising marginal costs. If most of the cost is long-run fixed investment in plant and equipment, rather than labor and materials, (as is usually the case in large scale, technically efficient industrial production), then marginal costs decrease with increasing output, and there are increasing returns to the own-demand production supply curve. And that, in turn, would explain the tendency to excess capacity being maintained in plant and equipment, both to deter competitors and to maintain response capacity to potential cost-lowering increases in demand, whether temporary or cyclical, aside from the fact that scale effect might mean that additional plant and equipment capacity might have little additional cost once a certain, discontinuous scale-level is achieved.

Nick Rowe said...

Peter:

The normal state of affairs for a capitalist economy is excess supply. Buyers can easily buy more if they want to, but don't. Sellers want to sell more, but can't. In recessions this excess supply gets bigger; in booms it gets smaller, but only in a really big boom does it disappear absolutely, and we hit the supply constraints, and get shortages. Yes. Absolutely.

And when you get to Macro, the standard Principles story gets even more logically inconsistent. Start in Long Run equilibrium. Then increase AD, assuming sticky prices. Why does output, employment, and sales increase? Aren't firms already selling as much as they want to, in LR equilibrium? The story makes no sense whatsoever. The SRAS curve should stop dead when it hits the LRAS curve. There's no way it should continue past the LRAS curve to the right.

But there's a much simpler solution than yours: drop perfect competition, and switch to monopolistic competition. (The assumption that individual firms face a downward-sloping demand curve is plausible anyway). But that is precisely what new Keynesian macroeconomists have done.

Here's my post on the same subject:
http://worthwhile.typepad.com/worthwhile_canadian_initi/2010/01/ad-as-y-output-gaps-cuba-monopolistic-competition-and-recalculation.html

Nick Rowe said...

And here's the same model in pictures: http://worthwhile.typepad.com/worthwhile_canadian_initi/2010/01/macroeconomics-with-monopolistic-competition-in-pictures.html

Just to be clear, I totally agree with your first 3 paragraphs. It bugs me too. But my solution is different from yours.

rosserjb@jmu.edu said...

Peter,

Another somewhat esoteric point is raised in Steve Keen's Debunking Economics. He points out that even in pure competition, demand curves are not perfectly horizontal. The mathematical ideal of atomless suppliers and consumers in the continuum of agents model is not realistic. The numbers on both sides are finite, and also prices are discrete at the one cent level (or whatever is the minimum unit of value of a given currency. Real world supply and demand curves are step functions, even if the steps are small. So, even a very small firm is operating on some step, and a change in its quantity supplied might move the market over or off a tiny step.

kevin quinn said...

Peter: what about getting excess supply from agency considerations where quality is non-contractible? The excess of price above MC is then a rent to enforce good performance by strict analogy with the Shapiro-Stiglitz efficiency wage model.

Peter Dorman said...

Nick, how does monopolistic competition give you excess supply? The downward-sloping D curve is a different issue, no?

Kevin, I agree that the use of price as a quality signal can generate excess supply. The problem I have is that excess supply strikes me as the norm in capitalism, not an exception to be explained in certain markets with asymmetric information.

Nick Rowe said...

Peter: suppose you estimate your demand curve, set your profit maximising price where MR=MC, expecting 100 buyers. Then you are surprised to see 110 buyers. And you can't change your price, because you have already advertised it. What do you do?

If you were a perfectly competitive firm, with P=MR=MC, and an upward-sloping MC curve, you would accept the first 100 buyers, and turn away the next 10, because MC>P once you get past 100 buyers. Or, if you felt you had a duty to serve them, you still wouldn't he happy about it. You would lose profits on the marginal buyer, past 100.

But if you are an imperfectly competitive firm, where P>MC, you would be very happy to see the extra buyers, and will happily get the extra profits by serving all 110 (just as long as your MC curve isn't too steep, and doesn't rise above P until after 110).

Once it has set its price, and can't change it till next year, a monopolistically competitive firm has MR=P.

Again, this insight underlies New Keynesian macro, with its assumption of monopolistic competition. (Though most New Keynesian macroeconomists have forgotten it, like everything else, because it's hidden in the math).

Peter Dorman said...

Nick, I'm still not seeing excess supply there. To be very precise, given a gaussian ex ante distribution of quantities demanded at any given price, why would the monopolistically competitive firm select a target output greater than the mean of this distribution? If they don't, and they select the mean instead, doesn't this mean that expected S equals expected D?

chrismealy said...

If I understand Bowles's and Gintis's contested exchange (which is a generalization of efficiency wages), when contracts are incomplete the supplier receives an enforcement rent. The buyer has the power to punish the seller by not renewing the contract. Because the equilibrium price is above market clearing suppliers would be happier to produce more at that price but buyers don't want any more. B and G apply the contested exchange approach to labor, consumer goods, credit, etc. I think it's pretty cool because it combines price, quantity, and quality. Economists hardly ever talk about quality.

(There's a case were the enforcement rent goes the other way, from the seller to the buyer, but I'm fuzzy on the details. Maybe it was the market for debt?)

kevin quinn said...

Chrismealy: yes, this is what I was alluding to as well, but the situation is exactly the same in both labor and product markets where quality is non-contractible and unobservable: the firm sells to the buyer just as the worker sells to the firm: in both cases it is the buyer who pays an enforcement rent, and in both cases the result is excess supply. But as Peter says, this can't work generally - only in cases where quality is non-contractible. I am persuaded by Nick's argument that monopolistic competition may be the way to go.

Nick Rowe said...

Peter: but suppose they don't set a quantity. Suppose they set a price instead. (Which nearly all firms do). Then they produce whatever is demanded.

Sure, they expect to produce where MR=MC. And on average they will produce where MR=MC. But once the price has been set, they are willing and very happy indeed to produce up to the point where MC=P. Because their profits increase if they produce and sell more, given the price.

Ex post they are very happy to produce more than the ex ante profit-maximising output, given the price they have previously set, which was at the ex-ante profit-maximising level, and is above MC.

Nick Rowe said...

I've done a post, with a picture, to try to explain it more clearly: http://worthwhile.typepad.com/worthwhile_canadian_initi/2010/11/excess-supply-under-monopolistic-competition.html