24 October 2021

When do markets fail to clear?

In a recent paper that went viral Jeremy B. Rudd, a Fed economist, wrote: "Mainstream economics is replete with ideas that 'everyone knows' to be true, but that are actually arrant nonsense."

Here I deal with the second "nonsense" idea mentioned by Rudd: "Over a sufficiently long span--specifically, one that allows necessary price adjustments to be made--the economy will return to a state of full market clearing."

Expositions of General Equilibrium Theory and neoclassical economics usually begin by assuming market clearing. In reality we know that markets do not always clear, a fact conceded even by Kenneth Arrow when he observed in his Nobel Prize lecture that "the history of the capitalist system has been marked by recurring periods in which the supply of available labour and of productive equipment available for the production of goods has been in excess of their utilisation, sometimes, as in the 1930s, by very considerable magnitudes."

So, when do markets clear and when do they not? That is what this post will examine.

Fig 1 shows a demand curve and a supply curve for a good that intersect at a point of equilibrium P. If the price is set at a level above the equilibrium price, then, at that point, the quantity that consumers are willing to buy is less than the quantity that suppliers are willing to sell; the oversupply is given by the length of QR. Suppliers therefore reduce the price until demand and supply are once again equal. P is a point of stable equilibrium because deviations from that point set into motion forces that return the equilibrium to P. The price at P is also a market-clearing price because the quantity that consumers are willing to buy at that price is equal to the quantity that suppliers are willing to sell at that price.

Fig 2 shows what happens when the demand curve falls from DD to D1D1. The point of equilibrium moves from P to P1. At this new point of equilibrium both the price and the quantity are lower than at P. What is more important is that the shift to P1 does not set into motion forces that restore the equilibrium to P. That happens only when the demand curve moves back to its earlier position. However, P1 can still be regarded as a market-clearing point because suppliers do not wish to supply a larger quantity at that price.

Thus, when the demand curve for a good shifts, we are confronted not with a single stable equilibrium but with multiple equilibria.

Curiously, Fig 2, which depicts the microeconomics of a single good, is consistent with Keynesian macroeconomics: when aggregate demand falls there is no automatic mechanism that returns the economy to its original position. The lower point of intersection of the aggregate demand curve with the aggregate supply curve is also a point of equilibrium. A common charge against Keynesian macroeconomics is that it has no microeconomics. And yet, as Fig 2 suggests, the microeconomics of demand and supply yield the same conclusion as Keynesian macroeconomics.

But how would market non-clearing be depicted in a diagram? In other words, if suppliers were willing to sell more than they do at the current market price what would the supply curve look like? Fig 3 shows the situation.

When the demand curve shifts from DD to DD1 the point of equilibrium moves from P to P1. Between P1 and P the supply curve is horizontal. Suppliers are willing to sell a greater quantity than at P1 at the same price as at P1 but cannot because demand is not high enough.

When the good being considered is labour Fig 3 looks plausible. During a severe recession, the unemployed are willing to work at the market wage but cannot find work. That wages do not rise for a long time after a recession even though employment increases lends credibility to Fig 3. The General Theory went a step further and considered the labour supply curve as sloping downward during a recession: "Men are involuntarily unemployed if, in the event of a small rise in the price of wage-goods relatively to the money-wage, both the aggregate supply of labour willing to work for the current money-wage and the aggregate demand for it at that wage would be greater than the existing volume of unemployment." Keynes was of course thinking of real wages, not nominal wages. Workers are willing to work for a wage even lower than the market wage because whether they obtain employment or not, they have to incur the expense of keeping themselves and their families alive.

The assumption of market clearing amounts to saying that the situation of Fig 3 is not possible. It thus depends on two other assumptions: 1. That the supply curve is nowhere horizontal, and 2. That the demand curve does not shift. We shall consider each of these assumptions in turn.

The idea that the supply curve is nowhere horizontal is refuted by the ideas in Chapter 6 of The General Theory, probably one of the most important chapters in the book and the least understood. I think of it as an anticipatory demolition of the Samuelson kind of neoclassical economics. The chapter can be summarised in two sentences: 1. Marginal cost is not equal to marginal factor cost, and 2. Fixed investment does not become zero at the margin of production. In my book Economics Redefined I have showed, for example, that the ideas in Chapter 6 disprove the mathematics of profit maximisation. But here we are concerned with its implications for the shape of the supply curve.

Rather than explain the idea using Keynes's terminology I use an example. Imagine that you are a manufacturer of shoes and have invested $1 million in a new production line. Let the variable cost of a pair of shoes (leather, labour, power etc) be $50. You set the price of a pair of shoes at $100. When you sell one pair of shoes you pay off $50 from the cost of your fixed investment. Imagine that you are at point P1 of Fig 3 where you sell 2,000 pairs of shoes a month and can pay off $100,000 of fixed investment. If the demand curve moves to DD where you can sell 4,000 pairs of shoes a month you would still be happy to sell at the same price because at that point you can pay off an additional $200,000 of your fixed investment each month. (Remember that it is only after you have paid off your entire fixed investment that you begin to make a profit.) Even if the variable cost goes up by, say, $5, it would still make economic sense to sell at the same price as before or even lower.

But this means that the supply curve can be horizontal or even slope downwards. And if supply curves are horizontal or slope downwards in an interval then it is obvious that the market does not clear over that interval.

That brings us to the second assumption in market clearing: that the demand curve does not shift, i.e., we are dealing with Fig 1 and not Fig 2. A common objection to using the three figures above is that they depict situations of partial equilibrium and, in particular, that they assume all other prices are constant. In a paper published in 2017 in real-world economics review (A diagrammatic derivation of involuntary unemployment from Keynesian microfoundations), and more elegantly in my book, I showed that this is incorrect. A downward sloping demand curve of the kind in Figs 1 to 3 cannot simultaneously fulfil the conditions that income is constant and all other prices remain constant. The proof requires nothing more sophisticated than school mathematics. There is only one exception to this rule and that is the demand curve in the form of the rectangular hyperbola.

Demand curves in the shape of the rectangular hyperbola have several interesting properties. For one, they can be aggregated arithmetically, so the aggregate demand curve can be derived from the demand curves of heterogeneous agents, thus dispensing with a representative agent; in fact, all demand curves have the same shape. Two, they do not assume that tastes are constant or that other prices are constant or that aggregate demand is constant. They are thus the most general demand curves. Three, the rectangular hyperbola which is a curve of constant demand is also a curve of constant money; this resolves the dispute between monetarists and Keynesians, the one contending that recessions are caused by a contraction of money and the other that recessions are caused by a contraction of aggregate demand.

But here we are concerned with another interesting property. In conventional Marshallian economics, when demand changes, we cannot be sure whether we must stay on the same demand curve or move to a different demand curve. When the demand curve is a rectangular hyperbola there is no such ambiguity. When demand (measured in money) changes, the demand curve has of necessity to shift; in other words, we have to deal with a different rectangular hyperbola. Where the curve in Fig 1 is a static curve, the rectangular hyperbola is a dynamic curve; it moves with every change in demand.

For small changes in demand, however, we can approximate the shift in demand with a single demand curve as in Fig 4 and thus revert to the static version. The figure shows two demand curves xy = a and xy = b. If demand shifts by small amounts then the two curves can be replaced by a single curve and the analysis thus reduces from the general Keynesian case to the particular Marshallian case. This is of course consistent with Keynes's claim that his book dealt with the general case in which aggregate demand changes whereas his predecessors dealt with the particular case in which aggregate demand does not change.

So, to return to the title of this post: when do markets fail to clear?

There are two conditions to be met. One, the demand curve should shift. But, as we have seen, when the demand curve is the rectangular hyperbola, it shifts with every change in demand. So, this condition is always fulfilled. However, for small changes in demand, the two rectangular hyperbolas can be replaced by a single curve. We can thus say that as long as demand stays within narrow bounds of full-employment equilibrium the market clears.

The second condition is that when the supply curve is horizontal over any interval, the market does not clear over that interval. This happens when a firm has made a substantial investment expecting rising demand and, instead, demand falls. In that case, the first priority of the firm is to recover its fixed investment as quickly as possible, and to do that it is willing to maintain its price or even lower it if demand rises.

In a recession both these conditions are fulfilled and it can be said definitely that there is then no market clearing in many or most markets.

Category: Economics

Philip George
Understanding Keynes to go beyond him

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