Uneasy Money

Just about the first thing taught to economics students is that there are demand curves for goods and services and supply curves of goods and services. Demand curves show how much customers wish to buy of a particular good or service within a period of time at various prices that might be charged for that good or service. The supply curve shows how much suppliers of a good or service would offer to sell at those prices.

Economists assume, and given certain more basic assumptions can (almost) prove, that customers will seek to buy less at higher prices for a good or service than at lower prices. Similarly, they assume that suppliers of the good or service offer to sell more at higher prices than at lower prices. Reflecting those assumptions, demand curves are downward-sloping and supply curve are upward-sloping. An upward-sloping supply curve is likely to intersect a downward-sloping demand curve at a single point, which corresponds to an equilibrium that allows customers to buy as much as they want to and suppliers to sell as much as they want to in the relevant time period.

This analysis is the bread and butter of economics. It leads to the conclusion that, when customers can’t buy as much as they would like, the price goes up, and, when suppliers can’t sell as much as they would like, the price goes down. So the natural tendency in any market is for the price to rise if it’s less than the equilibrium price, and to fall if it’s greater than the equilibrium price. This is the logic behind letting the market determine prices.

It can also be shown, if some further assumptions are made, that the intersection of the supply and demand curves represents an optimal allocation of resources in the sense that the total value of output is maximized. The necessary assumptions are, first, that the demand curve measures the marginal value placed on additional units of output, and, second, that the supply curve measures the marginal cost of producing additional units of output. The intersection of the supply and the demand curves corresponds to the maximization of the total value of output, because the marginal cost represents the value of output that could have been produced if the resources devoted to producing the good in question had been shifted to more valuable uses. When the supply curve rises above the demand curve it means that the resources would produce a greater value if devoted to producing something else than the value of the additional output of the good in question.

There is much to be said for the analysis, and it would be wrong to dismiss it. But it’s also important to understand its limitations, and, especially, the implicit assumptions on which it relies. In a sense, supply-demand analysis is foundational, the workhorse model that is the first resort of economists. But its role as a workhorse model does not automatically render analyses untethered to supply and demand illegitimate.

Supply-demand analysis has three key functions. First, it focuses attention on the idea of an equilibrium price at which all buyers can buy as much as they would like, and all sellers can sell as much as they would like. In a typical case, with an upward sloping supply curve and a downward-sloping demand curve, there is one, and only one, price with that property.

Second, as explained above, there is a sense in which that equilibrium price, aside from enabling the mutual compatibility of buyers’ and sellers’ plans to buy or to sell, has optimal properties.

Third, it’s a tool for predicting how changes in market conditions, like imposing a sales or excise tax, affect customers and suppliers. It compares two equilibrium positions on the assumption that only one parameter changes and predicts the effect of the parameter change by comparing the new and old equilibria. It’s the prototype for the comparative-statics method.

The chief problem with supply-demand analysis is that it requires a strict ceteris-paribus assumption, so that everything but the price and the quantity of the good under analysis remains constant. For many reasons, that assumption can’t literally be true. If the price of the good rises (falls), the real income of consumers decreases (increases). And if the price rises (falls), suppliers likely pay more (less) for their inputs. Changes in the price of one good also affect the prices of other goods, which, in turn, may affect the demand for the good under analysis. Each of those consequences would cause the supply and demand curves to shift from their initial positions. How much the ceteris-paribus assumption matters depends on how much of their incomes consumers spend on the good under analysis. The more they spend, the less plausible the ceteris paribus assumption.

But another implicit assumption underlies supply-demand analysis: that the economic system starts from a state of general equilibrium. Why must this assumption be made? The answer is that it‘s implied by the ceteris-paribus assumption that all other prices remain constant. Unless other markets are in equilibrium, it can’t be assumed that all other prices and incomes remain constant; if they aren’t, then prices for other goods, and for inputs used to produce the product under analysis, will change, violating the ceteris-paribus assumption. Unless the prices (and wages) of the inputs used to produce the good under analysis remain constant, the supply curve of the product can’t be assumed to remain unchanged.

On top of that, Walras’s Law implies that if one market is in disequilibrium, then at least one other market must also be in disequilibrium. So an internal contradiction lies at the heart of supply-demand analysis. The contradiction can be avoided, but not resolved, only by assuming that the market being analyzed is so minute relative to the rest of the economy, or so isolated from all other markets, that a disturbance in that market that changes its equilibrium position either wouldn’t disrupt the existing equilibrium in all other markets, or that the disturbances to the equilibria in all the other markets are so small that they can be safely ignored.

But we’re not done yet. The underlying general equilibrium on which the partial equilibrium (supply-demand) analysis is based, exists only conceptually, not in reality. Although it’s possible to prove the existence of such an equilibrium under more or less mathematically plausible assumptions about convexity and the continuity of the relevant functions, it is less straightforward to prove that the equilibrium is unique, or at least locally stable. If it is not unique or locally stable, there is no guarantee that comparative statics is possible, because a displacement from an unstable equilibrium may cause an unpredictable adjustment violates the ceteris-paribus assumption.

Finally, and perhaps most problematic, comparative statics is merely a comparison of two alternative equilibria, neither of which can be regarded as the outcome of a theoretically explicable, much less practical, process leading from initial conditions to the notional equilibrium state. Accordingly, neither is there any process whereby a disturbance to – a parameter change in — an initial equilibrium would lead from the initial equilibrium to a new equilibrium. That is what comparative statics means: the comparison of two alternative and disconnected equilibria. There is no transition from one to the other merely a comparison of the difference between them attributable to the change in a particular parameter in the initial conditions underlying the equilibria.

Given all the assumptions that must be satisfied for the basic implications of conventional supply-demand analysis to be unambiguously valid, that analysis obviously cannot provide demonstrably true predictions. As just explained, the comparative-statics method in general and supply-demand analysis in particular provide no actual predictions; they are merely conjectural comparisons of alternative notional equilibria.

The ceteris paribus assumption is often dismissed as making any theory tautological and untestable. If an ad hoc assumption introduced when observations don’t match the predictions derived from a given theory is independently testable, it adds to the empirical content of the theory, as demonstrated by the ad hoc assumption of an eighth planet (Neptune) in our solar system when predictions about the orbits of the seven known planets did not accord with their observed orbits.

Friedman’s famous methodological argument that only predictions, not assumptions, matter is clearly wrong. Economists have to be willing to modify assumptions and infer the implications that follow from modified or supplementary assumptions rather than take for granted that assumptions cannot meaningfully and productively affect the implications of a general analytical approach. It would be a travesty if physicists maintained the no-friction assumption, because it’s just a simplifying assumption to make the analysis tractable. That approach is a prescription for scientific stagnation.

The art of economics is to identify the key assumptions that ought to be modified to make a general analytical approach relevant and fruitful. When they are empirically testable, ad hoc assumptions that modify the ceteris paribus restriction constitute scientific advance.

But it’s important to understand how tenuous the connection is between the formalism of supply-demand analysis and of the comparative-statics method and the predictive power of that analysis and that method. The formalism stops far short of being able to generate clear and unambiguous conditions. The relationship between the formalism and the real world is tenuous and the apparent logical rigor of the formalism must be supplemented by notable and sometimes embarrassing doses of hand-waving or question-begging.

And it is also worth remembering the degree to which the supposed rigor of neoclassical microeconomic supply-demand formalism depends on the macroeconomic foundation of the existence (and at least approximate reality) of a unique or locally stable general equilibrium.