Archive for the 'supply-demand analysis' Category

General Equilibrium, Partial Equilibrium and Costs

Neoclassical economics is now bifurcated between Marshallian partial-equilibrium and Walrasian general-equilibrium analyses. With the apparent inability of neoclassical theory to explain the coordination failure of the Great Depression, J. M. Keynes proposed an alternative paradigm to explain the involuntary unemployment of the 1930s. But within two decades, Keynes’s contribution was subsumed under what became known as the neoclassical synthesis of the Keynesian and Walrasian theories (about which I have written frequently, e.g., here and here). Lacking microfoundations that could be reconciled with the assumptions of Walrasian general-equilibrium theory, the neoclassical synthesis collapsed, owing to the supposedly inadequate microfoundations of Keynesian theory.

But Walrasian general-equilibrium theory provides no plausible, much less axiomatic, account of how general equilibrium is, or could be, achieved. Even the imaginary tatonnement process lacks an algorithm that guarantees that a general-equilibrium solution, if it exists, would be found. Whatever plausibility is attributed to the assumption that price flexibility leads to equilibrium derives from Marshallian partial-equilibrium analysis, with market prices adjusting to equilibrate supply and demand.

Yet modern macroeconomics, despite its explicit Walrasian assumptions, implicitly relies on the Marshallian intuition that the fundamentals of general-equilibrium, prices and costs are known to agents who, except for random disturbances, continuously form rational expectations of market-clearing equilibrium prices in all markets.

I’ve written many earlier posts (e.g., here and here) contesting, in one way or another, the notion that all macroeconomic theories must be founded on first principles (i.e., microeconomic axioms about optimizing individuals). Any macroeconomic theory not appropriately founded on the axioms of individual optimization by consumers and producers is now dismissed as scientifically defective and unworthy of attention by serious scientific practitioners of macroeconomics.

When contesting the presumed necessity for macroeconomics to be microeconomically founded, I’ve often used Marshall’s partial-equilibrium method as a point of reference. Though derived from underlying preference functions that are independent of prices, the demand curves of partial-equilibrium analysis presume that all product prices, except the price of the product under analysis, are held constant. Similarly, the supply curves are derived from individual firm marginal-cost curves whose geometric position or algebraic description depends critically on the prices of raw materials and factors of production used in the production process. But neither the prices of alternative products to be purchased by consumers nor the prices of raw materials and factors of production are given independently of the general-equilibrium solution of the whole system.

Thus, partial-equilibrium analysis, to be analytically defensible, requires a ceteris-paribus proviso. But to be analytically tenable, that proviso must posit an initial position of general equilibrium. Unless the analysis starts from a state of general equilibrium, the assumption that all prices but one remain constant can’t be maintained, the constancy of disequilibrium prices being a nonsensical assumption.

The ceteris-paribus proviso also entails an assumption about the market under analysis; either the market itself, or the disturbance to which it’s subject, must be so small that any change in the equilibrium price of the product in question has de minimus repercussions on the prices of every other product and of every input and factor of production used in producing that product. Thus, the validity of partial-equilibrium analysis depends on the presumption that the unique and locally stable general-equilibrium is approximately undisturbed by whatever changes result from by the posited change in the single market being analyzed. But that presumption is not so self-evidently plausible that our reliance on it to make empirical predictions is always, or even usually, justified.

Perhaps the best argument for taking partial-equilibrium analysis seriously is that the analysis identifies certain deep structural tendencies that, at least under “normal” conditions of moderate macroeconomic stability (i.e., moderate unemployment and reasonable price stability), will usually be observable despite the disturbing influences that are subsumed under the ceteris-paribus proviso. That assumption — an assumption of relative ignorance about the nature of the disturbances that are assumed to be constant — posits that those disturbances are more or less random, and as likely to cause errors in one direction as another. Consequently, the predictions of partial-equilibrium analysis can be assumed to be statistically, though not invariably, correct.

Of course, the more interconnected a given market is with other markets in the economy, and the greater its size relative to the total economy, the less confidence we can have that the implications of partial-equilibrium analysis will be corroborated by empirical investigation.

Despite its frequent unsuitability, economists and commentators are often willing to deploy partial-equilibrium analysis in offering policy advice even when the necessary ceteris-paribus proviso of partial-equilibrium analysis cannot be plausibly upheld. For example, two of the leading theories of the determination of the rate of interest are the loanable-funds doctrine and the Keynesian liquidity-preference theory. Both these theories of the rate of interest suppose that the rate of interest is determined in a single market — either for loanable funds or for cash balances — and that the rate of interest adjusts to equilibrate one or the other of those two markets. But the rate of interest is an economy-wide price whose determination is an intertemporal-general-equilibrium phenomenon that cannot be reduced, as the loanable-funds and liquidity preference theories try to do, to the analysis of a single market.

Similarly partial-equilibrium analysis of the supply of, and the demand for, labor has been used of late to predict changes in wages from immigration and to advocate for changes in immigration policy, while, in an earlier era, it was used to recommend wage reductions as a remedy for persistently high aggregate unemployment. In the General Theory, Keynes correctly criticized those using a naïve version of the partial-equilibrium method to recommend curing high unemployment by cutting wage rates, correctly observing that the conditions for full employment required the satisfaction of certain macroeconomic conditions for equilibrium that would not necessarily be satisfied by cutting wages.

However, in the very same volume, Keynes argued that the rate of interest is determined exclusively by the relationship between the quantity of money and the demand to hold money, ignoring that the rate of interest is an intertemporal relationship between current and expected future prices, an insight earlier explained by Irving Fisher that Keynes himself had expertly deployed in his Tract on Monetary Reform and elsewhere (Chapter 17) in the General Theory itself.

Evidently, the allure of supply-demand analysis can sometimes be too powerful for well-trained economists to resist even when they actually know better themselves that it ought to be resisted.

A further point also requires attention: the conditions necessary for partial-equilibrium analysis to be valid are never really satisfied; firms don’t know the costs that determine the optimal rate of production when they actually must settle on a plan of how much to produce, how much raw materials to buy, and how much labor and other factors of production to employ. Marshall, the originator of partial-equilibrium analysis, analogized supply and demand to the blades of a scissor acting jointly to achieve a intended result.

But Marshall erred in thinking that supply (i.e., cost) is an independent determinant of price, because the equality of costs and prices is a characteristic of general equilibrium. It can be applied to partial-equilibrium analysis only under the ceteris-paribus proviso that situates partial-equilibrium analysis in a pre-existing general equilibrium of the entire economy. It is only in general-equilibrium state, that the cost incurred by a firm in producing its output represents the value of the foregone output that could have been produced had the firm’s output been reduced. Only if the analyzed market is so small that changes in how much firms in that market produce do not affect the prices of the inputs used in to produce that output can definite marginal-cost curves be drawn or algebraically specified.

Unless general equilibrium obtains, prices need not equal costs, as measured by the quantities and prices of inputs used by firms to produce any product. Partial equilibrium analysis is possible only if carried out in the context of general equilibrium. Cost cannot be an independent determinant of prices, because cost is itself determined simultaneously along with all other prices.

But even aside from the reasons why partial-equilibrium analysis presumes that all prices, but the price in the single market being analyzed, are general-equilibrium prices, there’s another, even more problematic, assumption underlying partial-equilibrium analysis: that producers actually know the prices that they will pay for the inputs and resources to be used in producing their outputs. The cost curves of the standard economic analysis of the firm from which the supply curves of partial-equilibrium analysis are derived, presume that the prices of all inputs and factors of production correspond to those that are consistent with general equilibrium. But general-equilibrium prices are never known by anyone except the hypothetical agents in a general-equilibrium model with complete markets, or by agents endowed with perfect foresight (aka rational expectations in the strict sense of that misunderstood term).

At bottom, Marshallian partial-equilibrium analysis is comparative statics: a comparison of two alternative (hypothetical) equilibria distinguished by some difference in the parameters characterizing the two equilibria. By comparing the equilibria corresponding to the different parameter values, the analyst can infer the effect (at least directionally) of a parameter change.

But comparative-statics analysis is subject to a serious limitation: comparing two alternative hypothetical equilibria is very different from making empirical predictions about the effects of an actual parameter change in real time.

Comparing two alternative equilibria corresponding to different values of a parameter may be suggestive of what could happen after a policy decision to change that parameter, but there are many reasons why the change implied by the comparative-statics exercise might not match or even approximate the actual change.

First, the initial state was almost certainly not an equilibrium state, so systemic changes will be difficult, if not impossible, to disentangle from the effect of parameter change implied by the comparative-statics exercise.

Second, even if the initial state was an equilibrium, the transition to a new equilibrium is never instantaneous. The transitional period therefore leads to changes that in turn induce further systemic changes that cause the new equilibrium toward which the system gravitates to differ from the final equilibrium of the comparative-statics exercise.

Third, each successive change in the final equilibrium toward which the system is gravitating leads to further changes that in turn keep changing the final equilibrium. There is no reason why the successive changes lead to convergence on any final equilibrium end state. Nor is there any theoretical proof that the adjustment path leading from one equilibrium to another ever reaches an equilibrium end state. The gap between the comparative-statics exercise and the theory of adjustment in real time remains unbridged and may, even in principle, be unbridgeable.

Finally, without a complete system of forward and state-contingent markets, equilibrium requires not just that current prices converge to equilibrium prices; it requires that expectations of all agents about future prices converge to equilibrium expectations of future prices. Unless, agents’ expectations of future prices converge to their equilibrium values, an equilibrium many not even exist, let alone be approached or attained.

So the Marshallian assumption that producers know their costs of production and make production and pricing decisions based on that knowledge is both factually wrong and logically untenable. Nor do producers know what the demand curves for their products really looks like, except in the extreme case in which suppliers take market prices to be parametrically determined. But even then, they make decisions not on known prices, but on expected prices. Their expectations are constantly being tested against market information about actual prices, information that causes decision makers to affirm or revise their expectations in light of the constant flow of new information about prices and market conditions.

I don’t reject partial-equilibrium analysis, but I do call attention to its limitations, and to its unsuitability as a supposedly essential foundation for macroeconomic analysis, especially inasmuch as microeconomic analysis, AKA partial-equilibrium analysis, is utterly dependent on the uneasy macrofoundation of general-equilibrium theory. The intuition of Marshallian partial equilibrium cannot fil the gap, long ago noted by Kenneth Arrow, in the neoclassical theory of equilibrium price adjustment.

What’s so Great about Supply-Demand Analysis?

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.

About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey's unduly neglected contributions to the attention of a wider audience.


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