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.
Uneasy Money 
I believe that Keynes used Marshall’s ceteris paribus methodology to establish causality in providing an analytical framework in which a logically consistent causal analysis of dynamic behavior is possible and not for the purpose of comparative static analysis. See:
Click to access KIMVT.pdf
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David,
Interesting essay however, I think it is a tad confused and misses the point.
I am not sure at times whether you are wanting to deal with partial equilibrium and general equilibrium analysis as microeconomics or macroeconomics. You seem to wind and wend you way through both territories. I would expect that it is more the later you are interested in.
PET and GET are essentially theories of the microeconomy and deal with relative prices and assume full utilization of resources, irrespective of whether it is of the Marshallian, Walrasian or Arrow/Debreu kind..
I have yet to see a cogent explanation for how changes in relative prices can bring about a macroeconomic effect, even where intertemporal behaviour is being considered. Theories of intertemporal behaviour explain how resource usage can be shifted from one time period to another. They do not explain how resource usage overall can be increased.
There is also the problem of the independence of demand and supply curves when dealing with macro issues. Both PET and GET assume that this independence exists. Where full employment of resources is assumed then the assumption of independence is valid. Where the level of income becomes a variable it is not.
Macroeconomics is about the level of spending and income. PET and GET do not deal with the level of spending or income.
Much is said about the microfoundations of macroeconomics. Microeconomics, strictly applied, cannot deal with macro issues. However, when the assumption of a fixed level of income is relaxed, microeconomics can be brought to bear on macro issues.
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Henry, You are not wrong to note that this post is not entirely coherent. In my own defense, I would just say that I am trying to tie together a number of different threads into a larger fabric of which this post is merely an introduction. So think of it as a first draft of a work in progress.
You ask whether I think of partial equilibrium as micro analysis or macro analysis. My answer is that partial equilibrium is appropriately the domain of micro analysis, but I point out that sometimes partial equilibrium analysis is deployed to handle topics such as involuntary unemployment that don’t conform to and can’t accommodate the ceteris paribus assumption that underlies partial equilibrium analysis.
General equilibrium analysis occupies the space between micro and macroanalysis so it offers a window or a path between them which helps us to identify the links between micro and macroanalysis and the points at which those links break down. It is those broken links or actual roadblocks that have to be identified and overcome before we can achieve a satisfactory or satisfying macroeconomic theory, which I’m sorry to say does not yet exist.
You make certain assertions which I don’t understand. Why do you say that supply curves and demand curves must be independent? The point of general equilibrium is that everything depends on everything else, so obviously supply and demand are not independent in GE. In PE, the ceteris paribus assumption allows independence to be maintained, but the analysis has to be carried out carefully to check if the assumption can be plausibly maintained.
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David,
“General equilibrium analysis occupies the space between micro and macroanalysis ”
This is where your comments gets confusing.
The assumptions that underlie pure PET and GET are essentially the same apart for the ceteris paribus condition.They are both theories of the microeconomy based on constrained optimal resource allocation. Strictly speaking, they assume a constant level of income. The constraint is a fixed level of income. Without a fixed level of income, optimization won’t work. PET is concerned with one market for a particular good or resource. GET is concerned with all markets. This does not mean all markets in aggregate but all markets individually setting price and output. GET is not a form of aggregate macroeconomics. It is the economics of multiple individual (dependent) markets. So I cannot agree with your statement above.
What drives all these individual markets to equilibrium is the setting of RELATIVE prices.
The markets of interest in microeconomics are not independent. What happens in one market will impact others. (E.g. given land is a fixed resource, the quantity of apples grown will impact on the quantity of pears that can be grown.) When I talk of independence of supply and demand functions I am not referring to markets being interdependent. I am referring to demand and supply functions within a particular market. PET and GET assume these to be independent and where the level of income is fixed they are independent.
Macroeconomics is interested in the general level of output, employment and prices, not the level of output, employment and prices in individual markets. Relative price adjustments affect price and output in individual markets not the economy as a whole. I have yet to see a cogent explanation of how relative prices can impact the macroeconomy. If you have one, please show me. And intertemporal optimization only deals with resource allocation across time. It does not deal with the level of resource usage over time.
What impacts the general level of output, employment and prices is the level of spending, not relative prices. The general level of spending affects the general level of income. PET and GET have nothing to say about the general level of spending and income other than to assume that the general level of spending and income is fixed. What shifts equilibrium in the macroeconomy is changes in the level of spending (and hence the general level of output and employment), not changes in relative prices.
When the assumption of a fixed level of income is relaxed questions of the general level of output and employment can be studied. This is where Keynes makes his contribution.
When the assumption of a fixed level of income is removed, supply and demand functions in individual markets are no longer independent. For instance, a rise in the general level of wages will impact every labour supply function. It will also impact every labour demand function which will in turn impact all goods demand and supply functions. A shift in the demand function will cause a shift in the supply function. Simply, if every worker gets an increase in his wage he can spend more. Relative wages need have not changed.
Here’s a way of looking at what I have suggested above. Take a simple GET model with a two dimensional Production Possibility Frontier (say consumer goods against capital goods). Overlay an indifference map and an income constraint. The income constraint sets which PPF is possible and the indifference map sets the balance between the production of consumer goods and capital goods. In the process, a set of relative prices will be determined. Changes in relative prices engendered by changes in the indifference map will shift the equilibrium point along the PPF, not on to a different PPF (this is fixed by the level of income – the income constraint).
If the income constraint is now chosen to be lower or higher a different PPF comes into play. The indifference curve map will set where on the new PPF the equilibrium point is.
So changes in the level of income/spending will change the level of output (and changes in relative prices will set the composition of output). Output becomes a function of spending, which is the relationship Keynes described in the GT. The 45d line in the Keynesian Cross expresses this relationship. The consumption function describes the behaviour of the equilibrium point on the PPF as the level of spending is changed. The marginal propensity of consumption is given by the relationship that emerges between the indifference preference map and the PPF. The Keynesian Cross is an artifact of this relationship between the PPF, the indifference curve map and the level of spending.
In this way it could be said that microeconomics is the foundation of macroeconomics. It is not the foundation of macroeconmics as is conventionally conceived.
What is at the root of this analysis is the decisions economic agents make. When an EA makes a decision to buy an apple instead of a pear, it has microeconomic implications. It changes relative prices and the relative level of output between apples and pears. If there is a general increase in the level of income, then EAs can buy more of both apples and pears. Changing the relative prices of apples and pears will not impact the overall quantity of apples and pears the EA decides to consume.
A businessman, when he is deciding whether to buy machine A or machine B, is making a decision with microeconomic implications. If businessmen in general are making decisions to buy new machines (because of a general change in expectations about future income, for instance), they are making decisions with macroeconomic implications.
So there are two kinds of decision sets. Strictly speaking, GET/PET only deal with one decision set – the one that has microeconomic implications.
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Henry,
You misunderstand what general-equilibrium theory (GET) is about, and you therefore misunderstand the relationship between general equilibrium theory and partial equilibrium theory (PET).
GET does not assume a constant level of income, it determines from given assumptions what level of output and income and spending is associated with a general income, which given certain other assumptions, also turns out to be the maximum output the resources available are capable of producing. PET takes that level of output and income as its starting point and focuses attention on how a parameter change affecting a single market that is small enough to cause more than a second order change in the GE would affect one or more variables in the market under consideration.
The maximization of output associated with general equilibrium depends on the consistency of plans that individual agents seek to execute. That mutual consistency is what relative price adjustments help to achieve in a well-functioning economy. But if individual agents are attempting to execute plans that are seriously incompatible then the inconsistency of the plans will cause output in the affected markets to be less than had been planned and consequently suppliers of inputs to those markets will observe smaller demand for their inputs and services than they had been expecting. The resulting slow down in the rate of output and the decline in income and spending may have a cumulative impact on total output and total production in the entire economy. The maximization of output associated with GE is contingent of the perfect coordination of plans that results from a system of relative prices consistent with that GE. If the relative prices are not at their equilibrium levels, then the maximization of output and income will not be realized.
Your little two-sector general equilibrium exercise hugely abstracts from the complexity of an actual n-sector (where n is some number way too high ever to be counted). You can’t just assume that the economy is automatically on the PPF. Actual economies can merely approach the actual PPF in n-dimensional space. So there is clearly an interaction between macroeconomics and microeconomics that depends both on Keynesian or monetary analysis of total spending and the complex structure of actual current and expected future prices in n*t*m-dimensional space where t is the number of future time periods encompassed by the plans of agents and m is the number of agents.
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David,
I do not think that Arrow and Debreu would agree with your explanation of what GET is as a formal abstraction. They made specific assumptions about perfect foresight/knowledge etc. and income being fixed, income being the constraint against which resource usage is optimized. This is pure value theory.
The GET you are referring to attempts to integrate value/price theory with income/money theory. I do not believe it has done this effectively. It does this by invoking price rigidities and co-ordination inconsistencies which distort relative prices. I would class these phenomena as frictions. They may cause markets to not clear, but I cannot see how they are necessary for a theory of the macroeconomy. And I have yet to see a cogent explanation for how relative prices have a macroeconomic effect.
Keynes developed a theory of income determination which does not require these frictions. He was able to explain why an economy can sit below full factor employment interminably. This was the essence of his revolution. His explanation, in essence, revolved around expectations about future levels of income, not relative prices. Pre-Keynesian economists may have recognized that economies can operate at less than full employment for a time but they believed adjustment was automatically possible with time.
My “little” model may not be of the all-dancing, all-singing variety. It’s purpose was to explain simply want I was proposing as a way of integrating microeconomic theory (value/prices theory) and macroeconomic theory (income/money theory). And I have to say that in reading your blog for the last five or so years I have yet to see any formal exposition of how your version of macroeconomics works.
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Henry,
I don’t know what you mean when you refer to “[my] explanation of what GET is as a formal abstraction.” Arrow and Debreu actually replaced unrealistic assumptions about perfect foresight/knowledge with even more unrealistic assumptions about an imaginary institutional setup with an auctioneer conducting a timeless tatonnement process. But you are misinterpreting the assumption that households are subject to a budget constraint (aka Walras’s Law).
That budget constraint is conditional on the specific price vector announced by the auctioneer. Given the budget constraint implied by that price vector, households and firms make choices that are inconsistent and the realized income at that price vector would fail to correspond to a point on the PPF. If you were to calculate the notional incomes corresponding to successive disequilibrium price vectors announced by the auctioneer, those successive notional incomes would all be less than the income level corresponding to the (Pareto-optimal equilibrium) price vector finally arrived at by the auctioneer. So your assertion that there is any assumption of a fixed income in GET is simply a category error. And trust me, Henry, I do not require your lessons in pure value theory.
Integrating value theory and monetary theory is not easy, and I have no problem admitting that it has not yet been done adequately. But the reasons have nothing to do with “price rigidities.” I regard price rigidities as a distraction. The problem is trading at disequilibrium prices, which is assumed away by the tatonnement process. But it is an unavoidable characteristic of any actual economy. Prices can more around freely and still not correspond to the equilibrium price vector of GET.
If you “have yet to see a cogent explanation for how relative prices have a macroeconomic effect,” that is your problem, not mine.
I have great respect for Keynes’s theory of income determination and there is a deep insight in his theory of underemployment equilibrium, but I don’t think that equilibrium is a good description of the underlying pathology he was analyzing. You are also wrong (for reasons implicit in what I wrote above) to posit a sharp distinction between expectations about future prices and future income levels).
Just because many, but not all, pre-Keynesian economists believed adjustment to unemployment is automatically possible with time, it is does not follow that they had nothing important to say or that we cannot benefit from their insight. Nobody ever described the problem of unemployment more succinctly or more insightfully than Keynes’s older and entirely orthodox contemporary Frederick Lavington who wrote: “The idleness of each is the result of the idleness of all.”
It may be true that “[you] have yet to see any formal exposition of how [my] version of macroeconomics works.” But I’m not overly impressed by formal expositions or formal model. Formal expositions have their place, but a proper understanding of the problem is necessary before any formal exposition can be useful. I’m more concerned with properly understanding and characterizing the macroeconomic problem than with providing a formal macroeconomic model.
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“If you were to calculated the notional incomes corresponding to successive disequilibrium price vectors announced by the auctioneer, those successive notional incomes would all be less than the income level corresponding to the (Pareto-optimal equilibrium) price vector finally arrived at by the auctioneer. ”
At equilibrium there is a particular income level. If this income level does not pertain there will be no equilibrium. Equilibrium is defined as the point where the budget constraint (the level of income) is tangent to the PPF. In that sense it is fixed. In a Walrasian tatonnement process no trading occurs until prices are set such that all markets clear, i.e. until there is equilibrium. If no level of income is specified, economic agents cannot make decisions about which goods they can purchase at the price vector offered by the auctioneer. If a given (maximum) level of income is not specified then equilibrium cannot be determined.
“If you “have yet to see a cogent explanation for how relative prices have a macroeconomic effect,” that is your problem, not mine.”
It is not my problem, it is general equilibrium theory’s problem.
“.. it is does not follow that they had nothing important to say or that we cannot benefit from their insight.”
I did not say that. I implied they had nothing of importance to say when disequilibrium conditions pertained. They were content in the belief that markets would automatically adjust.
“But I’m not overly impressed by formal expositions or formal model.”
Perhaps this is just me, but when you discuss these matters it seems you range and wander over all kinds of territory without being explicit. You wend and wind through abstract theory and real world applications as if there was no difference. I find this very confusing.
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Henry,
You wrote:
“At equilibrium there is a particular income level. If this income level does not pertain there will be no equilibrium.”
No, no, no. A thousand times no! At equilibrium, there are resource endowments and a production technology or a set of feasible technologies and a price vector announced by the auctioneer; that’s all; everything else — production and consumption by agents, output and income is determined simultaneously given that price vector. If you don’t understand that a system of equations in an equilibrium determines all variables simultaneously given the equilibrium price vector, you need to go and study until you do understand that. End of discussion.
You said:
“Equilibrium is defined as the point where the budget constraint (the level of income) is tangent to the PPF. In that sense it is fixed.”
Again, that’s just wrong. Equilibrium is defined as a set of prices at which all the optimal individual plans of agents are mutually consistent and can be executed without change or regret. The tangency of the budget constraints, individual indifference curves and marginal rates of substitution are properties of an equilibrium not the definition of an equilibrium. You are just mixing up concepts and making pronouncements as if they were authoritative. They aren’t. Income is not fixed, it is determined along with all other variables. If you don’t understand that, that’s your problem, not mine.
You said:
“In a Walrasian tatonnement process no trading occurs until prices are set such that all markets clear, i.e. until there is equilibrium. If no level of income is specified, economic agents cannot make decisions about which goods they can purchase at the price vector offered by the auctioneer. If a given (maximum) level of income is not specified then equilibrium cannot be determined.”
Agents in Walrasian tatonnement are able to formulate plans based on their resource endowments, their ownership shares in firm profits, and they can simultaneously calculate, subject to their budget constraints, how much they want to buy and how much they want to sell, of every good and service at every price vector announced by the autctioneer. So each agent can calculate his/her optimal income and expenditure conditional on the announced price vector. If the announced price vector is an equilibrium price vector the tatonnement is complete and all trades are executed at that price vector. Thus, income and expenditure are determined conditional on the equilibrium price vector, the equilibrium income and expenditure is not conditional on income. End of story.
You said:
“It is not my problem, it is general equilibrium theory’s problem.”
General-equilibrium theory has many, many problems. That is not one of them.
You said:
“I implied they [pre-Keynesian economists] had nothing of importance to say when disequilibrium conditions pertained. They were content in the belief that markets would automatically adjust.
Maybe some were; others, as the quotation from Lavington demonstrates, were not.
You said:
“Perhaps this is just me, but when you discuss these matters it seems you range and wander over all kinds of territory without being explicit. You wend and wind through abstract theory and real world applications as if there was no difference. I find this very confusing.”
This is just a blog, not a treatise. I write about topics that interest me. I may not always express myself as lucidly as I would like, and getting feedback from attentive readers like yourself helps me to clarify my thinking about many issues. That’s why writing this blog for 10 years has made me a much better economist than I was when I started. And I thank you and other readers for pushing me to explain my arguments more clearly when they don’t understand what I’m saying. But WADR, Henry, you just refuse to stop making the same objection over and over again even after I’ve patiently tried to explain many times why your objection is without merit. You are entitled to your opinion, but enough is enough.
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David,
I am sorry to return on this, because I know you are done with this discussion, but I cannot see the consistency in these two statements of yours:
“….and they can simultaneously calculate, subject to their budget constraints….”
and in the same paragraph
“…income and expenditure are determined conditional on the equilibrium price vector, the equilibrium income and expenditure is not conditional on income…”
So what is the budget constraint of the first statement if not income?
How can these two statements be consistent?
“..If you don’t understand that a system of equations in an equilibrium determines all variables simultaneously given the equilibrium price vector,..
Take a two good economy with goods X1 and X2 with prices P1 and P2 respectively. P1 and P2 constitute the price vector. It can be said that:
P1X1 + P2X2 = Y
For X1 and X2 to be determinable (forget for a moment that another equation is required), Y has to be specified. And what is Y in this case? – income.
“General-equilibrium theory has many, many problems. That is not one of them.”
If this is the case then where is the formal explanation for how changes in relative prices have an impact on the level of output and not just the composition of output?
“This is just a blog, not a treatise.”
That’s fair enough. The trouble is you make your musings public in this blog and you allow commentary on them. And from time to time, points of controversy, to some, will arise and discussion inevitably ensue.
And by the way, the words Lavington actually used were: “The inactivity of all is the cause of the inactivity of each”. 🙂
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Henry,
I’m happy to address a specific question as opposed to a general assertion that I don’t know what I’m talking about.
If we take a simple 2-good exchange economy, then the budget constraint of the nth trader
in every provisional round of trading at the price vector announced by the auctioneer looks like the following:
P1*x(e)1 + P2*x(e)2 = P1*x(f)1 + P2*x(f)
where x(e)1 is the quantity of good 1 endowed to the nth trader before trading starts and x(e)2 is the nth trader’s endowed quantity of good 2, and x(f)1 and x(f)2 are the final amounts of goods 1 and 2 after trade. Rearranging terms we get the following:
P1*dx1 + P2*dx2 = 0,
where dx1 and dx2 are the amounts by which the nth trader’s holdings of X1 and X2 change at the conclusion of trade.
The model can be generalized to include production, but income I is not specified in the trading process, though it can be calculated ex post. The budget constraint is Walras’s Law which says that the value of all sales equals the value of all purchases when all equivalent goods are being traded at the uniform prices. Putting in a term for money income into the budget constraint is just a simplification used in the elementary theory of consumer behavior in partial equilibrium analysis. In general equilibrium analysis, income is determined by the solution to equilibrium not an initial condition of the model.
Under appropriate assumptions about the limitations imposed by trading at disequilibrium prices, it can be easily shown that income (which only comes into the picture if traders are endowed with services that they offer to others in exchange for goods or other services provided to them) is greater at the equilibrium price vector than at any disequilibrium price vector. Again, that is just elementary and non-controversial.
I have given you the informal argument that shows that income is maximized at a general equilibrium solution. At any disequilibrium, efficient trading will not take place because trading will be limited at disequilibrium prices to the lesser of quantity demanded or quantity supplied, so the value of output actually produced must be less at any disequilibrium price vector than it would have been at the pareto-optimal equilibrium price vector.
I don’t mind being challenged. And I’m happy to continue any discussion, but I don’t see any need to constantly repeat the same points that I’ve already made and to be told that I don’t know what I’m talking about.
Thanks for giving me the exact quote from Lavington, which I occasionally quote correctly, but have misquoted previously from memory and then go back to the misquote and repeat.
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David,
I don’t think I have said that you don’t know what you are talking about. I have said that I find your “thinking out aloud” blog writings a little confusing. I guess I don’t have the wit to see through them.
Lavington’s book is well worth the read. Its informality is engaging and the notions exposed therein presage Keynes to some extent. However, he wanders over the same fields you do, playing with changes in prices. Still, there must have been something in the air lingering over Cambridge, air from which Keynes undoubtedly drew breathe when he came to formulate the GT.
I am having a think about your equations etc..
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David,
As far as I can see your model is not an economic model but an accounting model. It is an ex post description of the resulting transactions. It has no behavioural or functional content.
Where are the underlying choice theoretic considerations?
Where are the indifference curves?
Where are the production functions?
Your equations are true whether there is equilibrium or not.
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It is not a model. It is Walras’s Law, which is what serves as the budget constraint in a general equilibrium model, as opposed to a partial-equilibrium budget constraint for a consumer with a predetermined income.
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David,
“It is Walras’s Law,”
Yes I know. Model was your term.
However, it applies whether there is equilibrium or not.
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Your issue was with the budget constraint and how there can be a budget constraint if income (I) is not specified. I explained that to you. If you want the whole model, go read about it in a book or an article. There are lots of them.
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David,
“If you want the whole model, go read about it in a book or an article. ”
Which I have.
Both my parents being Italian, my penchant for good salami and cheese is understandable. However, unfortunately, I have to also consider my means. Good salami and cheese don’t come cheap. Mr. Walras, being French, perhaps didn’t consider there was a limit to how much of each could be consumed – perhaps there was such a surfeit of both in France at the time that it seemed they fell from Heaven like manna. 🙂
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Well, your grasp of it still seems somewhat tenuous.
Here’s a link to an overview that I found on the web. The first three sections address some of the points we have been discussing.
Click to access General%20Equilibrium.pdf
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Thanks David, I’ve read Levin some time ago. Perhaps I should read it again. 🙂
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David,
I’ve decided to stick to my guns.
Walras’ Law is essentially based on a simple tautology, the value of what is bought is equal to the value of what is sold. This is true whether in equilibrium or not. To define equilibrium, Walras invoked tatonnement. Without tatonnement, equilibrium can only be defined with indifference curves and a budget constraint. (See pages 3 and 4 of Levin.)
Pareto and Hicks do not invoke tatonnement. For them, equilibrium is dependent on choice theoretic considerations where a budget constraint is central.
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Henry, I never said that Walras’s law was anything but a tautology. A budget constraint is also a tautolgy. Walras did not invoke tatonnement to define an equilibrium. The definition of an equilibrium has nothing to do with the determination of an equilibrium. The determination of an equilibrium is a solution to a system of equations of which the budget constraint (AKA Walras’s Law) is one. Tatonnement was invoked as an imaginary method by which the equilibrium that can be found analytically by solving the system of equations could be found by a method trial and error. So you are completely confused about what it means to define an equilibrium or to determine an equilibrium analytically or to find an equilibrium solution by a “practical” method without solving the system of equations.
Having expended hours of effort to try to dispell your comprehensive confusion, I now announce that I am overwhelmed and defeated by that confusion and I hereby abjectly announce my surrender to it and withdrawal from this discussion. I now know exactly what President Biden must feeling at this moment, and I feel his pain.
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David,
“I now know exactly what President Biden must feeling at this moment, and I feel his pain. ”
Could I suggest a nice glass of Italian wine and a salami and cheese sandwich?
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The last time I ate a Salami sandwich I was 10 years old and got sick to my stomach. I haven’t touched salami since and have no intention of doing so ever again. But I do appreciate your thoughtfulness.
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David,
“A budget constraint is also a tautolgy.”
I don’t want to stir it up again but the budget constraint is not a tautology or identity but a genuine equality when it comes to an optimization algorithm.
Just have the wine and cheese then. However, given your Walrasian predilections, I expect you will want French wine (or may be not given your other predilections regarding the French gold hoarding in the 1920s. LOL!)
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🙄
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