In my two previous posts (here and here), I have argued that the partial-equilibrium analysis of a single market, like the labor market, is inappropriate and not particularly relevant, in situations in which the market under analysis is large relative to other markets, and likely to have repercussions on those markets, which, in turn, will have further repercussions on the market under analysis, violating the standard ceteris paribus condition applicable to partial-equilibrium analysis. When the standard ceteris paribus condition of partial equilibrium is violated, as it surely is in analyzing the overall labor market, the analysis is, at least, suspect, or, more likely, useless and misleading.
I suggested that Keynes in chapter 19 of the General Theory was aiming at something like this sort of argument, and I think he was largely right in his argument. But, in all modesty, I think that Keynes would have done better to have couched his argument in terms of the distinction between partial-equilibrium and general-equilibrium analysis. But his Marshallian training, which he simultaneously embraced and rejected, may have made it difficult for him to adopt the Walrasian general-equilibrium approach that Marshall and the Marshallians regarded as overly abstract and unrealistic.
In my next post, I suggested that the standard argument about the tendency of public-sector budget deficits to raise interest rates by competing with private-sector borrowers for loanable funds is fundamentally misguided, because it, too, inappropriately applies the partial-equilibrium analysis of a narrow market for government securities, or even a more broadly defined market for loanable funds in general.
That is a gross mistake, because the rate of interest is determined in a general-equilibrium system along with markets for all long-lived assets, embodying expected flows of income that must be discounted to the present to determine an estimated present value. Some assets are riskier than others and that risk is reflected in those valuations. But the rate of interest is distilled from the combination of all of those valuations, not prior to, or apart from, those valuations. Interest rates of different duration and different risk are embeded in the entire structure of current and expected prices for all long-lived assets. To focus solely on a very narrow subset of markets for newly issued securities, whose combined value is only a small fraction of the total value of all existing long-lived assets, is to miss the forest for the trees.
What I want to point out in this post is that Keynes, whom I credit for having recognized that partial-equilibrium analysis is inappropriate and misleading when applied to an overall market for labor, committed exactly the same mistake that he condemned in the context of the labor market, by asserting that the rate of interest is determined in a single market: the market for money. According to Keynes, the market rate of interest is that rate which equates the stock of money in existence with the amount of money demanded by the public. The higher the rate of interest, Keynes argued, the less money the public wants to hold.
Keynes, applying the analysis of Marshall and his other Cambridge predecessors, provided a wonderful analysis of the factors influencing the amount of money that people want to hold (usually expressed in terms of a fraction of their income). However, as superb as his analysis of the demand for money was, it was a partial-equilibrium analysis, and there was no recognition on his part that other markets in the economy are influenced by, and exert influence upon, the rate of interest.
What makes Keynes’s partial-equilibrium analysis of the interest rate so difficult to understand is that in chapter 17 of the General Theory, a magnificent tour de force of verbal general-equilibrium theorizing, explained the relationships that must exist between the expected returns for alternative long-lived assets that are held in equilibrium. Yet, disregarding his own analysis of the equilibrium relationship between returns on alternative assets, Keynes insisted on explaining the rate of interest in a one-period model (a model roughly corresponding to IS-LM) with only two alternative assets: money and bonds, but no real capital asset.
A general-equilibrium analysis of the rate of interest ought to have at least two periods, and it ought to have a real capital good that may be held in the present for use or consumption in the future, a possibility entirely missing from the Keynesian model. I have discussed this major gap in the Keynesian model in a series of posts (here, here, here, here, and here) about Earl Thompson’s 1976 paper “A Reformulation of Macroeconomic Theory.”
Although Thompson’s model seems to me too simple to account for many macroeconomic phenomena, it would have been a far better starting point for the development of macroeconomics than any of the models from which modern macroeconomic theory has evolved.
Uneasy Money 
David,
Isn’t Chapter 17 just making the argument that fiat money is not same as commodity money?
It has different characteristics which make it unique.
General Equilibrium Theory is the theory of the optimal allocation of scarce resources among competing uses. It is not a theory about the level of the utilization of resources. That is why it cannot constitute a macroeconomic theory.
Capital theory deals with the allocation of limited financial resources among competing capital assets. It is similarly not a theory about the level of capital goods production. That is why such a theory won’t be found in Keynes’ macroeconomic model.
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One further thought.
In Keynes’ world the rate of interest is not the mechanism by which resources are allocated intertemporarily. It is the mechanism (with expectations as a parameter) by which the level of capital goods production is determined.
The rate of interest in the GE model is not comparable with the rate of interest found in the GT.
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I think I mean intertemporally, not intertemporarily. 🙂
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Henry, We have been through this all before, so I will be brief. I view general-equilibrium theory as a method of taking into account the complexity and interdependence of economic activity. You may be right in your explanation of Keynes’s thought process, but that does not justify it. The rate of interest is an intertemporal price and Keynes in chapter 17 recognizes it as such. His explanation of interest in the GT as pure liquidity preference is simply indefensible, and I say that as an admirer of his contributions to economics
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While Keynes appears to have been deficient in spelling it out there is not necessarily a contradiction between claiming that ‘the market rate of interest is that rate which equates the stock of money in existence with the amount of money demanded by the public’, and that a ‘relationships …. must exist between the expected returns for alternative long-lived assets that are held in equilibrium’. In other words a major (but not the only) factor in people’s desire to hold money (either as a cash balance or in order to loan it out) will be the alternative returns available if they held their wealth in other forms.
If the money rate of interest is too low compared to the alternatives available
then a simple adjustment mechanism would be for people to attempt to move out of money and drive up the price level. With the resulting lower ‘real’ quantity of money higher interest rates on money will be needed to ‘equate the stock of money in existence with the amount of money demanded by the public’, which will (when it reached the appropriate level) equilibrate the money rate of interest with returns available elsewhere.
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Very ingeniously, David, although some economists like M. G. Hayes [Hayes 2010] will probably defend Keynes on the grounds that:
“…principle of effective demand, the backbone of The General Theory,
represents an alternative definition of equilibrium.
[Modern] …loanable funds theory can be no more separated from the
Walrasian concept of general equilibrium than Keynes’s liquidity-preference theory can be
from the principle of effective demand. Since these two concepts of system equilibrium are
structural incompatible, it is no surprise that the loanable funds debate has been at cross-
purposes.”
Bibliography
The loanable funds fallacy: saving, finance and equilibrium
M. G. Hayes
Cambridge Journal of Economics
Vol. 34, No. 4 (July 2010)
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.1004.3849&rep=rep1&type=pdf
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“The current rate of interest depends, as we have seen, not on the strength of the desire to hold wealth, but on the strengths of the desire to hold it in liquid and illiquid forms respectively, coupled with the amount of the supply of wealth in the one form relatively to the supply of it in the other.” (JM Kyenes, Collecgted Writings VII, p 213)
It is not at all the case that Keynes asserted that the rate of interest is determined in a single market (the market for money).
He understood money in a much broader sense (in fact, he spoke about “liquidity” preference), and was not concerned solely with the demand for money. The theory of liquidity preference is concerned with the demand for assets of various degrees of liquidity, and the rate of interest depends on both the demand for and supplies of assets across the whole of this spectrum.
Liquidity preference is the decision about the degree of liquidity at which savings should be held. It is a decision concerning the stock of savings – wealth – at any point in time and its composition, rather than any new flow of saving alone or the stock of any particular asset called money.
And the rate of interest is not determined by the supply of and demand for (flows of) saving or the supply of and demand for the stock of one particular asset called money, but by the supply of and demand for all assets into which holdings of (stocks of) wealth can be placed. Money is just one of these assets.
Why is all this so “undefensible”, as you say?
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In practice, the interest earned on assets held as stores of value is the reward for their relative illiquidity and can alternatively be seen as a premium on liquidity.
According to Keynes’ liquidity preference theory (LPT), money is a store of value, liquidity may include money as well as non-money liquid assets, and wealth allocation decisions are made by comparing all existing assets based on the cost to exchange them and their capacity to protect the value stored in them.
The interest rate, therefore, rests on a general equilibrium analysis of the whole spectrum of assets across the domestic and international economy (in the case of international financially integrated and open economies).
Essentially based, as it is, on preferences toward liquidity (vs illiquidity), LPT, by its very construction, cannot be a partial equilibrium analysis and must on the contrary reflect a general equilibrium approach.
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Finally, as regards the interest rate and capital assets, in the General Theory Keynes clarified that, “investment depends on a comparison between the marginal efficiency of capital and the rate of interest” (JMK, Collected Writings VII, p 151, fn 1), and denied any unique and stable relationship between debt and equity markets.
His account of “spot-the-convention-type” of asset-market play in Chapter 12 is clearly relevant to securities and derivative markets in general, including also FX and property markets, etc.
LPT is indeed a theory of asset prices more generally, not just of the price of one asset in one market.
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Biaggio, Many thanks for your very astute comments.I completely agree that the theory of liquidity preference can be expressed in an appropriate general equilibrium framework, as Keynes himself in chapter 17 and elsewhere did. My point is that he sometimes lapsed from that appropriate general equilibrium view of interest into a more extreme partial equilibrium view in which liquidity preference became the sole factor explaining the essence of the rate of interest which then governed his application of the simplified model (IS-LM) and governed his applied analysis in an aggregated macro model.
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Totally agree, David. Many thanks for your reply!
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David, Biagio,
I don’t believe there is any question of Keynes taking a partial or general equilibrium approach in the GT. Keynes was concerned with how changes in income and spending shift the equilibrium level of output and employment.
Relative price changes (that is partial or general equilibrium analysis), in his world, have no relevance to macroeconomic considerations, other than perhaps where output was at the full employment level.
That there might be a panoply of financial assets with characteristics of near money was not of critical interest to him, even though their existence might have been considered or implied in his analysis.
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Henry,
By combining 1) the theory of consumption (determined as a fraction of current income), 2) animal spirits (as the fundamental source of irreducible or radical uncertainty underpinning the process of capital accumulation), and 3) liquidity preference theory (LPT) (to explain the rate of interest as a “highly conventional…phenomenon” – to use his own words), JMK intended to demonstrate that capitalist economies may be charcaterized by permanent states of underemployment equilibrium.
You may not refer to Keynes’ analysis as General Equilibrium; in fact, one might call it General Disequilibirum Analysis (where disequilibrium may persist due to the lack of endogenous incentives to eliminate it). Yet Keynes’ analysis involved all relevant markets in the economy and it was certainly not partial equilibrium analysis. In this sense, “general” is used as opposed to “partial,” and not on whether the underlying adjustment mechanism is based on quantities rather rather than prices.
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Henry,
In an earlier comment, you had noted (correctly, in my view) that “in Keynes’ world the rate of interest…is the mechanism (with expectations as a parameter) by which the level of capital goods production is determined.” If you re-read carefully what I wrote in my comments, you will notice that a) they are consistent with that statement and b) they nowhere suggest that Keynes was concerned with “a panoply of financial assets with characteristics of near money”.
Keynes’ use of the term “liquidity” indicates that he was not concerned exclusively with the demand for money; he considered the demand for assets of various degrees of liquidity, and in his LPT the rate of interest depends on both the demand for and supplies of assets across the whole of this spectrum.
“Money,” however, does have a particularly crucial role in LPT and, more broadly, in Keynes’ general (dis)equilibrium approach; while illiquid assets offer holders a reward in the form of interest, the reward for holding money is the essence of liquidity itself: the rate of interest is the price of illiquidity.
To such extent, and to the extent that such a price determines the level of capital accumulation (and hence of future wealth creation), it inevitably plays a key role also in the economy’s process of intertemporal resource allocation. In fact, one cannot (I would even say, “may not”) think of Keynes’ interest rate theory as disjointed from its intertemporal dimension: time and the uncertainty that comes with it are of the essence in Keynes’ view of the inherent instability of a monetary production economy.
In Keynes, time, uncertainty, and liquidity are essentially interwoven.
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Henry and Biagio, I think Keynes at his best was reasoning in terms of a complex intertemporal general-equilibrium system in which markets are all interrelated but are not necessarily in equilibrium and the equilibrating forces are not necessarily very powerful. But to make his system tractable he also argued in terms of a highly aggregated model single period model that was not capable of accommodating the full complexity of the relationships underlying his analysis. My criticism of Keynes focuses mainly on his overly aggregated and overly simplified one period model, not his more complex understanding of how the economy works.
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David,
I think you are right and I tend to share your criticism (with all the humbleness that I feel due in being critical of such a gigantic master).
But while Keynes’ highly aggregate model was incapable of accommodating the full complexity of his vision, as you say, he did point to a fundamental way of how to turn (neo)classical economics on its head, and most of all he recognised that this was in fact necessary in order for Economics to become a useful social discipline.
The troubles of Economics, today, derive from the ineptitude of Keynes’ followers to build on his extraordinary intuition and complete what he was unable to complete, and the inability of contemporary economists to combine – as he successfully did – a vast theoretical knowledge with a high sense of realism and history.
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Biagio,
The word :”general” is problematic in the sense that it appears in the title of Keynes book and in part forms the name given to a theory of optimal resource allocation (General Equilibrium Theory – GET). So we have to be careful not to mix the two uses of the word. Keynes meant by “general” that he was considering all possible macro equilibrium points whereas the “general” in the GET applies to all markets in simultaneous equilibrium at only one point, viz., full employment.
I’m sure I’m not telling you anything new, but we have to be careful not to mix the two meanings as you almost seem to be doing above (?).
So while Keynes used the word “general” he of course was not referring to GET.
And I don’t agree that Keynes theory might have implications for intertemporal resource allocation. He was interested in the level of capital goods production in a given period. And in any event, it is relative prices which are the mechanism by which capital is allocated across time, not “price”.
Keynes specifically stated that the rate of interest was not the reward for not spending now but the reward for not hoarding. This is where the notion of liquidity preference is unique and plays into the question of uncertainty.
There was an intertemporal dimension to Keynes’ theorizing but not in the sense of optimal resource allocation.
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David,
Keynes was concerned with how an economy could be stable at levels of output and employment below the full employment level. He argued that the process of adjustment was driven by changes in income and spending not changes in relative prices (the mechanism of the GET). These are entirely two different adjustment mechanisms.
Whilst some of the elements of Keynes theory may have been “in the air” prior to the GT, he added to these elements and combined them in such a way that he could explain how an economy could be stable at a level of output below full employment.
This was the genius of Keynes and the essence of his revolution. A mantle unreasonably denied him by people like David Laidler. (I’m referring to Laidler’s ambiguously titled “Fabricating the Keynesian Revolution”).
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David Glasner: This comment might be belated, and I am no longer following the econoblogosphere as closely as I used to…but have you tried to decipher the equations found in Chapters 20 and 21 of The General Theory of Employment, Interest, and Money?
If not…I would like to redirect your attention to the following articles.
Click to access 21-A-4.pdf
Click to access 24-A-4.pdf
Click to access 25-A-13.pdf
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I believe that the fundamental confusion here arises from an attempt to understand Keynes from a Walrasian, general equilibrium perspective rather than from that of Marshall and the belief that, somehow, Walras’ Law is relevant to Keynes or in the real world that Keynes attempted to explain.
Keynes attempted to identify those factors that in themselves directly determined each of the variables in the system at each point in time, not just when the system was in equilibrium. This made it possible for Keynes to view the system as recursive in that it was possible for him to establish the temporal order in which events must occur, and thus to separate cause and effect. This made it possible for him to provide a logically consistent, causal explanation as to how the system changes through time.
His method of analysis in doing this was through a partial equilibrium analysis of each variable that does not assume that the rest of the system is in equilibrium or that Walras’ Law applies. The key to his being able to do this was his realization that the rate of interest is determined by the supply and demand for money, not saving and investment or the supply and demand for loanable funds, and that income is determined by saving and investment, not by the supply and demand for money.
I do not have the space to defend this view here, but I do have a paper posted online that attempts to explain the causal nature of Keynes’ theory of interest ( http://rweconomics.com/CIKGT.pdf ) and another that attempts to explain the recursive nature of Keynes’ methodology ( http://rweconomics.com/MKATN.pdf ) if anyone is interested.
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That may well have been Keynes’s view of causality, it is certainly not mine, and I think it would be hard — if not impossible — to defend such a view of causality. And few if any contemporary economists would subscribe to that view.
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It’s not at all clear to me that why you believe that it is hard to defend the notion that a cause must precede its effect. It seems to me that this has been the fundamental understanding of causality since the 18th century. I don’t know of anyone who would reject this proposition.
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There are many causes operating simultaneously one many variables, not one cause for each variable.
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There are many factors that determine the value of a variable at any particular point in time, but those factors do not necessarily change simultaneously in response to an exogenous change in the system. The factors that determine the values of individual variables will tend to change sequentially as the system evolves through time. Keynes’ methodology involved attempting to establish the sequential order in which those changes occur in order to establish cause and effect with regard to the way in which those changes occur through time. This kind of analysis may be difficult, but I do not see any reason to believe that it is impossible or that it can’t be fruitful. The only barrier I can see to this kind of analysis is Walras’ Law, a law that I personally view as nonsense. ( http://rweconomics.com/CIKGT.pdf pp. 2-4 )
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There are theories of equilibrium in which causation is simultaneous. There is no theory of sequential change derived from any basic principles in the way that equilibrium theory is derived from basic principles. There is no compelling reason to think that Keynes had any special insight into the sequence of change. His rejection of wage cuts makes sense only insofar as it is based on a rejection of partial equilibrium analysis of the labor market.
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“His rejection of wage cuts makes sense only insofar as it is based on a rejection of partial equilibrium analysis of the labor market.”
Partial equilibrium analysis relies on the assumption that supply and demand functions are independent.
Keynes’ analysis suggests to me he believed this to be not the case.
The issues of casuality, simultaneity, temporality are important – any model can be constructed on the basis of assumptions about these considerations. The question, in the end, is what is the relationship of the model to reality.
The fundamental problem with GET as a basis for macroequilibrium analysis is that it runs with changes in relative prices. I would like to see an explanation as to how changes in relative prices gives effect to a change in the general level of output and employment.
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You constantly, and without basis, identify GET with a particular set of assumptions. The framework can be adapted to different assumptions in which absolute prices, not only relative prices, can matter.
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“The framework can be adapted to different assumptions in which absolute prices, not only relative prices, can matter.”
If so, you have entered a Keynesian world.
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And to be complete, I would say you have entered a Keynesian world where Walras’ Law does not apply.
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You are free to use whatever terminology you like. I greatly admire Keynes; that doesn’t mean I endorse or accept everything he wrote.
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It is a mistake to believe that general equilibrium theory is based on basic principles and there is no theory of sequential change derived from any basic principles. This ignores Marshall’s fundamental contribution of marginalism to the theory of supply and demand, and Marshall’s use of these concepts to explain sequential change.
It is of course true that Marshall’s sequential analysis is not derived from the same basic principles as those of Walras, but that is because of the limitations of Walras, not a deficiency of Marshall. Walras’ basic principles shed no light at all on the determination of any variable at any point in time other than when the system is in a state of general equilibrium (a situation that seems to me to never exists in the real world), whereas, Marshall explicitly attempted to explain the determination of variables at any point in time in the real world in accordance with the basic principles of supply and demand. (See Hayes, 2006, The Economics of Keynes: A New Guide to The General Theory).
As I explain in http://rweconomics.com/CIKGT.pdf (pp. 2-4 ) the fundamental difference between Marshal and Walras arises from the fact that the Walrasian budget constraint assumes the choices of decision-making units are made simultaneously at a point in time and are constrained by realized income. This may be the way in which budgets are created in the real world, but it is not the way in which choices are made. Real-world choices are made sequentially through time, not simultaneously at a point in time, and neither households nor firms are constrained in their choices by income, realized or otherwise, at the point in time at which a choice must be made.
The real-world choices of decision-making units are constrained by:
a) the value and liquidity of their assets,
b) the availability of sellers of goods and assets at various prices,
c) the availability of buyers of goods and assets at various prices, and
d) by their access to credit.
The rate at which decision-making units receive or earn income at the point in time at which a choice must be made has no way of affecting that choice other than through its effects on expectations as anyone who has purchased a home, a car, or has simply walked the aisles of a supermarket knows implicitly, and as any business owner who has had to meet a payroll knows implicitly as well.
These are the kinds of basic principles on which Marshall’s (and Keynes’) theory of sequential change are based, and it seems to me that they make much more sense and can be used to explain and understand a great deal more of economic reality than those that underlie Walrasian general equilibrium theory.
While it is true that Keynes’ rejection of wage cuts makes sense only insofar as it is based on a rejection of the classical partial-equilibrium analysis of the labor market Keynes’ reason for rejecting this methodology in the labor market, as he explained in Chapter 2 of the GT, is that it doesn’t make sense to try to explain how the actions of demanders and suppliers of labor determine the real wage or level of employment by way of a partial-equilibrium model. And as I explain in the paper linked to above (pp. 8-13) it also doesn’t make sense to try to explain how the actions of savers and investors or suppliers and demanders for the flow of loanable funds can determine the rate of interest by way of a partial-equilibrium model, but it does make sense (pp. 21-5) to explain how the actions of suppliers and demanders of money determine the rate of interest by way of a partial-equilibrium model.
Finally, I would note in the other paper I linked to in my original post above ( http://rweconomics.com/MKATN.pdf ) demonstrates exactly how Keynes’ use of Marshall’s basic principles of supply and demand can be used to provide a causal explanation of the way in which the economic system moves from one short-run equilibrium position to another (pp. 22-6), and it explicitly includes non-debt assets as well as money and debt. This paper also explains how the level of employment is determined in Keynes’ general theory by way of a partial-equilibrium model and how a change in the money wage can be expected to effect the level of employment in this model (pp. 36-44).
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George,
I am very much interested in what you’re saying and will read your suggested contributions as soon as I can.
One question: are you familiar with monetary circuit theory, a branch of Keynesianism that has evolved from Keynes’ emphasis on money and time in a production economy, and has tried to combine a multi-market (general (dis)equilibrium) perspective with sequential time in choices?
If so, I’d be interested in hearing your views on it (even bilaterally, if you prefer; my email is biagio.bossone@gmail.com).
Thanks again, and thanks to David for hosting and nurturing this interesting debate.
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George,
I have printed out your papers and am looking forward to reading them.
For the time though I can’t see how partial equilibrium supply demand analysis can apply.
Supply and demand curves display a relationship between price and quantity.
At the level of macro analysis, it is changes in income and spending which shifts the economy from one level of output to another.
How is it that price is relevant? Did not Keynes assume a constant level of prices in the GT?
Also does not partial equilibrium analysis require that supply and demand curves be independent? At the macro scale, it would seem they are not.
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Henry,
Re: “For the time though I can’t see how partial equilibrium supply demand analysis can apply. Supply and demand curves display a relationship between price and quantity. At the level of macro analysis, it is changes in income and spending which shifts the economy from one level of output to another. How is it that price is relevant? Did not Keynes assume a constant level of prices in the GT?”
Income is the value of output produce in the GT which is given by the sum of prices times the quantities produced, and Keynes did not assume prices are constant. Keynes assumed that prices are determined by ordinary Marshallian supply and demand curves where the demand for consumer goods depends on income. The way in which this is accomplished is shown in Figure 1 and Figure 2 of http://rweconomics.com/MKATN.pdf .
Re: “Also does not partial equilibrium analysis require that supply and demand curves be independent? At the macro scale, it would seem they are not.”
Walrasian supply and demand curves are not independent at the macro scale because it is assumed that all choices are made simultaneously at a point in time and that choices are constrained by income. I argue that in the real world choices are not made simultaneously and are not constrained by income and that Keynes assumed choices are made sequentially through time rather than simultaneously at each point in time and that choices are not constrained by income. As a result, at any given point in time Keynes’ supply and demand schedules are independent at the macro scale.
Only the supply and demand for loanable funds schedules are not independent in the real world when these schedules are defined in terms of the flows of saving and investment. This is the reason Keynes rejected the LF theory of interest in favor of the LP theory of interest since the S and D for money are independent at the macro scale. This is explained in http://rweconomics.com/RTVK.pdf . I would also note that a formal model of Keynes’ LP theory that does not conflate stocks and flows is presented in: http://rweconomics.com/SFM.pdf .
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Henry:
Sorry. Wrong link:
. . . . This is the reason Keynes rejected the LF theory of interest in favor of the LP theory of interest since the S and D for money are independent at the macro scale. This is explained in http://rweconomics.com/RTVK.pdf . I would also note that a formal model of Keynes’ LP theory that does not conflate stocks and flows is presented in: http://rweconomics.com/CIKGT.pdf .
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Darn! I’m having trouble getting this right today.
That the S and D for money are independent at the macro scale is demonstrated in:http://rweconomics.com/CIKGT.pdf
The formal model of Keynes’ LP theory that does not conflate stocks and flows is presented in: http://rweconomics.com/SFM.pdf
I should also note that, as you pointed out, Keynes also demonstrated that the supply and demand in the aggregate labor market are not independent just as he demonstrated that the supply and demand for loanable funds are not independent.
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George,
Firstly, I have to say I have not yet read in depth your referenced papers – just skated through them – so I do not fully appreciate the reasoning behind your comments, if at all.
However, I find I am in disagreement with several of the fundamental points made in your comments above.
“Walrasian supply and demand curves are not independent at the macro scale because it is assumed that all choices are made simultaneously at a point in time….”
This is a tricky one. In Walrasian general equilibrium there is no time, there is only a point of equilibrium. Once equilibrium is determined, it remains immovable. There is no time before or afterwards, so there cannot be a point in time.Tatonnement is a sequential multi-event process which occurs with no reference to any point of time. It is a complete nonsense, compared to what occurs in the real world. I am sure you would agree. To talk of time in Walrasian equilibrium is not appropriate. A minor but important point.
Staying with the tatonnement process, it seems to me this has similarities to your real world sequential choice making. If so, if you believe that S and D curves are independent in this case then it has to be concluded that in Walrasian tatonnement, S and D curves are also independent, not not independent as you say in your comment referenced immediately above. So I would argue that your logic is inconsistent.
” I argue that in the real world choices are not made simultaneously and are not constrained by income and that Keynes assumed choices are made sequentially through time rather than simultaneously at each point in time and that choices are not constrained by income. ”
Whether considering the tatonnement process or your real world time sequential characterization of choice making, I cannot agree that income is no longer relevant to choice making. Choices are always influenced by income and expectations of future income.
In support of this I offer an extract from the preface to the French edition of the GT:
“My contention that for the system as a whole the amount of income which is saved, in the sense that it is not spent on current consumption, is and must necessarily be exactly equal to the amount of net new investment has been considered a paradox and has been the occasion of widespread controversy. The explanation of this is undoubtedly to be found in the fact that this relationship of equality between saving and investment, which necessarily holds good for the system as a whole, does not hold good at all for a particular individual. There is no reason whatever why the new investment for which I am responsible should bear any relation whatever to the amount of my own savings. Quite legitimately we regard an individual’s income as independent of what he himself consumes and invests. But this, I have to point out, should not have led us to overlook the fact that the demand arising out of the consumption and investment of one individual is the source of the incomes of other individuals, so that incomes in general are not independent, quite the contrary, of the disposition of individuals to spend and invest; and since in turn the readiness of individuals to spend and invest depends on their incomes, a relationship is set up between aggregate savings and aggregate investment which can be very easily shown, beyond any possibility of reasonable dispute, to be one of exact and necessary equality. Rightly regarded this is a banal conclusion. But it sets in motion a train of thought from which more substantial matters follow. It is shown that, generally speaking, the actual level of output and employment depends, not on the capacity to produce or on the pre-existing level of incomes, but on the current decisions to produce which depend in turn on current decisions to invest and on present expectations of current and prospective consumption.”
“…and Keynes did not assume prices are constant. ”
Perhaps, but he did say this on p. 27 of the GT:
“In this summary we shall assume that the money-wage and other factor costs are constant per unit of labour employed. But this simplification, with which we shall dispense later, is introduced solely to facilitate the exposition. The essential character of the argument is precisely the same whether or not money-wages, etc., are liable to change.”
I am willing to concede your point for the time being, but it seems to me that the above comes close to saying prices are assumed constant, given the relationship between prices and costs.
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Henry,
Thank you for your comments.
Re: “”Walrasian supply and demand curves are not independent at the macro scale because it is assumed that all choices are made simultaneously at a point in time….: This is a tricky one. In Walrasian general equilibrium there is no time, there is only a point of equilibrium.”
All I am assuming here is that everything takes place in time, not that time matters in some sense. If we can’t assume that Walrasian choices are made simultaneously at a point in time when and where are they made? This seems to me that this is a semantic issue rather than one of substance. I really don’t think we disagree on anything of substance here.
Re: “I cannot agree that income is no longer relevant to choice making. Choices are always influenced by income and expectations of future income.”
I did not say that choices are not “influenced” by income. I said that choices are not “constrained” by income. What you state with regard to “influence” is exactly my (and Keynes’) position:
“The rate at which decision-making units receive or earn income at the point in time at which a choice must be made has no way of affecting that choice other than through its effects on expectations as anyone who has purchased a home, a car, or has simply walked the aisles of a supermarket knows implicitly, and as any business owner who has had to meet a payroll knows implicitly as well.”
The above is taken directly from the text of http://rweconomics.com/CIKGT.pdf (pp. 2-3), and the very next sentence is:
“Decision-making units have no alternative but to be guided by their expectations with regard to the income they expect to receive in the future and are constrained by the way in which the income they have received in the past has affected the stock of assets they hold in the present, as Keynes insisted (1936, pp. 46-7, 50), but at the point in time at which a choice must be made they are not constrained by the rate at which they actually receive or earn income in the present or in the future.” I think this sort of issue will be clarified if you read the paper.
Re: “’In this summary we shall assume that the money-wage and other factor costs are constant per unit of labour employed. But this simplification, with which we shall dispense later, is introduced solely to facilitate the exposition. The essential character of the argument is precisely the same whether or not money-wages, etc., are liable to change.’
“I am willing to concede your point for the time being, but it seems to me that the above comes close to saying prices are assumed constant, given the relationship between prices and costs.”
Constant wages does not imply constant prices. If wages are constant profit maximizing behavior in the face of diminishing returns implies an upward sloping supply curve and increasing prices as output increases and falling prices as output falls
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George,
You said above in your comment:
“All I am assuming here is that everything takes place in time, not that time matters in some sense. ……….This seems to me that this is a semantic issue rather than one of substance. ”
Isn’t time at the centre of your thesis in your CIKGT paper? I think you have to be careful in the way you use language in describing the Walrasian tatonnement process. If something occurs in an instant, there is no time to be considered. The tatonnement process seems to occur in some land at the end of a golden rainbow. Once the auctioneer has discovered those prices in which there are no surplus demands or supplies in any market then he is done. This is the equilibrium point. (What happens next? Are all goods produced and consumed in an instant and then everyone and everything disappears in a puff of smoke? Or is there some kind of continuum implied? Does it make a difference?) I imagine you would have not much trouble accepting the above account of Walrasian general equilibrium? Of course, one of your main points is that in the real world decisions are taken sequentially. So Walrasian equilibrium is inapplicable to the real world. So time is important. (Sorry for the waffle on, but I think you have to be clear on this point. You are in your paper, but not so much in your comment above.)
“This may be the way in which budgets are created in the real world, but it is not the way in which choices are made.”
This seems to be the seminal point in your CIKGT paper (p.2). But aren’t choices made on the basis of (income) constraints? I can’t see how it can be otherwise.
Followed by:
“Real-world choices are made sequentially through time, not simultaneously at a point in time, and neither households nor firms are constrained in their choices by income, realized or otherwise, at the point in time at which a choice must be made.”
I’m afraid I cannot see the validity of this point. Yet you go on to say:
“The rate at which decision-making units receive or earn income at the point in time at which a choice must be made has no way of affecting that choice other than through its effects on expectations……..”
I wholeheartedly agree, but this seems to be in contradiction to the points made in the above quotes from your paper. I think you further confuse the argument with this (p.3):
“Decision-making units have no alternative but to be guided by their expectations with regard to the income they expect to receive in the future and are constrained by the way in which the income they have received in the past has affected the stock of assets they hold in the present……”
To be followed by this:
“…..but at the point in time at which a choice must be made they are not constrained by the rate at which they actually receive or earn income in the present or in the future.”
These are all assertions which need to be justified more cogently as they still seem to me to contradict even what Keynes said himself about income, spending and expectations.
I will keep reading and rereading. 🙂
P.S. Can you clarify a few reference issues? Hicks 1979 on page 1 and Malgrange 2011 on page 4 didn’t seem to make it to the reference list. Can you provide the details. Also Hawtrey on page 3 is undated, I presume it is 1933?
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George,
I cannot see why a non-Walrasian general equilibrium approach could not be used similarly to a partial equilibrium approach. Why can’t production possibility curves and budget constraints be moved inward as expectations of income and output change?
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Thank you so much for pointing out the typo in the reference to Hicks. The citation in footnote 1 should be to Hicks’ 1980 paper not 1979. As for Malgrange, the reference is to the paper jointly authored by de Vroey and Malgrange 2011.
When it comes to dealing with the Walrasian paradigm, I really don’t know how I can explain this more clearly. The Walrasian paradigm assumes that choices are made simultaneously and are constrained by income. People do not make choices simultaneously; they make choices sequentially, and when it comes to someone actually making a choice at any particular point in time they are not constrained by their income. They “are constrained by a) the value and liquidity of their assets, b) the availability of sellers of goods and assets at various prices, c) the availability of buyers of goods and assets at various prices, and d) by their access to credit. The rate at which decision-making units receive or earn income at the point in time at which a choice must be made has no way of affecting that choice other than through its effects on expectations as anyone who has purchased a home, a car, or has simply walked the aisles of a supermarket knows implicitly, and as any business owner who has had to meet a payroll knows implicitly as well. Decision-making units have no alternative but to be guided by their expectations with regard to the income they expect to receive in the future and are constrained by the way in which the income they have received in the past has affected the stock of assets they hold in the present, as Keynes insisted (1936, pp. 46-7, 50), but at the point in time at which a choice must be made they are not constrained by the rate at which they actually receive or earn income in the present or in the future.”
If I want to purchase a home, a car, or buy something impulsively at a supermarket how am I “constrained” from doing so other than by way of a) through d) above whatever my income may be at that point in time?
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George,
“…how am I “constrained” from doing so other than by way of a) through d) above whatever my income may be at that point in time?’
I would argue you are utterly constrained by your income.
Putting aside such things as winning the lottery, finding a gold bar in the street, gifts and inheritances, etc., assets are acquired with income. Loans have to be repaid out of income or by liquidation of assets acquired with income.
If you have no assets then the only way to acquire goods or assets is with income.
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“If you have no assets” is covered by a).
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The point is if you have sufficient liquid assets or sufficient access to credit and there are sufficient sellers of goods and assets at various prices you can purchase whatever you want to purchase, and if there are sufficient buyers goods and assets you can sell whatever you want to sell irrespective of what your income is.
If you have no assets or access to credit and only have income you can’t buy anything until that income is realized in the form of an asset, namely, money. At any point in time your choices are constrained by the value and liquidity of your assets, availability of credit, and the availability of buyers and sellers of goods and assets, not by your income.
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If you have no assets or access to credit, how do you get money?
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You don’t unless you have an income that gives you an asset, money, on payday. At that point you are constrained by that asset until the next payday if that’s all you have and no credit..
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“You don’t unless you have an income that gives you an asset, money, on payday.”
Exactly. No income, no nothin’.
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Keynes’ point is that “Decision-making units have no alternative but to be guided by their expectations with regard to the income they expect to receive in the future and are constrained by the way in which the income they have received in the past has affected the stock of assets they hold in the present, as Keynes insisted (1936, pp. 46-7, 50), but at the point in time at which a choice must be made they are not constrained by the rate at which they actually receive or earn income in the present or in the future.”
Past income yields you assets that constrain your choices in the present and expectations with regard to future income affect your choices, but current income does not affect your choices except with regard to the way in which it affects your expectations with regard to future income. It is the expectations with regard to future income that is causal in Keynes’ general theory, not your current or past income except by way of the way in which current and past income affects your assets and your expectations with regard to future income.
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George,
“It is the expectations with regard to future income that is causal in Keynes’ general theory…..”
Totally agree.
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George,
You have made constant reference to p.46-47 in the GT.
This quote seems apt:
“Thus, on each and every occasion of such a decision, the decision will be made, with reference indeed to this equipment and stock, but in the light of the current expectations of prospective costs and sale-proceeds.”
Keynes is saying that decisions are ultimately dependent on the businessman’s expectations about future income (i.e., prospective sale proceeds minus prospective costs).
His current ownership of assets (plant and stock) are only relevant in as far as they limit what can be produced in the future. He will only produce that quantity of output (and employ the requisite amount of labour) as his expectations allow him to produce (prospective sales proceeds), the maximum output he can produce given by his existing plant and stock. He may wish to add to his plant and stock if he expects future sales proceeds (i.e. income before deduction of costs) to exceed the output of his current plant and stock.
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That’s it exactly. The Walrasian budget constraint which assumes the current RATE at which income is being earned constrains his choices does not enter the picture.
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George,
Still scratching my head here.
Are you saying that past and current income do not constrain but future income does?
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I’m saying exactly what Keynes said.
At any point in time, past income can only affect current choices to the extent that past income has affected the existence of current assets or to the extent past income has an effect on current expectations with regard to the future.
Current income, as defined as the value of out being produced, can only affect current choices to the extent it has an affect on current expectations with regard to the future.
Future income can have no affect on current choices since future income cannot exist at the current point in time; only expectations with regard to future income can exist at the current point in time, not future income as such.
If something does not exist it cannot have an effect. Only a belief in something that does not exist or an expectation with regard to something that does not exist coming into existence in the future can have an effect, not the thing itself.
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George,
Then how is this consistent with this extract from p. 3 of your CIKGT paper:
“…but at the point in time at which a choice must be made they are not constrained by the rate at which they actually receive or earn income in the present or in the future.”
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How is it inconsistent?
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“Decision-making units have no alternative but to be guided by their expectations with regard to the income they expect to receive in the future and are constrained by the way in which the income they have received in the past has affected the stock of assets they hold in the present, as Keynes insisted (1936, pp. 46-7, 50), but at the point in time at which a choice must be made they are not constrained by the rate at which they actually receive or earn income in the present or in the future.”
The full piece is as above.
In the first half you use the word GUIDED and in the second half you use the words NOT CONSTRAINED.
You are say “decision-making units” are guided by expected future income but not constrained by future income.
So, by this, do you mean that there are factors other than expectations of future income which cause the level of spending by a “decision-making unit”? (These factors being the items a to d listed above.)
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The items a to d listed above constrain the choices of decision-making units. Decision-making units can do whatever they want within these constraints irrespective of the income the expect to receive in the future, but they are limited in their choices by these constraints, that is, they cannot do whatever they want irrespective of these constraints.
People are only “guided” by their expectations; they are not “constrained” by those expectation, and “guided” is Keynes’ choice of words (GT, p. 46) not mine as such.
The other factors that cause the level of spending to be what it is are delineated by Keynes in Chapters 8 and 9 in the GT.
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Keynes explains consumption spending in Chapters 8 and 9. He explains investment spending in Chapters 11 and 12.
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Would you not agree that if consumers believe that there will experience a considerable drop in their future income, that, despite what their “a to d” position is, this expected change in future income will have a considerable if not definitive impact on the choices they are making now?
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I really don’t know why you find this confusing. a)-d) do not determine choices; they constrain choices. Why do you think there is any question about whether or not an expectation of a change in future income will affect current choices?
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I think it is the way you use words. I find it very confusing, to the point I cannot get past the first few pages of your CIKGT paper. Must be getting too old and stupid!
To my mind, if expectations of future income took a serious turn for the worst, then I would say this would constitute a constraint on current choices, not just an influence.
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The Walrasian budget constraint is a mathematical relationship that includes income and assumes that the choices that determine supplies and demands must be consistent with that mathematical relationship. When the individual constraints are aggregated for the system as a whole the result is Walras’ Law which implies that the excess demands in the system must sum to zero. The issue is whether or not it makes sense to assume this law holds at any particular point in time and whether or not this way of looking at the way in which decision-making units make the choices that determine supplies and demands makes sense.
What constitute a ‘constraint’ in this situation is given by the terms that enter the mathematical relationship that defines the budget constraint, not simply anything that affects choices. Walrasians assume that current income enters this relationship, not future income nor expected income. If you wish to replace current income with expected income and work out the implications of that replacement in the Walrasian paradigm there is nothing wrong with that, but that’s not what Keynes did.
Keynes was a Marshallian, not a Walrasian, and he simply treated expectations as exogenous parameters in the Marshallian paradigm without including either current income or expected income in a mathematical formula that is assumed to constrain the choices of decision making units. Whether we call expected income a constraint within this context or not is beside the point. The point is that Walras’ Law is not relevant to the choices of decision-making units in Keynes’ general theory. Since I have not been able to make this clear I will have to think about how to explain it better.
Just the same it seems to me there is a fundamental difference between the way in which a)-d) constrain the choices of decision-making units and the way in which expectations constrain those choices, namely, that a)-d) exist in the real world and are outside the control of decision-making units while expectations exist only in the minds of decision-making units, but that gets us into Descartes’ mind body problem which we probably aren’t going to be able to resolve here 😉
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George,
” Since I have not been able to make this clear I will have to think about how to explain it better.”
I think it’s more me than you.
When you use the word “constraint” it is in reference to the “budget constraint” that appears in GET/Walrasian theory(WT). If so, that now makes sense.
But GET/WT goes even further does it not? It assumes that income is given. It defines how production is distributed among different goods given by their relative prices. At equilibrium, the ratio of prices equals the rate at which one good can be transformed into another. Correct?
Yes, I get that Keynes didn’t do this.
However, partial equilibrium also assumes a given income and strictly speaking, the derivation of a demand curve also involves a budget constraint, the only difference in the formal analysis (compared to GET/WT) is that the price of the good in question is variable while all others are held constant. At least that’s how I was taught intermediate micro.
Can the same be applied to aggregate economic analysis (or perhaps I am just way off beam in your view)?
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And I have left off the question of sequential decision making over time.
I see this as another complication which requires another level of thought, as you have pointed out and argued.
However, if you don’t mind, I would like to take it a step at a time and keep time out of the discussion for the moment.
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I’m afraid I don’t know how to leave time out of the discussion. The point of the http://rweconomics.com/CIKGT.pdf paper is that because Walrasian economics assumes all choices are made simultaneously it cannot be used to explain how the system changes over time, and because Marshallian economics does not assume all choices are made simultaneously it can be used to explain how the system changes over time. The http://rweconomics.com/MKATN.pdf paper gives an example of how Marshal can be used to explain how the system changes over time..
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George,
My point in the main was that formal partial equilibrium analysis assumes a budget constraint just as general equilibrium analysis does.
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How does that work?
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Take a two good economy, goods A1 and A2.
Imagine a set of indifference curves for these two goods.
Say the quantity of A1 demanded is mapped onto the vertical axis and the quantity of A2 demanded is mapped onto the horizontal axis.
The price of A1 is P1 and the price of A2 is P2.
Assume income is Y1.
The budget constraint formula is:
Y1 = (A1xP1) + (A2xP2)
Lay the budget constraint line (BCL) on the indifference curve map.
It will intersect the vertical axis at A1= Y1/P1.
It will intersect the horizontal axis at A2=Y1/P2.
Where the BCL is tangent to an indifference curve will define the bundle of goods, A1 and A2, demanded at the price ratio and income defining that particular BCL.
Assume P1 is fixed and P2 is variable.
As P2 is varied, the BCL will rotate around the indifference curve map, pivoting at the point on the vertical axis defined by A1=Y1/P1.
As the BCL rotates it will become tangent to different indifference curves.
So as P2 changes, the quantity of A2 demanded can be read off.
The coincident A2s and P2s can be mapped onto a price quantity chart. The locus of these points defines the demand curve for A2.
I can send you a diagram if you wish.
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And as income changes, the pivot point on the A1 axis will move up and down correspondingly.
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More completely:
And as income changes, the pivot point on the A1 axis will move up and down correspondingly, causing the demand curve to shift with changes in income.
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This has nothing to do with partial equilibrium. It’s just a way of showing that if a household maximize a utility function with a choice between two goods they will choose quantities such that the marginal rate of substitution is equal the ratio of prices. If this example is expanded to include to n goods, assets, and resources we end up with Patinkin’s general equilibrium model where income is an endogenous variable, all of the functions assume a general equilibrium, Walras’ Law holds for the system as a whole, and time does not play a role in the model since all choices are implicitly assumed to be made simultaneously, and everything is assumed to take place instantaneously.
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OK with all of the above.
That was my point. With no time, partial and general equilibrium were the same.
That was the first step.
The second step is to consider time and sequential decision making.
The problem for me is I can’t see the difference between the two (i.e., time/no time).
If income is not a constraint at any point in time in each and every decision, it is not a constraint at all.
This flies in the face of commonsense let alone high theory.
And we’re back where we started. 🙂
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That’s right. We are back to arguing semantics rather than substance. It comes down to whether or not that budget constraint aggregated over all decision units makes sense or not. It implies that there is no way to explain changes in S and D except through invocation of a mythical auctioneer. It makes no sense at all to me, and I have no idea why it makes sense to anyone else. And it has nothing to do with Marshall’s ceteris paribus, partial equilibrium methodology. Neither Marshall nor Keynes assumed that the choices of individuals in markets are constrained by a Walrasian budget constraint. Only Keynesians and neoclassical economists assume this.
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Re: “If income is not a constraint at any point in time in each and every decision, it is not a constraint at all.
“This flies in the face of commonsense let alone high theory.”
I really don’t see why this flies in the face of commonsense. When you are in a supermarket how does anything other than a)-d) constrain your choices? It seems to me that to assume that income rather than expected income constrains your choices in this situation flies in the face of commonsense.
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Perhaps the confusion here is in the difference between the way in which expected income ‘constrains’ choices and the way in which actual income is assumed to constrain choices in the Walrasian paradigm.
Realized income enters the Walrasian budget constraint. It is a physicals constraint on choices just as a)-d) are physical constraints on choices. They exist in the real world.
Expected income is a mental constraint, not a physical constraint. Expected income exists in the mind of the beholder, just as tastes and preferences exist in the mind of the beholder. They do not enter the budget constraint; they enter the utility function.
At any point in time at which you have to make a choice the only physical constraint on that choice is a)-d), not income. Only expected income can affect that choice, not current income, and the way it can affect that choice is through a mental constraint via your utility function, not via your budget constraint. Only a)-d) are physical constraints on choices at any point in time.
When you are in a supermarket, a)-d) physically constrain your choices, not your income. If you don’t have the money, etc. you can’t purchase if you want to irrespective of what your income is. If you do have the money, etc. you can purchase if you want to irrespective of what your income is.
Now this sounds like commonsense to me, and the idea that a Walrasian budget constraint constrains your choices via your income at every point in time seems like nonsense to me, especially when this idea forces one to the conclusion that there is no way to explain how the system moves from one point of equilibrium to another except through the magic of a Walrasian auctioneer.
It seems to me that economists hanging on to these nineteenth century beliefs in order to avoid having to face the reality of Keynes is akin to chemists hanging on to a belief alchemy or psychologist refusing to move beyond phrenology.
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George,
I’d like to tackle you on just about every sentence you have written in your last few comments. Of course this will further deepen the morass we have walked into.
However, a couple of things.
“Expected income is a mental constraint, not a physical constraint. ”
A mental constraint is as real as a physical constraint.
“They do not enter the budget constraint; they enter the utility function. ”
That’s akin to saying expected income is a factor in indifference map construction. That’s not the way I was taught it works formally. The preference curve map is independent of income and prices. Income considerations enter via the budget constraint. To think of it in any other way renders utility theory unworkable (the logic becomes very circular).
“Now this sounds like commonsense to me, and the idea that a Walrasian budget constraint constrains your choices via your income at every point in time seems like nonsense to me”
There is no time in formal Walrasian equilibrium. There is just equilibrium. Tatonnement occurs in some atemporal nether world. And as I have demonstrated above, formal partial equilibrium analysis is based essentially on the same assumptions as GET/WT except that all prices bar one are held constant. And partial equilibrium is equally, formally, atemporal.
Of course in the real world, as you have amply argued, things don’t proceed in an atemporal manner. And because of this, you argue that GET/WT is inapplicable. If you argue this then it should be argued that formal partial equilibrium theory is also inapplicable. But then you argue that Marshallian partial equilibrium analysis is different to formal partial equilibrium analysis and that is the way to proceed in analyzing real world macroeconomic behaviour. If that is the case then, stripping GET/WT of its tatonnement process could equally be used to analyze real world behaviour.
The problem to me seems to be that you have stripped income (particularly expected future income) effects from the analysis. And you argue in one breath that this is what Keynes did and then in another breath you quote from Keynes p.47.
One of the central relationships in the GT is:
C = f(Y)
If this is the case then I would argue that general and partial equilibrium analysis, whether formal or not, is inapplicable.
The GT essentially says that getting from one equilibrium point to another is effected by changing the level of spending. Simple.
Both general and partial equilibrium analysis assume that the level of income (spending) is given.
To render general and partial equilibrium analysis useful to macroeconomics, income changes have to be fed in.
Having said all that, I probably, horribly, have misunderstood you. Hopefully you can better see what I am arguing and can show me where I have wandered off into an incomprehensible wilderness. 🙂
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Re: “That’s akin to saying expected income is a factor in indifference map construction. That’s not the way I was taught it works formally. The preference curve map is independent of income and prices. Income considerations enter via the budget constraint. To think of it in any other way renders utility theory unworkable (the logic becomes very circular).” I don’t know how this works. Please give me a citation to someone who has included expected income in a budget constraint so that I can see what this means.
Re: “If that is the case then, stripping GET/WT of its tatonnement process could equally be used to analyze real world behaviour.” The problem is that you can’t strip GET/WT from the tatonnement process without getting rid of the Walrasian budget constraint. It’s income in the budget constraint that makes a realistic analysis of dynamic behavior impossible in the Walrasian paradigm.
Re: “The problem to me seems to be that you have stripped income (particularly expected future income) effects from the analysis. And you argue in one breath that this is what Keynes did and then in another breath you quote from Keynes p.47.” I have no idea where this is coming from. All I have done is restate what Keynes said on p. 47. What makes you think that p. 47 has anything to do with including expected income in a budget constraint?
Re: “The GT essentially says that getting from one equilibrium point to another is effected by changing the level of spending. Simple.” This is way out in left field. The level of spending is an endogenous variable in the GT determined by the propensity to consume, the MEC, liquidity preference, and the supply of money. Please read http://rweconomics.com/MKATN.pdf .
Re: “Both general and partial equilibrium analysis assume that the level of income (spending) is given.
“To render general and partial equilibrium analysis useful to macroeconomics, income changes have to be fed in.” This is true of Walras and Marshal, not Keynes, and the only reason it’s true of Marshal is that Marshal did not have Keynes’ theory of interest and assumed that income is determined by the “Cambridge Quantity equation.” Please read http://rweconomics.com/CIKGT.pdf and http://rweconomics.com/MKATN.pdf
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George,
“I don’t know how this works. ”
It was you who used the phrase “expected income” (“they enter the utility function”). In the case of pure Walrasian Equilibrium Theory (WET) and pure partial equilibrium theory (PET), there is no time, no past, no future so there cannot be expected income. The real world is a different matter and you want to deal with the real world. Expected income is a factor in spending. Keynes said so.
“The problem is that you can’t strip GET/WT from the tatonnement process without getting rid of the Walrasian budget constraint. ”
I can’t see why this is the case.
I presume when you say assuming away the tatonnement process you referring to working in the real world. As Keynes says (p.47), in the real world, expected income is a factor.
“It’s income in the budget constraint that makes a realistic analysis of dynamic behavior impossible in the Walrasian paradigm.”
I can’t see this. It’s not there is a budget constraint that precludes analysis of dynamic behaviour, it is that WET is inherentally atemporal and based on tatonnement.
And, as I demonstrated above, your preferred means of analysis, partial equilibrium, is also founded on a budget constraint.
“What makes you think that p. 47 has anything to do with including expected income in a budget constraint?”
How else can income (past, current or future) enter the analysis?
“This is way out in left field. ”
I can’t see the problem here. What I am saying is what you said (about the MPC, MEC and liquidity preference).
“This is true of Walras and Marshal, not Keynes….”
What happened to p.47?
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Re: “’The problem is that you can’t strip GET/WT from the tatonnement process without getting rid of the Walrasian budget constraint.’”
“I can’t see why this is the case.”
The reason is because the Walrasian budget constraint assumes all choices are made simultaneously, whereas, in the real world choices are made sequentially. If you can explain to me how to specify a non-tâtonnement GE system which assumes the Walrasian budget constraint I will be more than happy adopt it.
Re: “And, as I demonstrated above, your preferred means of analysis, partial equilibrium, is also founded on a budget constraint.”
You have not demonstrated that Marshallian partial equilibrium analysis is founded on a Walrasian budget constraint. How does your ‘demonstration’ apply to my partial equilibrium analysis in Figures 1 and 2 in http://rweconomics.com/CIKGT.pdf ? How does the Walrasian budget constraint or Walras’ Law apply to this analysis?
Re: “’What makes you think that p. 47 has anything to do with including expected income in a budget constraint?’”
“How else can income (past, current or future) enter the analysis?”
Past income affects current choices only to the extent it affects current assets. [a) in a)-d)] Current income can affect current choices only to the extent it affects current expectations and even then only to the extent those expectations affect the preferences in the objective functions of decision-making units: If people expect a high income in the future they will choose to consume more in the present than if they expect a low income in the future; if firms expect high sales in the future they will produce more today to meet that expected future demand than if they expect low sales in the future. These effects on choices have nothing to do with a Walrasian budget constraint that contains current income. Only a)-d) constrains current choices. As for future income, future income can have no effects on current choices; only expectations with regard to future income can have an effect on current choices. This is what p. 47 is all about.
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George,
“only expectations with regard to future income can have an effect on current choices. This is what p. 47 is all about.”
Where I have used the term “future income” I should have said expectations about future income. I presumed this was implied at all times.
“The reason is because the Walrasian budget constraint assumes all choices are made simultaneously, whereas, in the real world choices are made sequentially.”
If you say all choices are made sequentially and none of them are given by income (whether past, current or expectations of future income) then the corollary is that income never enters into any spending considerations, which is contra p.47.
“You have not demonstrated that Marshallian partial equilibrium analysis is founded on a Walrasian budget constraint. ”
Does Marshall’s demand curve assume that income is given?
Marshall writes on p.80 of Principles:
“The larger the amount of a thing that a person has the less, other things being equal (i.e. the purchasing power of money, and the amount of money at his command being equal), will be the price which he will pay for a little more of it….:”
Marshall assumes that the amount of money at the individual’s disposal is given. The amount of money he has is given by income in large part. So if his income changes then presumably the demand curve will shift. This is what happens when the budget constraint shifts because of a change in income.I can’t see that Marshall’s demand curve is any different than any demand curve found in PET.
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Re: “If you say all choices are made sequentially and none of them are given by income (whether past, current or expectations of future income) then the corollary is that income never enters into any spending considerations, which is contra p.47.”
This is starting to get bizarre. I have no idea how you come up with this. I stated quite clearly in my reply on 9/4: “At any point in time at which you have to make a choice the only physical constraint on that choice is a)-d), not income. Only expected income can affect that choice, not current income, and the way it can affect that choice is through a mental constraint via your utility function, not via your budget constraint. Only a)-d) are physical constraints on choices at any point in time.” I said quite clearly that “EXPECTED INCOME CAN AFFECT THAT CHOICE” which is exactly what p. 47 implies.
Re: “Does Marshall’s demand curve assume that income is given?
“Marshall writes on p.80 of Principles:
“’The larger the amount of a thing that a person has the less, other things being equal (i.e. the purchasing power of money, and the amount of money at his command being equal), will be the price which he will pay for a little more of it….:’
“Marshall assumes that the amount of money at the individual’s disposal is given. The amount of money he has is given by income in large part. So if his income changes then presumably the demand curve will shift. This is what happens when the budget constraint shifts because of a change in income. I can’t see that Marshall’s demand curve is any different than any demand curve found in PET.”
Money is a) in a)-d); it is not income! “[I]f his income changes then presumably the demand curve will shift.” The question is: Why will it change? Will it shift because the demanders are constrained by a Walrasian budget constraint that contains income? Or will it shift because it causes a change in expectations with regard to future income?
If you assume the former you are a Walrasian; everything changes simultaneously, and you are stuck with tâtonnement dynamics. If you assume the latter you are following Keynes; changes occur sequentially; it’s possible to use Marshall’s supply and demand analysis to separate cause and effect and give a causal explanation of dynamic behavior.
You really should read http://rweconomics.com/CIKGT.pdf where I explain why expectations must change BEFORE a change in realized income can CAUSE a change in behavior. You should also look at: http://rweconomics.com/RVKPS.pdf
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George,
It seems to me we agree on most things.
It seems to me we disagree on one thing – the notion that expected income cannot express itself as current income does through a budget constraint such as the one in the Walrasian system.
It seems to me that you believe that if there is a budget constraint in operation then a Walrasian system must be in consideration.
How does income then, even expectations of future income, express itself within a real world situation with sequential decision making without the operation of a budget constraint. How can a formal explanation for how expected income affects current spending be considered otherwise?
Expected income cannot work in a Walrasian system – a Walrasian system is atemporal – there is no past, no future.
“..the way it can affect that choice is through a mental constraint via your utility function..”
You repeat this again. I am not aware of any theoretical construction in consumer theory which will support this. Can you explain this some more because it seems to me you have plucked this out of the air. I am very happy to be corrected on this.
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Re: “It seems to me that you believe that if there is a budget constraint in operation then a Walrasian system must be in consideration.
“How does income then, even expectations of future income, express itself within a real world situation with sequential decision making without the operation of a budget constraint. How can a formal explanation for how expected income affects current spending be considered otherwise?”
It’s very simple. If you get paid on Friday, how does the income you earn on Wednesday affect the expenditures on Wednesday? How does income enter your budget constraint on Wednesday? Writhe it out.
How does income constrain your choices on Wednesday other than by the way in which Friday’s income payment affects the amount of money you have on Wednesday, and what you expect to receive next Friday mentally influences what you are willing to buy today?
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George,
Your papers, as far as I can see, are about formalizing what you assert to be Keynes implicit use of partial equilibrium methodology.
It seems to me the only way to formalize the effect of income is via a budget constraint.
I have not read your MKATN paper – perhaps your formal approach is explained there.
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Re: “It seems to me the only way to formalize the effect of income is via a budget constraint.”
Explain to me the budget constraint you face on Wednesday if you get paid on Friday.
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Within the agent’s economic planning horizon the budget constraint is:
current and expected sources of funding = current and expected expenditure
current and expected sources of funding = current liquid assets + expected income + borrowing capacity
current and expected expenditure = a1p1 + a2p2 +……………+ debt repayments
a = good
p = price of good.
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Very good! Now I can see what you are getting at. I don’t have any problem with this constraint. Since it is entirely in terms of money, the flow or rate of income does not enter it, only current money balances (and other assets and liabilities) and expected future income (payments). If you maximize utility subject to this constraint current income will not enter the resulting demand functions, only expected future income. This seems to be perfectly consistent with Keynes, but I’m not quite sure what the utility function that is maximized subject to this constraint looks like or how the system works, but this is not a Walrasian budget constraint and I’m pretty sure it won’t lead to a Walras’ Law with regard to current excess demands. I think it would be simpler to include expectations in the utility function and maximize this function subject to current assets, liabilities, and expenditures, but either way I think it will work.
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Glad you like it, however:
“…the flow or rate of income does not enter it..”
I’m still missing something here. Is not expected income a flow rate? It is income expected over a period of time.
“…but this is not a Walrasian budget constraint…”
The only difference I can see is that one I laid out above is not atemporal.
” I think it would be simpler to include expectations in the utility function..”
OK if you want to rewrite consumer theory. 🙂
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It’s a question of units of measurements. You can’t add apples and oranges without a common unit of measurement. You can add pounds or bushels of apples plus pounds or bushels of oranges, but when you do that the sum is neither apples nor oranges; its just pounds or bushels fruit. Even then this only makes sense if you are not interested in the composition of the sum, only its weight or size, for example, if you are a truck driver and want to know if your truck can handle the weight or has enough room for the load.
For the same reason you can’t add income which is measured in dollars per hour, day, week, month, or year and assets which are measured just in dollars. The only way to make sense out of “current liquid assets + expected income + borrowing capacity” in your constraint is if they all have a common unit of measurement. Since current liquid assets and “borrowing capacity” are measured in dollars the only common unit of measurement that seems to make sense to me for this sum is dollars, not dollars per unit of time.
This means that current and expected income must also be measured in dollars to avoid the apples, oranges, fruit problem, that is, they must be interpreted as dollars of money received in the form of money payments. As a result, it seems to me that for your constraint to avoid this problem current income must be interpreted as dollars of money received currently and, thus, is part of currently held liquid resources, and future expected income must be interpreted as dollars of money payments made in the future. As a result, the flow or rate of income which is measured in dollars per unit of time does not enter your constraint.
The only alternative to this interpretation that I can see is to find a way to interpreted “current liquid assets” as a flow or a rate measured in dollars pre unit of time which I do not know how to do.
I explain the way in which Keynes dealt with this problem in The General Theory as it relates to his discussion of wage-units in footnote 3 of http://rweconomics.com/MKATN.pdf .
I would also note that if you include expected income in the utility function everything is converted to utils which is, of course, a kind of fruit, but it is the kind of fruit we are interested in since it is what we imagine people want to maximize.
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George,
Dimensional analysis works in the physical sciences however I am not sure it applies here.
Take the stock of money at a point in time (assume other net asset changes at zero):
Current stock of money = past stock of money + income
So here there is:
stock = stock + flow.
You yourself use the same approach in your MAKTN paper.
Your first equation relates the interest rate to the stock of money and the flow of money.
Your third equation relates changes in price to the difference in demand and supply of investment goods.
So here we have dimensionally:
$/quantity = $ x quantity – $ x quantity
Doesn’t strictly work.
You are inconsistent with your own argument in your last comment.
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The apples, oranges, and fruit problem is not a problem of physics. It is a problem of math, logic, and reason. If the units of measurement in an equation or an argument are inconsistent the equation or argument is fallacious, full stop, end of discussion,
The third equation that you refer to is not: $/quantity = $ x quantity – $ x quantity. It is: $/quantity/time = A FUNCTION OF ($ x quantity/time – $ x quantity/time). The units in this equation are assumed to be reconciled by the functional form of the equation in the same way in which the units of a demand function are reconciled by the functional form of the equation.
Perhaps the easiest way to understand this is to look at the equation of exchange: MV=PQ. P is $/quantity, Q is output/time, M is $, and the only way to make sense out of this equation is if V is 1/time, that is, the average number of times M turns over per unit of time in producing PQ where the value of V depends crucially the unit of time considered days, months, quarters, or years. If the value of V is interpreted in this way both sides of the equation reduce to $/time, and the equation makes sense. Any other unit of measurement for V is nonsense.
(I would note that the http://rweconomics.com/MKATN.pdf paper has been revised where the revised version is shorter, and the first section that contained the equation you commented on has been eliminated. Likewise in http://rweconomics.com/MKATNEqus.pdf .)
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Strictly speaking my last equation should be:
$/quantity = $/quantity x quantity – $/quantity x quantity
Still doesn’t work dimensionally.
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I guess we are both mistaken here.
The equation is the rate of change in the price of investment goods which has the units $/time/time is equal to a function of the difference between the quantities of investment goods demanded and supplied which are measured in quantity/time not $/quantity/time as I stated above. Supply and demand are measured in quantities per unit of time. Value doesn’t enter into it. Sorry about that.
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I submitted a reply to your original comment, but I guess it hasn’t been posted yet, perhaps because it has links in it. If it isn’t posted by tomorrow I will post it again.
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“If the units of measurement in an equation or an argument are inconsistent the equation or argument is fallacious, full stop, end of discussion,”
So stock = stock + flow is an invalid equation?
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By definition, a stock is measured in dollars and a flow is measured in dollars per unit of time.
If you add the $10,000 in your bank account to the $50,000/year you earn in income you get 60,000 what?
You can only add, subtract, or set equal to each other magnitudes that have a common unit of measurement. You can’t add bushels of apples and pounds of oranges and get a single number. You can only add bushels or pounds of apples and oranges and get a single number, and even then the resulting number is only relevant if you are interested in the unit of measurement you have used.
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George,
You said:
“For the same reason you can’t add income which is measured in dollars per hour, day, week, month, or year and assets which are measured just in dollars.”
Then you said:
“You can only add, subtract, or set equal to each other magnitudes that have a common unit of measurement.”
You are being inconsistent.
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You will have to explain the inconsistency.
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George,
In the first quote you say magnitudes in $/time can’t be added to $.
In the context of the second quote you say:
“If you add the $10,000 in your bank account to the $50,000/year you earn in income you get 60,000 what? ”
I presume here you say they can be added?
Is that correct?
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This id an example of why magnitudes with different units can’t be added. When you add them you don’t know what you end up with.
When you add 5 bushels of apples to 10 pounds of oranges you get 15 what? The answer is that you get is 15 units of nonsense.
To make sense out of a sum you have to have a common unit of measure.
With regard to apples and oranges you can convert bushels of apples to pounds of apples or pounds of oranges to bushels of oranges and then add the result to get pounds or bushels of fruit, but it only makes sense to do this if you have a use for the sum without caring about its composition in terms of apples and oranges. This may make sense for a truck driver, but not for a green grocer.
You have the same problem if you add a stock and a flow. Again:
If you add the $10,000 in your bank account to your $50,000/year income you get 60,000 what?
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“If you add the $10,000 in your bank account to your $50,000/year income you get 60,000 what?”
You get $s. So is this not valid?
“current and expected sources of funding = current liquid assets + expected income + borrowing capacity”
You were willing to accept the above which has a mixture of stock and flow items.
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My response to your constraint was:
“Very good! Now I can see what you are getting at. I don’t have any problem with this constraint. Since it is entirely in terms of money, the flow or rate of income does not enter it, only current money balances (and other assets and liabilities) and expected future income (payments). If you maximize utility subject to this constraint current income will not enter the resulting demand functions, only expected future income. This seems to be perfectly consistent with Keynes, but I’m not quite sure what the utility function that is maximized subject to this constraint looks like or how the system works, but this is not a Walrasian budget constraint and I’m pretty sure it won’t lead to a Walras’ Law with regard to current excess demands. I think it would be simpler to include expectations in the utility function and maximize this function subject to current assets, liabilities, and expenditures, but either way I think it will work.”
The point is the only way you can make sense of this constraint is if “it is entirely in terms of money, the flow or rate of income does not enter it, only current money balances (and other assets and liabilities) and expected future income (payments);” any other interpretation is nonsense. Money balances and other assets and liabilities are all measured in units in $. The only way to make sense out of this constraint is if future income is interpreted as future income payments of money. If you want to assume future income is measured in terms of $/year this constraint is nonsense. I was giving you the benefit of the doubt here when I assumed you understood this.
Re: “You get $s. So is this not valid?” How do you get dollars? If the $10,000 in your bank account is bushels of apples and your $50,000/year is pounds of oranges you can’t add them together to get bushels/$ without a conversion factor to convert the $/year to $. The only conversion factor that will convert this sum into $60,000 is 1 year is equal to $50,000 of income.
If you multiply your $50,000 by 1 Year you get $50,000 which you can add to the $10,000 of money in your bank account to get $60,000 which is $60,000 of neither money nor income; it’s $60,000 of economic fruit.
The question now becomes how do you make sense out this result? Why does the composition of this economic fruit not matter such that it makes no difference whether it is all income or all money? Why to you want to measure this economic fruit in the first place? What are you going to use this measure of economic fruit for?
I really don’t know what is so confusing here. It seems to me that I was told in the first or second grade that you can’t add apples and oranges. I have never before been told that, somehow, the rules are different for economists.
Income and money are not the same thing. You can’t add them together unless you have a common unit of measure. That means to add them you must find a way to either convert the money to $/year or income to $. Once you do that you end up with either $/year or $ of economic fruit. Having obtained the result the question becomes how do you make sense out of this result?
These are the rules, and I can see no reason why they should not apply to economists.
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George,
I’m afraid I think your prior comment was a load of nonsense.
“When you add 5 bushels of apples to 10 pounds of oranges you get 15 what? ”
The analogy is inappropriate. The appropriate equation is 5 bushels of apples added to 10 bushels of apples/time to get 15 bushels of apples at the end of the time.
The stock = stock + flow equation is a fundamental equation of accounting and economics.
Lavoie and Godley wrote a book on macroeconomics based on this equation.
It appears some economists think your rules don’t apply.
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Re: “The appropriate equation is 5 bushels of apples added to 10 bushels of apples/time to get 15 bushels of apples at the end of the time.”
Good point. But still, my point is that simply adding 5 bushels of apples to 10 bushels of apples/time to get 15 does not tell you anything about what that 15 is without adding the fact that “the end of time” is 1 time unit, and you can’t add these two numbers and get 15 bushels without multiplying the 10 bushels of apples/time by 1 time unit which is, of course, the only way to make sense out of this sum being equal to 15.
This conversion makes it possible to add these two magnitudes, but after you make this conversion and do the addition you don’t end up with a homogeneous magnitude; you end up with the sum of bushels of apples that exist either independent of time or at a point in time and bushels of apples that are related to the flow of time. At this point you have to ask: What is this magnitude of bushels of apples useful for?
Re: “The stock = stock + flow equation is a fundamental equation of accounting and economics.”
The stock = stock + time x flow equation (or some version of it, e.g., equation (7) in http://rweconomics.com/SFM.pdf ) is a fundamental equation of accounting, not stock = stock + flow, and I think it is useful in economics only when economists understand it. I suspect that a failure to understand this equation is responsible for most of the fallacious nonsense we see in economics today because economists in general do not have a clear understanding of what this kind of economic fruit is; what kinds of conclusion can be drawn from an analysis of this kind of economic fruit, and what kinds of conclusions cannot be drawn from an analysis of this kind of economic fruit. (See., http://rweconomics.com/RTVK.pdf )
Re; “It appears some economists think your rules don’t apply.”
This is obvious from the fact that the confusion between stocks and flows has led to so much nonsense in economics such as the nonsense I explain in http://rweconomics.com/RTVK.pdf
As for Lavoie and Godley, I presume you are talking about their Monetary Economics book. I haven’t read It so you will have to give me an example of what they actually say. I don’t know whether there book is nonsense or not, but it does sound interesting.
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George,
“This conversion makes it possible to add these two magnitudes…”
There is no conversion required. It is patently clear if you add $10 at beginning of period to income of $15 over period you end up with $25 at end of period. Simple. Incontrovertible. Uncontroversial.
Perhaps it has been abused, but I see no problem using it in a budget constraint.
Lavoie’s and Godley’s book is available online as a pdf if you google it. You should read it for yourself.
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You are absolutely right, but the only reason you are able to figure this out is that you know that to convert the $/year to the amount of payments you receive in a year is to multiply the $/year by 1 year, and for 2 years you have multiply by 2 years, and for 3 years ….
It would appear that we have come full circle. As I said from the beginning, once you make the conversion from income to money income payments your constraint is logically and mathematically correct. Why can’t you see this? It’s not that complicated. It’s simple junior high school math: distance = speed x time. You have to multiply your speed by the amount of time you travel at that speed in order to calculate the distance you will travel.
And, again, as I have said before, you can use this as a budget constraint if you want to and maximize utility subject to it, but what can you then say about the resulting demands? How do they correspond to what actually happens in terms of the willingness to buy and sell in markets? What does this constraint tell you about how your income on Wednesday measured in terms of the $/time enter into these demands and constrain your choices on Wednesday? How does income enter into these demands in any way other than as an expectation? How do these demands differ from demands implied by a constraint that includes only assets and the availability of credit with expectations treated as a parameter in the utility function?
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I should also note that “income of $15 over [a] period” is not a flow. It is a stock measured in $ only. Treating this stock as if it is a flow leads to the kinds of fallacious arguments and conclusions I discuss in http://rweconomics.com/RTVK.pdf .
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“I should also note that “income of $15 over [a] period” is not a flow”
C’mon George, if that is not a flow nothing is.
BTW, I corrected myself in comment which hasn’t been posted yet. Waiting for David to put it thru.
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“As I said from the beginning, once you make the conversion from income to money income payments your constraint is logically and mathematically correct. Why can’t you see this?”
Fine. But it starts with income.
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Re: ““C’mon George, if that is not a flow nothing is.” If you can’t tell the difference between your bank account and your income there is no point in our continuing this conversation.
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I can tell the difference and I can also tell what difference my income will make to my bank account.
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