Home > Uncategorized > The gross substitution axiom

The gross substitution axiom

from Lars Syll

Economics is perhaps more than any other social science model-oriented. There are many reasons for this — the history of the discipline, having ideals coming from the natural sciences (especially physics), the search for universality (explaining as much as possible with as little as possible), rigour, precision, etc.

Mainstream economists want to explain social phenomena, structures and patterns, based on the assumption that the agents are acting in an optimizing (rational) way to satisfy given, stable and well-defined goals.

The procedure is analytical. The whole is broken down into its constituent parts so as to be able to explain (reduce) the aggregate (macro) as the result of interaction of its parts (micro).

Building their economic models, modern mainstream neoclassical economists ground their models on a set of core assumptions (CA) — describing the agents as ‘rational’ actors — and a set of auxiliary assumptions (AA). Together CA and AA make up what I will call the ur-model (M) of all mainstream neoclassical economic models. Based on these two sets of assumptions, they try to explain and predict both individual (micro) and — most importantly — social phenomena (macro).gs
The core assumptions typically consist of completeness, transitivity,  non-satiation, optimisation, consistency, gross substitutability, etc., etc.

Beside the core assumptions (CA) the model also typically has a set of auxiliary assumptions (AA) spatio-temporally specifying the kind of social interaction between ‘rational actors’ that take place in the model.

So, the ur-model of all economic models basically consist of a general specification of what (axiomatically) constitutes optimizing rational agents and a more specific description of the kind of situations in which these rational actors act (making AA serve as a kind of specification/restriction of the intended domain of application for CA and its deductively derived theorems). The list of assumptions can never be complete, since there will always be unspecified background assumptions and some (often) silent omissions (like closure, transaction costs, etc., regularly based on some negligibility and applicability considerations).

The hope is that the ‘thin’ list of assumptions shall be sufficient to explain and predict ‘thick’ phenomena in the real, complex, world.

Empirically it has, however, turned out that this hope is almost never fulfilled. The core — and many of the auxiliary — assumptions turn out to have preciously little to do with the real (non-model) world we happen to live in. And that goes for the gross substitution axiom as well:


The gross substitution axiom assumes that if the demand for good x goes up, its relative price will rise, inducing demand to spill over to the now relatively cheaper substitute good y. For an economist to deny this ‘universal truth’ of gross substitutability between objects of demand is revolutionary heresy – and as in the days of the Inquisition, the modern-day College of Cardinals of mainstream economics destroys all non-believers, if not by burning them at the stake, then by banishing them from the mainstream professional journals. Yet in Keynes’s (1936, ch. 17) analysis ‘The Essential Properties of Interest and Money’ require that:

1. The elasticity of production of liquid assets including money is approximately zero. This means that private entrepreneurs cannot produce more of these assets by hiring more workers if the demand for liquid assets increases. In other words, liquid assets are not producible by private entrepreneurs’ hiring of additional workers; this means that money (and other liquid assets) do not grow on trees.

2. The elasticity of substitution between all liquid assets, including money (which are not reproducible by labour in the private sector) and producibles (in the private sector), is zero or negligible. Accordingly, when the price of money increases, people will not substitute the purchase of the products of industry for their demand for money for liquidity (savings) purposes.

Paul_Davidson_01These two elasticity properties that Keynes believed are essential to the concepts of money and liquidity mean that a basic axiom of Keynes’s logical framework is that non- producible assets that can be used to store savings are not gross substitutes for producible assets in savers’ portfolios. If this elasticity of substitution between liquid assets and the products of industry is significantly different from zero (if the gross substitution axiom is ubiquitously true), then even if savers attempt to use non-reproducible assets for storing their increments of wealth, this increase in demand will increase the price of non- producibles. This relative price rise in non-producibles will, under the gross substitution axiom, induce savers to substitute reproducible durables for non-producibles in their wealth holdings and therefore non-producibles will not be, in Hahn’s terminology, ‘ultimate resting places for savings’. The gross substitution axiom therefore restores Say’s Law and denies the logical possibility of involuntary unemployment.

Paul Davidson

  1. March 17, 2016 at 2:09 pm

    Thank you Lars Syll and Paul Davidson.
    Thank you, RWER for allowing this article to be recorded.
    It breaks the rules of engagement. It allows for “understanding”.
    “So elaborately has the real nature of
    this ridiculous proceeding been surrounded with
    confusion by some of the cleverest and most
    skillful advocates the world has ever known, that
    it still is something of a mystery to ordinary
    people, who hold their heads and confess they
    are ” unable to understand finance “. It is not
    intended that they should.” Frederick Soddy (The Role Of Money)

  2. March 17, 2016 at 5:33 pm

    Most importantly, ‘mechanical’ price substitution implies that values-in-use between commodities consumed are identical. If these values-in-use are not identical — if, indeed, consumption/use of different goods serve different purposes and/or provide different levels of clearly defined benefits in use — then price substitution fails.

    Put differently, the neoclassical substitution hypothesis requires that if the price of food goods goes up then one rationally substitutes other non-food goods whose price is unchanged.

    This is an impossibility if the consumer is an organic life-form.

  3. March 18, 2016 at 12:59 am

    This is all very enlightening. And entertaining. But I don’t see the point in all this debate. Economics claims to be a science. Even if it’s neoclassical economics. Two statements at the beginning of the post make that impossible.

    “Mainstream economists want to explain social phenomena, structures and patterns, based on the assumption that the agents are acting in an optimizing (rational) way to satisfy given, stable and well-defined goals.”

    “Building their economic models, modern mainstream neoclassical economists ground their models on a set of core assumptions (CA) — describing the agents as ‘rational’ actors — and a set of auxiliary assumptions (AA). Together CA and AA make up what I will call the ur-model (M) of all mainstream neoclassical economic models.”

    These leave no room to examine anything except what you begin with. And they leave no room for the actual economic actors – people, nations, corporations, etc.to be heard or seen. Using a lost phrase from the 1960s – economists end up contemplating their own navels. And don’t learn a damn thing about economic actions or actors. Waste of time, energy, and resources in my view. Plus the danger of all the wrong decisions that have been and will be made because of economists.

    • March 18, 2016 at 2:46 am


      When models are based on observations, then patterns within those observations are revealed.

      When models are based on axioms, with any observations ‘fitted’ to these axioms and deductions from them, then the actual patterns within those observations are ignored, and no progress as a science is possible … for there is no science to begin with, only a ‘framework’ for analysis much like the Ptolemaic framework.

      The elasticity of percepts disguised as concepts within mainstream economics allows one to ‘prove’ just about anything the axioms deductively permit.Utility is such a percept disguised as a concept, one which displaces actual well-being or its lack which are observable. So, for that matter, is the marginal propensity to consume out of income. Neither describes any reality we know of. Simple observation shows that what changes with income are the options available to people … in terms of the range and diversity of consumption, including the use of money to provide for a rainy day or retirement.

      Not only do mainstream economists not know where we are going, they also believe only the path they have imagined into existence will get there, a pseudo-paradise where the actual benefits from the use of goods is not permitted to interfere with what they have imagined.

  4. Blissex
    March 19, 2016 at 9:05 am

    Well, the quote from Davidson about gross substitution not applying to money is pointless, because “money” as Keynes described it is simply not part of the neoclassical-style (plus “rational expectations” update) models.

    That “money” which can be hoarded is simply irrelevant in the neoclassical-style models because they are fundamentally based on “tatonnement” resolving all “market” transactions once and for all. There fore there is no need of “money”, and it cannot be hoarded. That’s why money is called a “veil” in them; it is purely a unit of accounting.

    What actually “gross substitution” means is indeed the latter: it means that in essence there is only one “good” that is used both as capital good and consumption good, as every good can be substituted for any other good. Therefore the whole system can be rewritten in terms of “dollars”, where all markets trade dollars against dollars.

    «values-in-use between commodities consumed are identical. If these values-in-use are not identical — if, indeed, consumption/use of different goods serve different purposes and/or provide different levels of clearly defined benefits in use — then price substitution fails» »if the consumer is an organic life-form.»

    That seems irrelevant to me because in neoclassical-style models there is a single immortal agent that trades with itself in infinite markets impersonating infinite buyers and sellers, all with the same supply and demand schedules.

    «if the price of food goods goes up»

    In neoclassical style-models that just cannot happen. “Tatonnement” results in equilibrium prices in all markets at once and for all time.

    «These leave no room to examine anything except what you begin with»

    In Neoclassical-style models there is indeed nothing but this, because the equilibrium quantities of infinite markets across all time in which a single immortal agent trades with itself a single good impersonating infinite buyers and sellers depends solely on the assumed demand or supply schedule (exactly one of each) and an initial allocation of that good. But the latter assumption is as a rule never mentioned when the desired result, that the distribution of income of the sole immortal agent is determined by productivity.

    Look, to understand neoclassical-style models one the most important detail is that central truthiness of Economics, that the distribution of income is uniquely determined by agent productivity absent government regulation.

    Every assumption in neoclassical-style models *must* be compatible with that truthiness. otherwise they are simply discarded. Most important is that time must be effectively expunged from neoclassical-style models as time-dependency leads as a rule to path-dependency and thus multiple equally possible equilibria each with a different distribution of income, which then depends on (exogenous) interest rate paths, because of what are called Wicksell effects. This for example happens also if there are multiple capital goods, or there are non substitutable consumer goods, or multiple agents with different production or consumption schedules. Gross substitution is just one small detail in a single “marvelous” edifice.

    Economists who “prove” that the distribution of income is optimally and uniquely determined by agent productivity absent government regulation go on to well-compensated careers and the chance of becoming quite wealthy thanks to generous sponsorship. Mere political economists who “waste” time on models in which that truthiness cannot be “proven” at best get middle class careers in a few academic backwaters.

    • March 28, 2016 at 8:09 pm

      Two points from a non-economist.

      First, Walras’s notion of tâtonnement (trial and error), as the route to equilibrium is fascinating. Walras obviously didn’t get out much. Trial and error involves “trials” and “errors” in interactions with the others around us (human and non-human). The interactions quite often go wrong and fail. Emphasis on “FAIL.” And on top of that each time we interact the circumstances are not the same as they were before. Some things almost always change. How this process can lead to equilibrium eludes me. Especially since going in none of the actors know what equilibrium is.

      Second, optimal is a hobgoblin. It does not exist. Any scientist who says s/he is pursing it is either a fool or lying.

      • March 28, 2016 at 11:09 pm

        The myth of the Walrasian auctioneer is based upon his ability to ensure that no trades [i.e., no exchanges] take place until market clearing prices have been found by the auctioneer.

        This, of course, begs the question of ever being able to find market clearing prices.

        And, certainly, in a world where exchanges take place at various prices all of the time, there is no inherent mechanism that could lead to an equilibrium in any market much less all of them.

      • March 29, 2016 at 4:07 am

        Which brings me to what to seems the obvious question — why would any sensible person “buy into” such nonsense?

      • March 29, 2016 at 4:48 am

        Well, no sensible person should ‘buy into’ such nonsense. Walras simply assumed that there would be a set of market prices that would clear markets, and the whole point of the auctioneer is to find that set which does so — which is assuming away the problem of whether such market clearing prices exist.

        Another problem, so to speak, is that the traders have ‘endowments’ of goods with consumers having ‘endowments of money, such that the costs of production do not enter into ‘offer prices’ [or any other matters for that matter], and such that if there is a set of prices that will clear markets, that set is divorced from whether or not those prices provide profits and/or are independent of the distribution of income underlying the ‘bids’ being considered.

        Put differently, there is no set of mechanisms that relates aggregate supply to aggregate demands in ways that must ensure equilibrium. It is entirely possible that amounts offered at some prices differ from amounts people are willing or able to purchase at those prices. In that sense, a market clearing price might lead to a loss among producers whose costs of production were higher than the market clearing prices if they had to sell at such prices.

        Walras ignores whether such a market price equilibrium is a sustainable equilibrium. He does not consider the dynamics of losses at market prices which, to the extent these occur, imply non-sustainable equilibria owing to producer losses :: capital and financial losses :: and/or the necessary unemployment effects which result in serious effects upon the distribution of incomes.

        And, off the top of my head, those are all serious problems with Walrasian type analysis or any analysis based upon endowments.

  5. Blissex
    March 19, 2016 at 1:39 pm

    The point I am trying to make is that Economists choose economic models primarily based on whether adopting them gives a better chance to win tenure at prestigious institutions and makes more likely to get $1,200/hour consulting fees as for G Hubbard.

    There is a market for ideas, and ideas that reduce the chances of tenure or getting $1,200/hour consultancy fees don’t sell too well in that market, regardless of their other qualities, as to “real-world economics”.

    Thus models that “prove” the central truthiness of Economics that the income distribution is optimally and uniquely determined by productivity absent government intervention sell a lot better in the market for ideas, regardless of whichever assumption need to be adopted to “prove” that truthiness.

    If endowed chairs at Harvard and $1,200/hours consultancy fees were funded by minimum wage workers and the unemployed, or at least by the non-existent All-American Union of Walmart Shelf Restockers, perhaps “heterodox” political economy would become more attractive in the market for ideas.

    That is, probably “nearly everybody” realizes how unrealistic and contradictory are the assumptions behind “orthodox” models, but very few care, because those models sell well in the market for ideas, and it is largely pointless to go on about it; the lesson of the Cambridges Capital Controversy whose outcome was judged a “waste of time” by Economists benefiting from tenure at prestigious institutions and $1,200/hour consultancy fees, should be relevant here.

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