Wave goodbye to the invisible hand

Adam Smith's contention that the self-interested drive for profits leads "as if by an invisible hand" to an outcome that is socially beneficial to all is one of the most potent propositions ever uttered. Generations of conventional "Neoclassical” economists since have gone on their own version of the Quest for the Holy Grail, trying to prove that Smith's Invisible Hand is real: that the metaphor actually describes how a market economy functions.

According to economic textbooks, this quest was successful: the invisible hand exists. Politicians have long accepted that economists are right, and that the best government is one that allows the invisible hand to weave its magic and convert self-interest into social harmony.

There's just one sticking point: these same textbooks teach that a pre-requisite for the invisible hand to function is that the market price must equal what economists call "marginal cost" – the cost of the very last item produced. If it does, then price is set by the intersection of supply and demand – Alfred Marshall's famous "two blades of the scissors" that determine both price and quantity – and the invisible hand works: not only is individual profit maximised, so too is social welfare.

But if the market price is higher than marginal cost, then the invisible hand breaks down: profit can still be maximised, but social welfare suffers.

This condition that price equals marginal cost can be achieved in one of two ways: either firms behave as 'price takers' who ignore what their competitors do, or they play a game of strategy with those same competitors that is named after the mathematician John Nash (who was made famous by Russell Crowe in the movie A Beautiful Mind).

If these two conditions sound somewhat contradictory to you, you're onto something: they are. But economists often don't realise this, since they learn the first, relatively easy explanation as freshers, and only learn the far more complicated "Cournot Nash Equilibrium" model as Masters or PhD students.

According to the 'easy' model (which is attributed to Alfred Marshall), all firms behave the same way, whether they’re in a competitive industry or they are a monopoly – they strive to find the level of output that maximises their profits. They do so by producing the quantity at which the very last unit sold adds just as much to their revenue as it cost to produce it. In econospeak, they equate 'marginal revenue' – the increase in revenue from the last unit sold – to 'marginal cost' – the cost of producing that output. When a monopoly does this, it maximises its profit but sets its price above marginal cost. But competitive firms, following exactly the same rule, also maximise their individual profits, but cause the market price to be equal to marginal cost – and they produce about twice as much output as the monopoly as well.

The paradox that exactly the same behaviour by competitive firms and monopolies leads to very different outcomes occurs, so the Marshallian model alleges, because the individual competitive firm has a 'horizontal' demand curve: it can sell as much as it likes without affecting the market price, even though the market demand curve slopes down – demand rises as the market price falls. Therefore a competitive firm’s 'marginal revenue' is identical to the market price, whereas a monopoly has to reduce its price if it wants to sell additional output.

When I wrote the first edition of Debunking Economics in 2001, I focused just on this Marshallian model, and pointed out what Al Gore would call "an inconvenient truth": The proposition that the market demand curve slopes downwards while individual demand curves are horizontal is a mathematical fallacy. Once the fallacy was corrected, the upshot was that a 'competitive' industry would produce the same amount as a monopoly.

This claim elicited howls of protest from conventional economists – how dare I claim that the invisible hand doesn’t work! Tim Worstall’s recent piece in Forbes Magazine is an echo of this debate, which raged for about four years.

Figure 1: Tim Worstall's column in Forbes


Without fail, critics either misinterpreted my argument (by, for example, alleging as Worstall does that it relied on the impossibility of infinite number of producers, or by defending the mathematically false Marshallian model using the very different mathematically correct Cournot-Nash model, as Chris Auld does in a paper Worstall links to).

The debate led me to refine my argument, and also to find that I wasn’t the first to make it: that honour belongs to the impeccably conservative, Nobel-Prize-winning Chicago economist George Stigler. Writing in the equally conservative Chicago University journal The Journal of Political Economy, Stigler proved in 1957 that the demand curve for the individual firm could not be horizontal, using possibly the simplest rule of calculus, the Chain Rule.

What Stigler did was calculate marginal revenue for a competitive firm by breaking the slope of the individual firm’s demand curve (how much market price changes because of a change in a single firm’s output) into two bits: how much market price changes if market output changes, multiplied by how much market output changes if one firm changes its output (see figure 2). The first bit is negative (since market demand rises as market price falls), while under the Marshallian assumption that firms don’t interact with each other, the second bit is one. Therefore the slope of the demand curve for the individual firm is exactly the same as the slope of the market demand curve – contrary to what is asserted in every economics textbook ever published.

Figure 2: Stigler's use of the Chain Rule


It’s not amazing that economists ignore me – I’m a self-declared economic heretic after all – but how can they justify ignoring Stigler?

Partly, I think, because Stigler also thought he had found a way to neutralise this Inconvenient Truth. Though the conventional pedagogy was clearly false, he then argued that, if each firm set its marginal revenue equal to its marginal cost, then with a sufficiently large number of firms, market price ultimately converged to marginal cost (and as few as 100 firms were enough for the difference to be less than 1 per cent if market demand was elastic).

Stigler set this out in a formula in which, rather strangely for a mathematical economist, he used whole words rather than just symbols:

Figure 3: Stigler's "convergence to perfect competition” argument


His argument was mathematically correct – and perhaps economists who knew about Stigler’s paper then thought: "why bother changing? The textbook fallacy and Stigler’s accurate mathematics reach the same conclusion, the fallacy is easier to teach, let’s stick with it”. But my reaction was that it was logically impossible for a fallacy and a correct argument to reach the same conclusion – there had to be something wrong with the 'correct' argument as well.

A bit of calculus quickly revealed the problem: equating marginal cost and marginal revenue, which economists describe as "profit maximising behaviour” doesn’t actually maximise profits. Instead, for any firm other than a monopoly, it results in a production level where the firm produces more than the profit-maximizing level. In the economists’ 'ideal' model of perfect competition, firms don’t just break even on the last item produced, as economists allege: they lose money on almost 50 per cent of the output that the theory recommends they produce.

I’ve yet to have any neoclassical economist engage with this substantive part of my argument (which I explain verbally on pages 96-98 of the new edition of Debunking Economics as well as academic papers like this maths-heavy one, or this one in the physics journal Physica A). And I’m sure they’d distort my words if they did, because it goes to the heart of the Holy Grail: maximising profit and maximising social welfare are incompatible.

This result is also not new: this is one way of interpreting the outcome of the Cournot-Nash model of competition. In that model, strategic reactions to what their competitors might hypothetically do push firms into a 'Nash Equilibrium' where they produce more than the profit-maximizing output level, but end up unintentionally maximising social welfare.

Why then do economists continue to teach the mathematically false Marshallian model to new students, when they could teach a mathematically sound one instead? Again, I expect the sloppy pedagogy that characterises this pseudo-science is partly to blame: "why teach a difficult correct model when a simple false one reaches almost the same result?”

But the quest for the mythical Holy Grail is also important. The vision of a perfect society in which individual profit and social welfare are compatible is so seductive that economists teach that as part of the initiation rite into their discipline, which is far more a religion than it is a science. Admitting that the Holy Grail doesn’t exist is just too difficult for this intellectual priesthood.

Steve Keen is a professor of economics and finance at the University of Western Sydney and author of Debtwatch and Debunking Economics.

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Why are so few economists real millionaires? (Wave goodbye to the invisible hand, September 17.)
Steve - I have followed a lot of your work over the years and have realised that you are a very smart dude (one PhD to another).
Unfortunately you are probably too intelligent for a lot of your critics and they just can't understand where you are coming from.
Keep up the good fight - it's a joke how much the neo-classical crowd can get in wrong yet their beliefs & policies still govern our economic/political world (Wave goodbye to the invisible hand, September 17).
Hi Steve
Consider shopping centre industry that I have studied for 20 years. Winner takes all vs balanced.
1. Current asset bubble;
2. Signal where floor price (rent) is above equilibrium (S & D curves), more supply gets added to given market;
3. Centres get bigger;
4. Businesses outside centres including “landlord’s business” i.e. smaller property owners close down as asset is duplicated and triplicated;
5. To keep monsters alive, and propping up “valuations”, there is a “leasing machinery” designed to keep jamming newly capitalised businesses into (new business capital, to be depleted of capital through disproportionate rents) centres and keep justifying “business model” on steroids;
6. On top of it, many tricks to keep “dream” alive eg. longer trading hours adds more “supply” on to give market, without physical construction, but the “model” of trading longer hours allows bigger centres to gain market share against smaller centres;
7. By working longer hours to cover rent, operators do not see their families to pay rent (cannot afford penalty wages). Their capital is “entrapped” into bad system;
8. There are onerous fitout and defit works to supposedly comply with leases through related companies i.e. third line forcing; etc.
In end more fossil fuel is used by an aging population to get to fewer bigger centres.
So far it has blown up $65.0 billion in shareholders’ funds, plus resorted to seek more capital from shareholders, plus now issued corporate bonds ranking shareholders second.
The behaviour has not changed; another correction is immanent. Here is an industry trying too hard rather than allowing natural forces of S & D and “demand driven” demand, to drive supply.
That is because the “supply” is justified by related entities who also profit from dumping more “supply” on to the given market. Show me the winner?
Steve, I agree with your conclusions but must add that it is quite unnecessary to use mathematics to debunk the supposed connection between economic self-interest and social benefit (Wave goodbye to the invisible hand, September 17). Rather than the somewhat remote abstraction inherent in mathematics, all you need to understand is the psychology of individuals and the dynamics of groups. A knowledge of history helps a lot too.
As for the so-called free-market rationalists who seem to dominate the profession,these are the same intellectual giants who:
- couldnt forecast the GFC,
- told us that private debt
didn't matter (except that it
was central to the GFC!)
- informed us that the free
market had produced the Great
Moderation (except that it
was soon followed by a gut-
churning plunge off the
economic cliff!)
- reckoned that current account
deficits don't matter (except
that they are a key issue in
many of the Eurozone's problem
- tell us that foreign
investment is good for
Australia no matter how many
of our national assets are
foreign-owned (while failing
to observe that three
decades of massive foreign in-
flows have not even looked
like yielding us one current
account surplus!)
Bill Edwards
Hi Steve,
What we have now is crony capitalism and not free market economics (Wave goodbye to the invisible hand, September 17).
Free market is a philosophy and not something one can write well with charts and graphs. The reason is core to the argument of the 'invisible hand', which you seem to have missed consistently for the last few years you have been writing about economics. No one can actually predict how businesses pan out and how forces that shape demand and supply reach an equilibrium. Free market is required to achieve this equilibrium at all times.
The imbalance we see today is due to the regulatory capture by the banking system and political entities which has slowed innovation and led to mal-investments. If the underwriting laws were not relaxed by the above vested interests, we would have seen criminal prosecutions against the wreckers of free market, at a stage where it would not have resulted saving them under the pretence of "too big to fail". Another factor of imbalance is the lack of equity held by financial institutions and executive compensation which is based on the thin sliver of equity deployed and not on the total capital deployed along with debt. After doing that "Mr Keen' see the "invisible hand' becoming 'visible'.
There is no such thing as capitalism/free market/invisible hand any more. Too much of regulation has made capitalism redundant and consequently 17th century Adam Smith's theory is not relevant now (Wave goodbye to the invisible hand, September 17).
As you correctly point out, the invisible hand is a metaphor (Wave goodbye to the invisible hand, September 17). Your debunking of the mathematical assumptions behind the neoclassical definition of "profit maximising" does not affect the relevance or importance of the metaphor.
To truly wave goodbye to the invisible hand you will need to provide a verbal critique that shows how individuals are harmed by other people offering them goods and services that they want enough to exchange for money.
One of the difficulties is that people take economics as a precise science that can be calculated and the components of the visible hand can be defined ( Wave goodbye to the invisible hand, September 17). That is not reality.
Smooth curves (demand or supply, margial cost or marginal revenue) do not or at best rarely exist. All you can ever do is approximate them round the vagaries of running a business, constrained as it is by so many unchallengable monoply cost factors.
The invisble hand was developed to create a shorthand for these vagaries that are often difficult to describe. The positive aspect of the invisible hand is to create a paradigm. It portrays market competition that in turn helps drive costs down, through innovation, use of technology and responding to the market in ways monopolies can never do.
As summer comes along and power shortages occur on hot days, thank the monopoly system in play that have created the environment in which we live.
It is a valid argument to say that social welfare isn't maximised perfectly by people pursuing their own self-interest in market transactions (Wave goodbye to the invisible hand, September 17).
However what is your alternative?
Perfect competition, etc is very, very rare. The principle however applies.
The whole idea of the invisible hand is that in general people must find mutual benefit in order to profit. That's a true principle and that's all it is. Mathematical measurement of utility is a fallacy to begin with.
What we can take away from the "invisible hand" principle is that you'd expect privately owned resources to be used more efficiently that publicly owned resources. We can also say that profit-seeking businesses have an incentive to serve consumers.
We must be watchful of monopolies and duress however a centrally-planned economy has clearly and decisively proved to be worse for social welfare.
Finally, saying that "crazy free market economists" failed to forecast the GFC is factually untrue. If people are forcibly categorised by such labels you could find people of various schools of economic thought who forecast the GFC.
In saying that, virtually all schools of thought have made mistakes and needed refining and debate.
Understanding economics is essential in our market economy, and we can do it usefully with spending little time on econometric models and with spending little time on tax and budget 101 style discussions
(Wave goodbye to the invisible hand, September 17).
Economics is all about resources development, all kinds, HR mining etc.
If you get the most from your resources HR etc... you have more “stucks and stuffs” of all kind available than you need ... and you do not have to worry about budget and taxes, as it all becomes a piece of cake.
Economics is resources development, the rest is academic.
I think a lot of economists these days get hooked on the mathematical solution to what is actually immeasurable subjective behaviour by market players (Wave goodbye to the invisible hand, September 17). These economists love solving abstract puzzles and producing mathematical or econometric models only capable of remotely echoing real events.
In the real world, markets are trial and error situations where sellers copy each other and gradually improve performance (better efficiency, including the adoption of new technology). Innovators set the pace and get the early profits when price can be above costs until the competitors catch up and increase supply. These short term profits are the incentive to innovate and in no way should we discourage this process by claiming there is damage to social welfare, a very vague term which I doubt anyone could mathematically assert is greater under some system without profit incentives.
Ultimately, whatever the measuring frustrations of the mathematical economists, markets do produce the highest prosperity for all because they comprise many decentralised competitive learning locations where the knowledge problem is best solved and where self interest, despite being politically incorrect, drives competition, efficiency and innovation and therefore is best able to serve the most diverse needs for the most individuals.
There are very few true monopolies where there is no possible competition; most cases are those with excessive entry costs but even these must be watchful of overzealous pricing or the pressure of consumers will lead to their elimination through new technologies or alternative goods provided by ever lurking potential competition.
Yes, there are laws of economics but these concern ordinal relationships, not precise or cardinal measurement. It would be preferable, in my opinion, to avoid handicapping markets and students with high-sounding abstract nonsense.
I agree with Alan Bedkober(17 Sep 2012 3:12 PM), the market forces and innovation as he describes it act in synergy with resources development, actions of the government must concentrate on keeping the market loop alive. Derivatives and other punting systems overkill the market, besides the potential fraud problem.
(Wave goodbye to the invisible hand, September 17).
With so many conflicting views amongst economists, I believe the penny is finally dropping that economics is itself more religion than science and is awash with mathematical formulae that can accurately analyze history but trip over themselves in their relevance to the future. Occasionally, when a economist gets a prediction right, there's much cause for back-slapping but, of course, its contribution to mankind is zip (Wave goodbye to the invisible hand, September 17).
Adam Smith's contention that the self-interested drive for profits leads "as if by an invisible hand" to an outcome that is socially beneficial to all is one of the most potent propositions ever uttered.but he did not know that the 'invisible hand' how to move from the market to the terrorism or the human war (Wave goodbye to the invisible hand, September 19).
From a number of comments I would be surprised if you had not heard of the so called Austrian School of economists who accurately predicted the 2008 debacle (Wave goodbye to the invisible hand, September 19).
For a more thorough investigation of economics please see www.mises.org
You start with A Smith's invisible hand which is a product of individuals' self-interest (Wave goodbye to the invisible hand, October 3). Smith's idea is sound in his time when nature has not been threatened by environment degradation which is the result of human over-consumption and over-production coupled with intensive use of natural resource-demanding technologies. It is unfortunate that Smith's idea has led to the now obsolete quantity theory MV=PQ which ignores the role of nature in the determination of Q. In a moneyless economy (for example Cambodia 1975-1979), Q is not zero and PQ however defined should be MV + aG where aG represents the value of utilised natural and human resources. Big economic development projects have to pay increase attention to their impact on nature nowadays and a new definition of GDP is required.
On microeconomic ground, Smith's idea is too brief and has led to many misunderstanding on the connection between self-interest and social benefit, especially the confusion of firm's profit maximisation and optimisation of social welfare. Surely firm's profit is maximised if P=MR=MC, however optimisation of social welfare needs the distributive efficiency where P equals consumers' marginal valuation of the product. Too much focus on individual firms production and their profit maximisation process while overlooking the distributive efficiency leads to over-focusing on the 'ideal' perfect competition among firms; to ignoring the long-run impact on consumers' valuation of a product and its feedback on producers' decision; and to the conclusion that the slope of the demand curve for the individual firm is the same as the slope of the market demand curve which is true only in the short-run.