Wave goodbye to the invisible hand

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.