Debunking Economics Part 4: Monopoly vs Competition

I became aware of an interesting piece of trivia recently: the game of monopoly was actually invented, not by any fervent capitalist, but by a Quaker: Elizabeth Phillips. She was interested in the land value taxation theories of Henry George and created what she called “the landlord’s game” to show the unfairness of a monopoly over the supply of land.

What the properties on the London monopoly set are worth today, according to the Daily Mail: http://www.dailymail.co.uk/home/moslive/article-1393521/How-London-Monopoly-board-look-2011-Do-collect-200m.html

This post is about monopolies in general, and in particular about a claim often made by the libertarian right, that monopolies only exist thanks to government interference in the free-market – that without this interference free-market competition would prevent monopolies occurring. The claim is that one can “prove” that in the absence of subsidies monopolies always lose out to free-market competition. Like the “proofs” considered in my previous posts in this series, this one also collapses under the most cursory of examinations.

What economists claim they can prove is something called perfect competition. This means that for an economy comprised of many small, competitive firms, those firms will sell goods at their social costs. Whereas a monopoly firm would sell goods only until revenue from the last good sold was equal to the cost of producing it, and so would tend to both under-supply and over-charge society for its goods. But there is a logical absurdity implicit in the economists’ “proof” of perfect competition. Prof. Keen begins the chapter of his book about monopolies by asking us to imagine the following:

“Try this party trick: convince someone that the world is flat, starting from the premise that it is a sphere. The argument is simple. If you take a small enough segment of the world – say, the two [square] feet you victim is standing on – then the curvature of that segment is so small that it is for all intents and purposes, flat. Then consider the segment you’re standing on – it is also so small that it is effectively flat.

Next, consider the angle between two [adjacent] segments: it too is so small that it is effectively zero. So these two small segments are effectively flat. Finally, extrapolate your argument from these two tiny segment and the angle between them up to the entire globe. If you consider the segment your victim occupies and the segment behind him/her, that part is also effectively flat. Keep on going and the entire world is flat.”

Now the above “proof” is clearly absurd! The point is that a small operation, if done many times, can produce a big effect. Many almost flat segments joined together many times gives a different shape to that of many completely flat segments joined together many times – the former is a sphere, the latter is flat. For those familiar with calculus an integral is the sum of infinitely many infinitesimally small things – and this is generally finite, not zero.

It will turn out that to prove perfect competition, economists basically play the “party trick” Prof. Keen describes above! It will turn out that economists can’t integrate and moreover that they think all integrals are zero! They are as confused about limits as the Ancient Greeks were when they formulated Zeno’s paradoxes.

Fun with limits – this dinosaur comic takes an infinite amount of time to read! But it also fits onto a finite space. Sexy! See  http://www.qwantz.com/index.php?comic=1328

Is it really this bad? Let’s go through the economists’ “proof” to see if the “party trick” analogy was justified. Prof Keen begins with the generous assumption that the economists’ theory of supply and demand (which I have explored in parts 1-3) is basically correct. However:

“even if we accept, for the sake of argument that the market demand curve is smoothly downward sloping [see part 3] and represents community welfare [see part 1], that production is subject to diminishing returns [also see part 3] so that the supply curve represents the marginal cost of production and that static analysis is valid [see part 2], the economic argument for the superiority of the perfectly competitive market over the monopoly is still internally flawed.”

Prof. Keen first considers a monopoly. Like the firm described in part 3, a monopoly is assumed to produce until its revenue from selling one more good on the market (a.k.a. marginal revenue) is equal to its extra cost of producing that one more good (a.k.a marginal cost). Due to the law of diminishing marginal returns – an assumption going into the economists’ theory of the firm (see part 3 for criticisms) – if the monopoly were to then produce any more goods it would start to make a loss on its goods, whose price is falling as their supply increases. According to economic theory then, monopolies produce goods until falling marginal revenue equals rising marginal cost.

Then Prof. Keen considers a competitive firm. “Competitive” means that the firm is assumed too small to have any influence on the price goods sell for in the market. Imagine, for example, you go into business as a baker, having bought up a small shop to sell bread. You are, so to speak, “a drop in the ocean”. However much bread you do or don’t supply, the total amount of bread available on the market is basically unaltered by you. Hence your supply curve is almost flat (note the word almost – it’s important!) – changing your supply of loaves has very little effect on the price of bread on the entire market. This is the analogue of the (valid) “party trick” assumption that “the two square feet I’m standing on is almost flat, and the angle between it and the next two square feet is almost zero.

The above implies that the competitive firm will sell its goods at (almost) the market equilibrium price – the price that goods settles down to in the abscencee of your additional supply of them, based upon what people on average agree to pay [we assume the market can actually be in equilibrium! See part 2]. Why? Well, were you to sell goods at a higher price than this, people would buy these from your competitors instead and you wouldn’t sell anything. Were you to sell at a lower price, people would flock to buy your goods over those of your competitors. But because we are assuming the law of diminishing marginal returns, the rate at which you can produce goods is fixed in the short term [see part 3] – you would soon run out of your supply and disappointed customers would go back to your competitors, who would sell instead at the market equilibrium rate, thus making more profit than you.

So far so good. The next step of the “proof” is to add up the effect of all competitive firms to find their overall effect compared to the monopoly – and this is where the sleight-of-hand enters in. Economists now claim that that the total effect of a large number of competitive firms supplying at almost the market equilibrium/market demand adds up to a total supply (QC below) at a price (PC below) equal to exactly the market equilibrium price/market demand – hence the name “perfect competition”! Whereas a monopoly sets its supply and price dependent upon its own marginal return, and so will supply too few goods (QM below) at too high a price (PM below).

The graphical “proof” of perfect competition. Red curve = marginal revenue, blue curve = marginal cost, green curve = market demand.

But the sleight-of-hand employed to get out the above plot is every bit as invalid as the “party trick” proof that the Earth is flat. The cumulative impact of a large number of firms selling goods at prices almost equal to equilibrium prices is not a total supply sold at prices almost equal to equilibrium price. Each firm is actually incentivised to slightly under-supply and slightly over-price its goods. These many small deviations, caused by every competitive  firm slightly altering the total supply of goods, actually add up to a large total deviation – just as many almost flat pieces of earth added up to a spherical Earth. In other words, integrals are not zero, as economists seem to have assumed to get their “proof”!

What happens if we recall some basic facts of calculus that the economists have forgotten and decide to add all the competitive firms together correctly? The result is that adding together a large number of marginal revenue curves for all the competitive firms, which are almost (but not exactly) equal to the equilibrium price curve, gets a total marginal revenue curve that is *drumroll please* the same as the monopoly curve! That’s right – in a highly amusing twist, the set of competitive firms gives the same social outcome as the monopoly according to economic theory – at least when it remembers to pay attention to basic facts of mathematics.

This result is actually quite intuitively obvious and matches up to the “party trick” analogy beautifully. The Earth IS a sphere, regardless of whether or not one imagines cutting it up into many segments and joining these back together again! Achilles CAN catch the tortoise, regardless of whether one imagines splitting the race up into smaller and smaller intervals of time, then adding these back up. And when the economists’ theory of the firm is applied to all firms, no matter what their size, an economy split into smaller firms works THE SAME as an economy with one large firm – a monopoly.

Behold! The Earth is a sphere! The famous “blue marble” image, taken by the Apollo 17 crew in 1972 and possibly the most widely distributed image in human history.

Now all this would be rather funny, if economists were simply ignored by serious people. Unfortunately, policy makers are supposed to take perfect competition seriously. The holy writ of neo-classical academics sanctifies various ideologically motivated attempts to dismantle existing public services, or prevent new ones emerging, which may very well operate more efficiently than a system of private firms. Consider for example the US private healthcare system, which carries about twice the per-capita cost of equivalent state subsidized systems in Europe. Special pleading to the contrary often makes use of the kind of graphical “proof” I rubbished earlier.

So, having established that economic theory has nothing sensible to tell us about monopoly verses competition, what is the situation back in the real world? Prof. Keen gives a simple example of a large firm acting more optimally that a series of small ones. He asks us to imagine a farm with square fields. One cost of producing food is the fencing needed for the perimeter of these fields. This is proportional to the length of the field. Whereas a farmer’s revenue is proportional to this length squared – it’s set by the area of field he can grow his crops on. So larger farms make more profit (until some other cost factor kicks in at a larger scale, presumably). We’re back to “the landlord’s game” I began this post with, in which owning more land secured you an advantage over competitors. This is a simple example of economies of scale.

Neither Prof. Keen nor myself is saying that a monopoly is always a good thing of course. That would be every bit as absurd as the economists’ claim that a monopoly is always a bad thing! Monopolies may indeed be harmful and Prof. Keen gives some examples of how and when:

“The fact that there is no substance to the economic critique of monopolies does not mean that monopolies are good. There are plenty of reasons why monopolies can be ‘a bad thing’: they can bully and stifle potential competitors, set higher markups than more competitive markets, and use their monopoly power to exploit other markets. All these practices occurred in the 19th century with the ‘robber barons’, and these practices explain why America has its system of anti-trust laws.

Unfortunately the economic argument against monopolies has redirected attention away from these qualitative nuances to the simple issue of whether a monopoly exists – defined by the proportion of a market dominated by one firm. This simplistic criterion treats all monopolies as tainted, whereas the old anti-trust philosophy attacked monopolies for particular types of behaviour. The economic argument can therefore lead to monopolies being broken up where there were no signs of such behaviour, or where there were extremely good reasons why a single firm was far more efficient than a number of competing firms. Far from being a guide about how to achieve greater economic efficiency, economics may encourage us to dismantle effective companies and replace them with inefficient ones.”

The point of these examples is to show that it’s not sensible to merely say “large firms are good” or “small firms are good”. Rather, a firm will have some optimal scale at which it works best for society, given the market conditions specific to that type of firm. If the “firm” in question is supplying healthcare, or mass-transit, or telecommunications say, then perhaps the optimal scale is a nation state? Perhaps a government monopoly is more socially optimal than a set of many competing private firms? For other types of firm, perhaps the optimal scale is much smaller? Perhaps a system of competing private firms is then more socially optimal than a government subsidised monopoly?

I conclude my post with Prof. Keen addressing rather succinctly the issue posed by my title, that of monopoly vs competition:

“The proper manner in which the issue of monopolies verses competition should be approached is a case by case basis, where the merits of one form or the other of organising production can be dispassionately considered. The instinctive economic bias against monopoly should be replaced by something rather more intelligent.”

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~ by freedomthistime on January 14, 2012.

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