Two damning but rather technical arguments against the neoclassical theory of the firm were left out of the book because the technicalities could confuse a first-time reader. These are (1) that the conditions required for economists to be able to reach their definitive conclusion that monopolies are worse for welfare than perfectly competitive industries are contradictory; (2) that setting price equal to marginal cost does not maximise profits for the supposedly profit-maximising perfectly competitive firm.
Monopoly and perfect competition can’t be compared
One assumption economists make when they compare monopolies to perfectly competitive firms is that the marginal cost of production of many small firms is equivalent to the marginal cost of production of one single large firm, at all possible levels of output.
This assumption is necessary because without it the marginal cost curve which would be drawn for the monopolist could be different to the sum of the curves drawn for the competitive industry. If they are different in theory, then it is impossible to say that monopoly output will necessarily be less than perfectly competitive output, and that a monopoly's price will be higher. If the curves are different, then it would be quite possible for monopoly output to be greater and monopoly price lower than the competitive price, even if competitive firms did set marginal cost equal to price.
This possibility is shown in Figure 1: the sum of the small competitive firms' marginal cost curves is much higher than that of the monopoly. As a result, even if the competitive industry sets price equal to marginal cost, its output of Qpc is less than the monopoly output of Qm—even though the monopoly's price is much greater than its marginal cost. Similarly, the competitive price of Ppc exceeds the monopoly price of Pm.
Figure 1: if the marginal cost curve for a monopoly isn't identically equal to the sum of the marginal cost curves for competitive firms, then you can’t definitively say that competition is better than monopoly
So for the theory to be able to argue that a competitive industry will produce a higher output at a lower price than a monopoly—given the assumptions that a competitive industry sets price equal to marginal cost, whereas a monopoly sets price where marginal revenue equal to marginal cost—then the sum of all the marginal cost curves of the competitive firms must be equivalent to the marginal cost curve of the monopoly, at all levels of output.
This requirement means that there are restrictions on the shape that the marginal cost curves can take, in addition to the requirement that they must be upward sloping.[1] As you will shortly see, the only marginal cost curve that fits this additional requirement is a horizontal straight line. [2]This dilemma is rather similar to that outlined in Chapter 2, that in order to aggregate individual utility to social utility, all individuals have to have the same preferences regardless of income.
This argument is very easy to prove using mathematics, but it takes a bit of intellectual legwork to understand the proof without maths.
To explain it to you, I first have to remind you of some details from Chapter 3. First, you will remember that marginal cost—the cost of producing the last unit of output—is derived directly from marginal product (the productivity of the last worker if labour is the 'variable factor of production') and the real wage. Since, in this comparison of monopoly to perfect competition, economists assume that firms can hire as many workers as they like at the going rate, the only thing that can cause marginal cost to change is a change in marginal product. Marginal product is in turn derived directly from the 'production function', which economists argue displays diminishing returns (because of the impact of adding more and more units of the variable factor of production to the fixed factor).
OK. This economic chain of logic means that we can work in terms of marginal product, rather than in terms of marginal cost—since the former determines the latter. Now, if the marginal cost of producing the billionth unit of a commodity is the same for a monopoly as it is for 100,000 competitive firms, then the marginal product of the worker who produced that billionth unit is the same too.
The next step in the logic uses a simple rule of mathematics which tells us that if the marginal products are the same—the rates of change of total products—then the total products can only differ by a constant. Furthermore, if we use labour as the variable factor, then that constant will be zero, because employing zero workers will lead to zero output.
What the previous two paragraphs establish is that the initial condition—that the marginal costs are identical—is the same as the requirement that the total output curves are identical. The total output of a competitively organised industry that employs a million workers, ten to a factory, has to be the same as the total output from a monopoly employing the same number in the one factory.[3]
This is shown in Figure 2: the output curve for the competitively organised industry has to be the same as the output curve for the single monopoly. If point C for the monopoly (on the right) is equivalent to one million workers, and the output Q is equivalent to one billion units, then points C and Q have to be the same for the competitive firms (on the left)—even though there are 100,000 of them, each employing ten workers.
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Figure 1: The total product curves must be identical if the supply curve for the competitive industry is to equal the marginal cost curve for the monopoly
Here comes the problem. The competitive industry output curve is derived by adding up the outputs of numerous small firms. The output of many small firms can be aggregated by simply putting the firms' output curves together head to tail, as in Figure 2.[4] If we join together numerous product curves that are subject to diminishing marginal returns, then we get a jagged curve.
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Figure 2: Adding up the total product curves of lots of small firms, all of whom experience diminishing marginal productivity
This will not be the same as the smooth output curve for a single large firm. The only way the output curve of many small firms can equal that of one large firm is if the output curves are straight lines with the same slope, as shown in Figure 3.
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Figure 3: The only way you can get a smooth total product curve from adding up lots of small product curves
But a straight-line production function means that each additional worker produces just as many units as all previous workers. Marginal product is constant, and therefore so is marginal cost. The supply curve for both perfectly competitive and monopoly firms would have to be the same horizontal line.
This presents no insurmountable problems for the model of monopoly producer facing a downward-sloping demand curve. But for the model of perfect competition, it presents another paradox. If the marginal cost 'curve' is a horizontal straight line, and the marginal revenue curve is also a horizontal straight line as economic theory assumes, then either they never intersect or they are the same line. In either case, the theory can't determine how much a firm will produce.
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\Figure 4: The models of monopoly and perfect competition without diminishing marginal productivity
Figure 4 illustrates this dilemma. The conditions under which aggregation of output is possible make it impossible for the fiction of the horizontal demand curve to be maintained, since in this case, as illustrated in Figure 4(b), the level of output is indeterminate. However, a horizontal supply curve for a monopoly presents no dilemmas, since it faces a downward-sloping demand curve.
It seems that the theory which prides itself on describing everything in terms of curves—diminishing marginal utility, increasing marginal cost, etc—cannot escape straight lines. This cause of this recurrent nightmare is explained in Chapter 11.
Neoclassical rejoinder
Since this argument has yet to be published in an academic journal, there is no published attempt to rebut it. Possible rebuttals that have been put to me to date include (a) that the assumption of free entry will keep price equal to marginal cost; (b) that I have neglected the assumption of 'perfect information'; and (c) that other theories of competition—such as 'contestable markets'—will give the outcome that marginal cost equals price.
The belief that free entry will restore the theory has already been discussed. Why would profit-maximising firms enter an industry where a substantial proportion of output is being produced at a loss? Profit-maximising firms would feel no incentive to enter such an industry.
'Perfect information' is the proposition that all consumers in a perfectly competitive market know the prices being charged by all the suppliers. Since they have no brand loyalty, if one supplier charges a higher price that the rest, she will immediately lose all her sales to the rest of the industry. Conversely, if she drops the price, then she will be inundated with the entire market demand curve.
The reply to this rejoinder is simple. Dealing with the second case first, the firms in a perfectly competitive firm are constrained by their size. If one firm charges a lower price and attracts a flood of customers, then it will be forced to put prices up again.
If, on the other hand, a firm charges slightly above the going price, then other firms will receive its customers. Since the model assumes diminishing marginal returns, these firms will all incur slightly higher costs and will put their prices up. Though the effect on the marginal revenue of each will be slight, the effect on the entire industry will counterbalance the effect of the loss of the output of the initial firm.
But in fact the assumption of perfect information supports our critique. As our argument in (5) above shows, the assumption of perfect information spreads to all firms the beneficial impact of a reduction in sales by one firm. Thus if one firm 'breaks ranks' and reduces output from the level at which price equals marginal cost, all other firms are likely to follow.
The final comment to make here is that the concept of perfect information itself is flawed, both practically and theoretically.
It is practically flawed because the information demands it makes are enormous—individual consumers would require processing and memory power well beyond that which is humanly feasible (this is due in part to the 'curse of dimensionality', noted in Chapter 2). Perfect information requires costless, instantaneous knowledge of the prices being charged by an almost infinite number of firms, and the ability to access any firm's output at zero transportation costs. This concept was possibly defensible before the Information Age taught us about data processing, storage and retrieval; it is manifestly indefensible now.
It is theoretically flawed because, like so many other assumptions in economic theory, it is schizophrenic. All consumers are assumed to have perfect knowledge about all firms but no knowledge about other consumers, while firms are assumed to have no knowledge about other firms. 'Perfect ignorance' is thus required as an adjunct assumption to perfect knowledge, since if consumers were aware of each other, they could collude to lower the market price, while if firms were aware of each other, they could collude to raise it.
Perfect information thus requires consumers to be schizophrenic and irrational supercomputers who devote all their immense processing power to keeping tabs on firms, but who forgo using this formidable apparatus to collude with other consumers to lower the market price. Firms, on the other hand, have to be essentially dumb terminals whose only knowledge of the outside world comes from the market price.
The third rejoinder, that other models of competition may ensure that marginal cost equals price, is even more easily dealt with. Whatever model is proposed, for an industry to produce where marginal cost equals price requires that industry to produce part of its output (the amount in excess of the monopoly level of output) at a loss. The socially rational objective of marginal cost equals price thus requires individually irrational behaviour. Since economics is founded on the concept of individual rationality, I doubt that economists will embrace any 'solution' to this dilemma which relies upon individual irrationality.
So what?
Economics has championed the notion that the best guarantee of social welfare is competition, and perfect competition' has always been its ideal. This critique shows that economic theory has no grounds whatsoever for preferring perfect competition over monopoly. Both fail the economist's test of welfare, that marginal cost should be equated to price.
Worse, the goal of setting marginal cost equal to price is as elusive and unattainable as the Holy Grail. For this to apply at the market level, part of the output of firms must be produced at a loss. The social welfare ideal thus requires individual irrationality. This would not be a problem for some schools of economics, but it is for the neoclassical school, which has always argued that the pursuit of individual self-interest would lead to the best, most rational outcome for all of society.
Economics can no longer wave its preferred totem, but must instead choose between the two shown in Figure 13.[5] Either the demand curve can be drawn downward sloping (if we ignore the consequences of the Sonnenshein-Mantel-Debreu conditions), but supply can only be shown as a point determined by intersection of the marginal cost and marginal revenue curves, which are an integral part of this modified totem. Or, worst of all, if the theory wants to be able to compare perfectly competitive firms to monopolies, then the marginal cost curve in Figure 13(b) must be drawn horizontally—in which case the model of perfect competition collapses.
Perfect competition is thus decidedly less perfect than economists have believed. But the preceding critique is not the end of the bad news. Not only does it fail to provide a higher welfare level than monopoly, it may also be unstable and liable to collapse into monopoly over time—as Sraffa pointed out in 1926.