Edward Chamberlin

When Samuelson arrived, the most well known member of this group was Edward Chamberlin. His reputation rested on a book based on a PhD thesis he had submitted to Harvard in 1927, published as The Theory of Monopolistic Competition (1933), which appeared in the same year as The Economics of Imperfect Competition (1933a), by the young Cambridge econo­mist Joan Robinson.

h. See chapter 8 this volume. to be found in Alfred Marshall’s Principles of Economics (1920), widely used as a graduate textbook in economic theory. The received theory, associated above all with Marshall, was based on a distinction between two types of market. Monopoly meant that there was a single seller who could raise or lower the market price so as to achieve the combination of price and quan­tity sold that maximized profit. Competition involved markets in which there were too many sellers for any one of them to influence the market price and in which high profits would attract new sellers into the market, pushing prices down to the point where no one earned more than the “nor­mal” rate of profit. Chamberlin’s “monopolistic” and Robinson’s “imper­fect” competition covered the intermediate case in which each seller had some market power (as with monopoly), but in which high profits would attract new sellers into the industry (as with perfect competition). For his whole career, Chamberlin was concerned with differentiating his theory from Robinson’s. Not only had his doctoral thesis been submitted before the controversy had even begun out of which Robinson’s book emerged, but the two books were methodologically very different. Whereas Robinson’s book was an exercise in abstract economic theory, Chamberlin had sought to create a realistic theory to account for companies’ behavior in a world in which advertising led to product differentiation and where companies might respond to changes in market conditions not by changing their prices but by investing more in marketing.²³

Though Chamberlin was considered the rising star of Harvard’s depart­ment, Samuelson was not impressed with his course.

i. The reason for this was no doubt Chamberlin’s obsession with defending his youthful work.

It was the norm for many visiting foreign scholars to drop into this lecture, and one day, instead of Chamberlin, when Samuelson was pre­senting his own paper on “duopoly theory,” Nicholas Kaldor came into the class. As soon as the discussion following the report had con­cluded, he walked towards the lectern proffering his hand in greeting with a “Congratulations, Professor Chamberlin. It was an excellent lecture.” It was a perplexed Samuelson who was being offered the handshake, and he was at a loss as to how to respond. Kaldor, who real­ized his mistake immediately, turned towards the real Chamberlin and came up with a specious excuse saying he was expressing his gratitude for guiding such a brilliant student to this level. A few years later, I asked Kaldor about it, asking “Was it an act?” He only responded with a suppressed smile and “Why, of course!”

Twenty years later, when Chamberlin was on leave from Harvard, Samuelson agreed to teach this course as a visiting professor. Chamberlin provided him with the reading list he used, prompting Samuelson to remark that it had barely changed since he had taken the course.²⁶

Samuelson’s papers contain an undated and incomplete manuscript on the problem of oligopoly.

Samuelson’s main point was that the problem of oligopoly, includ­ing the special case of duopoly (two agents interacting with each other), was indeterminate in that the specification of the problem did not make it possible to determine a unique solution: there was an infinite number of possible outcomes. In this respect, it was fundamentally different from problems of monopoly and competition as traditionally conceived, includ­ing Chamberlin’s monopolistic competition. He wrote down an expression for what each agent was trying to maximize, but concluded that, except for special cases, “there can be no objectively correct judgment by any seller as to the form of this function.”²⁸’’ For example, in a duopoly each seller could influence its rival's belief about how it would react to the rival's actions: the functions describing behavior were, Samuelson wrote, “essentially unstable and depend upon the past behavior of each seller, his ‘bluff,' etc. And is no more stable or predictable than would be the result of the nigglings of two equally powerful bilateral monopolists.”²⁹ He concluded,

We must agree with Professor Chamberlin that in the absence of Uncertainty as to what one's rival is going to do we get deterministic solutions.

Samuelson attempted to be more general than the existing literature in at least three respects. He did not specify whether his oligopolists were choos­ing prices or quantities, thereby claiming that his statement of the problem was more general than those found in the previous literature.^k He argued, in an appendix to the paper, that the problem of duopoly was equivalent to that of bilateral monopoly, implying that his theory covered both. And his argument ran in terms of “individuals,” who need not be the firms or com­panies discussed by Chamberlin: he seems to have been consciously aiming for a more general theory of human interaction and not just a theory of how companies behaved. These individuals were assumed to be rational, causing Samuelson to write,

We mean by a determinate solution that set of values of the variable involved to which the individuals under discussion must eventually arrive at if they behave rationally, being in full knowledge of the situation. When there are an infinite set of such values possible, we speak of the solution as being indeterminate.³¹

This definition, he claimed, was generally accepted, especially among math­ematical economists.³² He was seeking a general theory of the interaction

j. Individual i = 1,.. n maximizes Z_i = Z.(q_ι, q₂,... q.,... q^ where the q’s are interdependent. In most cases, individual i is assumed to control q,. As explained in the text, the qs could be prices or quantities.

k. He cited the early nineteenth-century mathematician Augustin Cournot, as well as Chamberlin, on this point.

between rational individuals, trying to focus on the general problem and avoid getting sidetracked by “the arithmetic of particular solutions” found in the existing literature.³³

Though Samuelson was engaging directly and in detail with Chamberlin’s work, he approached it from the perspective of Leon Walras and Wilfredo Pareto. One of the points he criticizes Chamberlin for is that of failing to see the problem of indeterminacy in the way that the turn-of-the-century economist, Pareto, with his mathematical training, did: in terms of having the wrong number of equations to determine the unknowns.³⁴ Given that it is possibly the earliest example of Samuelson’s making an analogy with phys­ics (something that was to become a habit), it is worth quoting the relevant paragraph in full:

In the year 1887 two young scientists puttered in the basement of Ryerson Laboratory at the University of Chicago on an experiment the results of which were eventually to blast the Scientific Cosmos of the Victorian Age into confusion and chaos. What the Michelson-Morley experiment did to the Victorian Synthesis, the theory of Duopoly may be said to have done to equilibrium theory in economics. Just as Newtonian mechanics is still taught in most physics classes, we still teach in our economics classes the conventional Walrasian system in economics, but on the forefront of economic thought lies the shadow of duopoly.³⁵

It was no doubt the enthusiasm of a recent graduate for his alma mater that led him to overlook the fact that the Michelson-Morley experiment—which raised doubts about the concept of aether, through which light waves would propagate as sound waves travel through the air, by establishing that light traveled at the same speed in all directions—was undertaken before Michelson had moved to Chicago and before the Ryserson Laboratory was set up. The passage shows the level at which Samuelson had set his ambitions: not simply to settle the theory of duopoly for good, but also to overthrow the standard theory of economic equi­librium, which he associated with Walrasian theory. Chamberlin, too, sought “a reorientation of the theory of value” (the subtitle of his book), but he did not associate the theory he was trying to change with Walras.

Moreover, though Samuelson agreed with Chamberlin that the problem was determinate if there was no uncertainty about one's rival's behavior, Samuelson went further in arguing that there would always be uncer­tainty because this was a consequence of having more than one “free-will” operating in an interdependent system. Certainty was impossible. He also challenged the significance of Chamberlin's analysis (in chapter 5 of The Theory of Monopolistic Competition) of how monopolistically competitive markets respond to changes in demand. This is perhaps what Samuelson meant when he wrote that he was comparing chapter 3 (on duopoly and oligopoly) with chapter 5 (on product differentiation and the theory of value): he was using the first of these chapters to undermine the argument found in the second.^[6]

The paper is also important because it shows that Samuelson was familiar with the content of parts of Pareto's major work on economics, which was not to be translated into English for another four decades. It seems most likely that he read it in French, something that would not have been difficult given that he had passed an examination in the sub­ject and that Pareto's use of mathematics would have made reading much easier.^m Given this, it seems safe to suggest that he would also have looked at Walras's Elements d’economie politique pure. He was simultaneously taking a course with Schumpeter, who would certainly have mentioned Walras, piquing Samuelson's interest.

Though Chamberlin's course was in the fall term, Samuelson wrote another paper for Chamberlin in the winter, presumably in December 1935 or January 1936. This built on the earlier paper, which it cited, but it was completely different in style.³⁶ That earlier paper tackled a problem that was perhaps too difficult for him to handle rigorously. It followed Chamberlin closely in the way it analyzed change, and it is perhaps not a coincidence that it tackled the one topic on which Chamberlin's book provided, in an appendix, an algebraic treat­ment. Samuelson's second paper abstracted from time and all other complica­tions, providing a rigorous algebraic discussion of the simplest possible case, where a firm was maximizing the difference between revenue and cost, where these depended solely on output. Interactions between firms, advertising, product differentiation, and other factors were assumed away so that he could derive the conditions under which profit would be maximized—that marginal cost equaled marginal revenue.³⁷ Perhaps because it was a criticism of those he saw as his rivals at Cambridge (UK), Chamberlin had noted “Good” in the margin at the point where Samuelson observed, “It is perhaps a reflection on modern economists that it should have received attention only after its presentation by means of involved (and practicably useless) Euclidian geometry (Cf. Robinson et al.)”³⁸ His target here, which Chamberlin would have appreciated, was Joan Robinson, whose Economics of Imperfect Competition spurned algebra (which she did not understand) and made extensive use of geometry.

Samuelson then introduced advertising, deriving the maximum condi­tions, this time using partial derivatives. This led to a discussion of the best way to represent a problem that now had three dimensions rather than two (price, output, and advertising expenditure). After rejecting the method of “contour lines, or so called lines of indifference,” he opted to use the method of envelopes, on the grounds that it could equally be applied to an n dimen­sional problem. After drawing revenue curves to illustrate the effects of dif­ferent levels of advertising, and drawing the envelope (the curve that showed revenue given the optimal level of advertising for each level of output), Samuelson showed how this problem could be reduced to one that was for­mally the same as the previous one, by replacing revenue with “net gross revenue”—revenue net of optimal advertising cost. Product differentiation could be handled in precisely the same way, this time by introducing “prod­uct quality” as a variable. Here, however, he went in another direction, in that product quality need not be a single variable but might involve a num­ber of attributes, each of which could be chosen by the firm.

After this, Samuelson turned to joint production, where a firm produces more than one product using more than one factor of production, deriving optimum conditions that include the marginal productivities of different fac­tors. This involved more variables but the required mathematics was no more complex than partial differentiation of a function of several variables. More complicated mathematics was required to handle the next generalization— production for sale to customers who are spread out over an area, incurring transport costs proportional to the quantity of goods sold and the distance over which they had to be transported.ⁿ It was at this point that he intro­duced the problem of indeterminacy, for if each firm serves a specific area,

n. To solve this problem it was necessary to introduce integral calculus and to describe space in terms of polar coordinates so as to reduce the dimensions involved. then it must be in competition with those firms that produce in neighboring areas, implying oligopoly (competition between a small number of sellers). Because output would depend on the actions of competitors, “these interrela­tionships would in general be indeterminate,” leading to the same conclusion as in duopoly, “that in the absence of the specification of given (arbitrary?) extra conditions as to these interrelationships, our result is indeterminate.”³⁹ There was, he concluded, “no presumption in favor of a symmetrical or ratio­nal [sic] settling along the line [or over the area].”⁴⁰

Finally, he turned to “the most difficult problem of all,” that of time. Even this problem could, so long as there was no uncertainty, be simplified so that it fitted into the same framework, through discounting the net income expected at each point in the future to obtain a present value. What increased the mathematical complexity of the problem was that Samuelson assumed that net revenue depended on advertising, which meant that the firm had to decide how to set its advertising expenditure over time.

In this case, before we know our quantity to be maximized, namely net value of assets, we must know the value of advertising expense at every instant of time, since, for every different function between E [advertis­ing expenditure] and T [time], we get a different value of V [profit]. Thus we have here a functional instead of a function.... Our problem becomes one in the Calculus of Variations.⁴¹

At this point, Samuelson drew the paper to a close because he considered it long enough. Going further would require even more advanced mathemat­ics, raising the problem that “to the trained mathematician the results would seem, I am afraid, more or less trivial,” whereas “to the economist, ‘almost entirely innocent of mathematics,' the results would be unintelligible.”⁴² What is interesting about this remark is that he was seeing himself as poten­tially addressing audiences of mathematicians and economists. He closed with remarks on the relationship of his analysis to reality. He had defended the most abstract part of the paper, on choice over time, by claiming that “the business man is constantly in every experiment and in every decision, going through a process exactly comparable to this mathematical one, except that he is always dealing with averages of finite intervals, over a total finite interval” (his mathematics assumed an infinite time horizon).⁴³ However, a page later, in his conclusions, he stressed the lack of realism in his analysis:

In the real world, there are no economic men behaving under the sim­ple conditions envisaged by our theories. Actually, decisions are made upon the basis of more or less hazardous guesses as to the nature of the complex form and relationships of the infinite number of related and relevant “variables,” and upon the basis of complex motivations. For this reason, our analysis, while internally consistent, does not present us with a picture of reality.⁴⁴

To give a “true picture of the complexity of economic life,” Samuelson claimed, the theory would have to be so cumbersome that it would constitute no more than an “extended description of a particular situation” that would have no explanatory power. For this reason, he continued, the analysis should be as formal as possible so that it did not lead to premature judgments about its relevance to policy.

Samuelson described the paper as comprising “fragmentary notes” on the grounds that he provided a series of disconnected models. He was, however, doing himself an injustice, for there was a clear logical development from one model to the next. Moreover, there was a unity to the paper, for it showed that all the problems could be analyzed in a similar way, and that results fol­lowed naturally from the mathematics. This was the reason why he neither claimed originality nor cited sources for all the theories.

Moreover, little claim is made to originality in what follows since I am unable to trace the origins of many of the conclusions which I have presented, and since moreover, so many of the interesting propositions presented develop naturally from the mathematics so that they cannot rightly be attributed to any individual, but must be owned in com­mon by all who even contemplate these problems.⁴⁵

Aside from a question mark in the margin by a point he did not understand, and some trivial corrections to the language, Chamberlin’s only comment, written on the front page, was “A very interesting paper. EHC.” One won­ders what Samuelson would have had to do on the course to have earned a straight A rather than the A- that Chamberlin gave him.^o