What is the limit on firm size?

Miles Kimball wrote,

Given the replication argument, there is no scale of operation that is beyond efficient scale. There may be ample reason to make different plants or divisions quasi-independent so they do not interfere with one another’s operations. But that is not an argument against scale per se. There may even be reason to set up incentives so that different divisions are almost like separate firms, headed by someone in an entrepreneurlike position. But that still is not, properly speaking, an example of diseconomies of scale.

Read the whole post.

So what are we to make of this?

1. For the economy as a whole, the law of diminishing returns applies. You cannot grow all the world’s wheat in a single flower pot.

2. But the size of any one farm is not limited to a single flower pot. Any one farm can keep adding land (until it gets to be large relative to the earth’s arable land).

3. Kimball sees the assumption of diminishing returns at the firm level as a staple of standard pedagogy. But it is more than that. Dropping that assumption takes you away from the perfectly competitive equilibrium, as Kimball spells out in his important follow-up.

4. What about the notion that the entrepreneur’s time or skill is a fixed factor? This appears to be a way to show that firm size must be limited. But it also is like question-begging or hand-waving. If you start with a traditional production function, with output a function of the two factors of homogeneous labor and homogeneous capital, then you have a hard time rationalizing diseconomies of scale until the firm gets to be really big relative to the whole market. So you tack on a fixed factor, and call it “entrepreneur’s time.” But the original production function assumed away the entrepreneur to begin with, and you never did spell out the entrepreneur’s role in that context.

5. Kimball’s approach in the second post consists of postulating a demand curve and zero profits and solving for firm size. That also strikes me as hand-waving, with math. Call it math-waving.

6. Think of a real-world example of monopolistic competition. I like to use ethnic restaurants in Wheaton, Maryland, near where I live. What stops a single owner from taking over multiple restaurants under the auspices of one firm? What stops an owner from then expanding to other locations far away, where the local demand curve is not a limiting factor?

7. When you do this thought experiment, you realize that firm size is not determined by the tangible variables that are central to neoclassical economics. Instead, you have to turn to principal-agent problems and whatever else might help deal with the “boundary of the firm” problem that has been articulated but not necessarily solved in a satisfactory way by Coase, Williamson, and Alchian and Demsetz.

8. Why are farms in two different states separate businesses? I would say that it is because it is costly for the Iowa farmer to observe the Kansas farmer’s effort, giving rise to a principal-agent problem. This may turn out to be a testable hypothesis. It predicts that as the cost of monitoring goes down (because of cheaper surveillance technology), we will see mergers take place that would have been unthinkable until recently.

9. This year, Amazon bought Whole Foods. Where does it stop? Where are the diseconomies (of scope, if not of scale)? Suppose that in order not to incur management costs, Amazon leaves Whole Foods executives in place and adopts a hands-off approach. Then from the point of view of somebody who owned shares in both firms, the merger only changed the form of ownership. You used to own a sort of mutual fund, and it was your choice how to weight the shares of Amazon and the shares of Whole Foods in that fund. Now you own shares in a conglomerate, with the weight fixed–you can no longer simultaneously reduce your holdings of Whole Foods while increasing your holdings of Amazon.

10. From the foregoing, it would appear that shareholders always lose in a merger, because they lose the option to alter the weights of their holdings. In fact, mergers have other effects, but they involve those intangible “boundaries of the firm” phenomena.

11. Suppose that a major element in a corporate merger is ego. The CEO of the company being acquired gives up status but gains wealth for the firm’s shareholders. The CEO of the acquiring firm does the opposite. The ego hypothesis predicts that immediately after the merger the acquiring firm will not give the post of CEO to someone from the acquired firm. It also predicts that the merger will be positive for the shareholders of the acquired firm but not for those of the acquiring firm. I haven’t kept up with the literature, but it used to be that those predictions held up.

12. In conclusion, the attempt to rationalize diminishing returns at the level of a firm in neoclassical economics opens up a can of worms, and Kimball’s math-waving with the demand curve does not close it.

7 thoughts on “What is the limit on firm size?

  1. On the farm side, farm states have legal barriers to farm expansion that don’t apply to other industries – especially limits to corporate ownership of farm land. These are breaking down in the livestock industries through leasing arrangements and other work-arounds. Crop farming is also consolidating as land prices increase and the current generation ages out, but it seems less amenable to the work-arounds.

  2. A growing firm faces a tension between economies of scale and the self-interest of each employee.

    In a firm with one entrepreneur and one employee, the entrepreneur can easily supervise the employee toward profit-maximizing activities. In addition, the employee’s prospects for continued employment are closely tied to the firm’s ongoing profitability. However, this firm could never manufacture cars, for example, profitably, because it lacks the necessary economies of scale.

    As the firm grows, each employee’s self-interest is slightly more separated from the owner-entrepreneur. As the firm gets larger, the joint production of all employees is increasingly divergent from what the market requests. Instead, some of the employees’ joint production is used to create longer coffee breaks, more internet shopping, and more personal story-telling. Eventually this firm is no longer competitive in the market, because too much cost and effort is channeled into non-profitable activities.

    This problem is exacerbated when, as in the modern corporation, even the top managers of the firm are not owners, and act to create wealth for themselves as opposed to pursuing profit-maximizing strategies for the firm.

    Therefore the employees’ individual pursuits of self-interest are constrained by the discipline of competing in the marketplace, and that’s why firms don’t continue to grow boundlessly.

    Government bureaucracies are not constrained by the discipline of the market. They therefore grow largely to serve the needs of their employees.

  3. In terms of size, when taking Econ Industrial Organization, I did have a Professor that large firms did have options to avoid the size of the factory/airplane marginal cost issues. (In 1992 this was less accepted.) So he talked multiple factories, different locations/nations and better run managers which of which did happen in the post-manufacturing US economy. So is there a limit to the size of the firm: Probably but it is a lot larger than ever. Why?

    1) When I think the consolidation in tech, I always rationalize this as the marginal cost of byte is exceptionally small. The cost to go from 1M to 2M app users is very small so that is why tech and large companies can grow so large. So what is the marginal

    2) A lot of consolidation is buying power of large firms. Wal-Mart can simply buy cheaper than anybody else and that reinforces their largeness long term. (It is not just claims as it is really true.) Look at banks. If Chase and Wells Fargo can borrow .10- .25% cheaper than anybody else, then any hope of a thriving small local banking system is not going to happen.

    3) I sort of assume one reason firms, say Wal-Mart, can’t too large is shareholders want profits not sale size. So Amazon ability to protect share price despite relatively merger profits is a wonderful economic experiment long term.

    4) Probably the area large firms have issues is their CEOs are becoming more political figures and running large firms, they will need degree of politician versus business experience.

  4. Aren’t many of these questions answered in Sraffa (1926) and Allen and Lueck (1998)?

    Allen, Douglas W. and Dean Lueck (1998). ‘The Nature of the Farm’, Journal of Law and Economics, 41(2) October: 343-86.
    Sraffa, Piero (1926). ‘The Laws of Returns under Competitive Conditions’, Economic Journal, 36(144) December: 535-50.

  5. What is the upper limit on military size? There isn’t one.

    At least if one is talking about theoretical maximums where resource / funding constraints aren’t dispositive issues. Furthermore, economies of scale are large, especially since variety is limited by uniformity. You might need a “standard setting” body of around 100 officers whether your military has ten thousand men or ten million. A constellation of GPS satellites adequate to serve unlimited needs has a fixed cost, and so forth.

    Militaries are fractal organizations, and so they are inherently scalable and can expand indefinitely within the fundamental bounds of the overall population and economy, bounds which also apply to firms and to “the state” as well.

    Scope is a more important concern, but even with scope, there doesn’t seem to be much limit if most of the “peripheral competencies” are in areas that are more or less “steady-state, stably solved problems” and which any competent senior officer or director can learn to manage very quickly. For instance, a Commanding General of a base overseas essentially manages all the functions of a small city to include waste collection, utilities, roads, police and law enforcement, schools, etc. all of which they seem to handle with competence and ease, and which are of course all far out of scope of core war-fighting competencies.

    The big issue for the size of a private firm is being able to be productive enough to be able to afford to recruit and retain the requisite proportion of capable managers and cognitive talent needed to solve that firm’s particular problems.

    But that may be more of a question of the limits of a particular “sector” rather than a firm in a sector. The question is whether there is any evidence that there is something special about any particular sector such that no firm, or combination of just a few firms, can expand to take over the entire sector?

    I think there might be a key difference between “personal services” and other types of goods and services.

    Consider that prostitution and drugs are both illegal. We see the “wholesale” side of the drug industry dominated by large cartels, and even the “retail” side tend to be members of gangs or organizations instead of sole proprietors or independent contractors. But that a “goods” sector, and prostitution is a “personal services” sector, and that industry seems to be dominated by independent providers and small “firms” with a few employees.

    So it seems firms run into limits when there are human limits relating to the particular personal services which are being provided. For all other sectors, there may be no inherent limit to scale and centralization / consolidation.

  6. I think you should read more of Miles Kimball’s articles, and like your response here, especially coining “math waving” as a phrase.

    Yet your critique seems a bit unfair because of a different emphasis.

    Miles’ article is about the inferiority of teaching a U shaped average cost curve relative to the teaching regime he lays out, with his math matching his assumptions. Kimball concludes: it seems better to me to teach returns to scale and imperfect competition in market equilibrium than it is to teach U-shaped average cost curves. In any case, there are always tradeoffs.

  7. http://blog.irvingwb.com/blog/2016/11/the-changing-nature-of-the-firm.html

    Professor Case says “But firms are not to be analyzed the way I did it in The Nature of the Firm, [which] talked about the firm as if it was an entity in economic theory. . . Firms are organizations in which the different parts of the firm have an interchange with other parts of the firm,… it is a sociological problem not an economic problem…”

    There is probably a sociological dis-economy of scale not captured well in any econ model.

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