Theoretical arguments against decreasing returns to scale

There is actually a fairly well known argument against the existence of decreasing returns to scale. The economist Miles Kimball gives an excellent treatment of the argument on his blog. The argument is also briefly mentioned in some graduate microeconomics textbooks, for example Microeconomic Theory by Mas-Colell and Whinston.

The argument goes as follows. Suppose we have a production arrangement that produces a certain amount of a good with a certain amount of input. If we have decreasing returns to scale then when we double the amount of inputs our output should less than double. However if we are doubling all inputs of production we could simply run the same production process twice. There is no need to have any connection between the two production units. If a business ever finds their efficiency of production decreasing they can always operate many smaller production operations in parallel to achieve constant returns to scale.

The above argument, which I like to call the duplication argument, might appear somewhat theoretical and abstract, but in some ways it is actually extremely practical. In fact, if a real world business is facing decreasing returns to scale the can given them a blueprint for improving production. Businesses facing decreasing returns should simply run two smaller uncoordinated production units. If decreasing returns to scale were widespread there would be good money to be made going around telling businesses to decentralise production.

There are of course some qualifications to the above argument. In order to duplicate production arrangements all inputs of production must be duplicated. This might require duplicating managerial talent, or land. If more of an input of production cannot be obtained then duplication is impossible. The argument only applies over the time scale it takes to create a duplicate production unit. Firms might face decreasing returns to scale temporarily until duplicate production arrangements are built.

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Mas-Colell says the following of the duplication argument in his textbook

“It is important to not lose sight of the fact that the production set describes technology, not limits on resources. It can be argued that if all inputs (including, say, entrepreneurial inputs) are explicitly accounted for, then it should always be possible to replicate production. After all, we are not saying that doubling output is actually feasible, only that in principle it would be possible if all inputs (however esoteric, be they marketed or not) were doubled. In this view, which originated with Marshall and has been much emphasized by McKenzie(1959) decreasing returns must reflect the scarcity of an underlying, unlisted input of production. For this reason, some economists believe that among models with convex technologies the constant returns model is the most fundamental. “

This paragraph outlines what is probably the most common response to the duplication argument. If one factor of production is fixed, for example entrepreneurial talent, then duplication is not necessarily possible.

The idea that there is an element of production which is fixed, while definitely possible, is somewhat at odds with the other assumptions made in neoclassical economic theory. Neoclassical theory tends to assume that markets exist for all goods, and that the market is efficient. Perfect competition requiring that entreprenurial talent cannot be bought on the market would mean that in order for some markets to be efficient markets cannot exist for all products.

A more natural way to model the scarcity of an input is by saying the costs of that input rise quickly with quantity. Instead of entreprenurial inputs being impossible to obtain the cost of hiring additional entrepreneurial talent would be rapidly increasing. However the price of inputs ought to depend on the total market for inputs, not on the amount used by an individual firm. If the cost of entrepreneurial talent was rising so quickly that a firm could not duplicate production at the same cost then the costs of all other firms would rise as well. Perfect competition requires firms costs to rise based on their own production, not on the total production of all firms in an industry.

If firms are small, as is usually assumed in perfect competition, the amount of inputs they use will be small relative to the size of those input markets. The impact of an increase in their usage of production imputs on the price of those inputs will then be negligible. For small firms rising factor prices cannot cause rising marginal costs. Marginal costs are possible if the firm is large relative to the size of the market, but in that case the perfectly competitive model breaks down.

All of the above potential justifications for increasing marginal costs are also incompatible with the assumption of free entry. If a new firm can enter the market, then obviously all the inputs that are required to increase production are available. Assuming increasing marginal costs and free entry requires two things: that new entrants to the market are able to obtain the goods needed to start production, but that existing firms cannot hire those same inputs. Such a scenario seems highly unlikely.

The incompatibility between increasing marginal costs and free entry in my opinion renders perfect competition as taught in introductory microeconomics textbooks logically inconsistent. I cannot think of any situation in which it would apply. Critics of economics often criticize perfect competition for a variety of reasons, but in my opinion doing so is misguided. The above criticism is all you need, and, since it is the strongest criticism, focussing on others simply weakens your case.

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The other interesting thing to note about how Mas-Colell discusses the duplication argument is that he says the duplication argument is why some economists think that, among production functions that are convex, constant returns to scale are fundamental. Production functions with convex technologies are production technologies that do not exhibit increasing returns to scale. Mas-Colell says elsewhere in the book that the assumption of convex production sets is “the fundamental assumption of microeconomics”.

Yet the duplication argument gives no reason to assume convexity of the production set. The duplication argument in fact says that the only way production sets can be convex is if there are absolutely no benefits from operating at scale: constant returns to scale is the worst outcome. Despite that, nonincreasing returns to scale is taken as the fundamental assumption of microeconomics. This assumption is not justified in the Mas-Colell’s textbook.

The duplication argument actually indicates that increasing returns to scale ought to be the rule, with constant returns to scale a rare exception. Real companies can centralise or decentralise different aspects of production depending on whether or not that aspect benefits from being centralised. For example, franchise restaurants centralise marketing and menu creation, likely because those aspects of the business are more efficiently done at scale. Other aspects, such as hiring and the individual decisions of running a particular franchise are not centralised. The only way a business can face constant returns to scale is if no elements of the business benefit from centralisation. If there is a single task that benefits from having a single person doing it, for example hiring a company accountant for several plants, instead of having each manager struggling through accounting individually, then increasing returns to scale exist.

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There can still be upward sloping supply curves at the industry or economy level despite the duplication argument if input prices are increasing. As I discussed in the last post, input costs can increase fast enough to compensate for increasing returns. However, if increasing returns are prevalent we would expect for at least some of the firms in the economy to face non-increasing costs. For firms in those situations, output is limited by demand. Those situations can be important to macroeconomic analysis, and seem to have an immediate connection to Keynesian macroeconomic ideas. Yet are largely ignored by mainstream macroeconomics.