# Let’s reject the notion of marginal product

Lately, I’ve been thinking about the inadequacy of the notion of marginal product for economic analysis.

Consider a shop with only one employee which would be unprofitable if the selling process were automatized. What is the marginal product of the employee? Or, more exactly, what will be the product of the shop without that employee? Zero. This example demonstrates that it’s impossible in this case to mathematically strictly separate the contribution of various factors of production the way it is usually done.

But suppose the question is about the productivity of the addition of another employee to an enterprise that can function without her. Can we say that her marginal product will be reflected in the change in revenue which will happen after her hiring absent other changes? No, because the change in the revenue will be not just because of the net impact of the worker but because of the changed productivity of capital or even other workers.

In other words, productivity isn’t a mathematical function of several variables like, say, the height of a mountain (even if you consider everything in strictly monetary terms). It is with regard to the latter that you can strictly mathematically separate the impact of movement in a particular direction on the height. But you can’t calculate even in principle the marginal contribution of small factor units.

If this is correct then a big question arises about how factor prices are determined in the market. The current theory has it that they tend to be paid the monetary equivalent of their discounted marginal product. What can we say if we abandon the notion of marginal product?

I think we can build a market process theory of factor price determination. We can say that factor prices reflect the extent to which the opportunities of using the relevant factors profitably are discovered by entrepreneurs.

To illustrate what I’m saying consider an employee in a certain business who gets, say \$1000 per month. From this fact we can say that entrepreneurs have not yet discovered the opportunity to employ her in a way which would be profitable enough to allow to pay her a higher salary.

This approach has the big advantage that it doesn’t require the postulation of the superhuman ability of entrepreneurs to somehow calculate the exact contribution of each factor to the product of their enterprises but at the same time leaves completely intact the logic of economic calculation.

# The Central Contradiction of Capitalism That Isn’t

Capital in the Twenty-First Century, by Thomas Piketty, Belknap/Harvard, 685 pages, \$39.95.

The book on how capitalism supposedly necessarily causes increasing inequality, which French economist Thomas Piketty initially wrote in French a year ago, has recently been published in English and became an immediate success with readers reaching No. 1 in the book bestseller list on Amazon. It also received a lot of praise from the commentators on the left of the ideological spectrum.

It is beyond the scope of this review to analyze all or even most of the arguments Piketty makes in the book. I will also not deal with the potential adverse consequences of implementing Piketty’s recommendations which have been addressed fairly well in other reviews (see, for example, Tyler Cowen’s take). Instead, I will focus on the soundness of Piketty’s main argument from the perspective of the dynamic market process theory mainly developed by the Austrian School of Economics.

Piketty’s main point, and what he calls the “central contradiction of capitalism” in a nutshell is that in the conditions when the economic activity is not significantly depressed (as it was the case in the period between 1929 and 1945), capitalism tends to result in ever increasing inequality, as measured by the ratio between the total value of capital (in which Piketty curiously includes housing) and the national income (which is calculated as GDP minus the depreciation of capital plus net income received from abroad). Another way to put the same idea is in terms of the ostensibly fundamental inequality r > g meaning that the rate of return on capital is higher than the rate of economic growth. The mechanism which is postulated to underlie this phenomenon is that in a relatively low-economic growth conditions the rate of savings will tend to be higher than the rate of economic growth.

But do the calculations cited by Piketty measure the dynamics of inequality, and even to the extent that they do, are those increases inherent in capitalism?

The national income is calculated on the basis of the actual purchase and sale transactions where all the monetary amounts that go into the total figure actually change hands during the year. Thus, all the products purchased in those transactions are (however, imperfectly) evaluated by their buyers. At the same time, capital is defined by Piketty as “the total market value of everything owned by the residents and government of a given country at a given point in time, provided that it can be traded on some market” (p. 48). With regard to the calculation of such market value, the technical appendix to Piketty’s book refers to the data appendix to his 2013 study co-authored with Gabriel Zucman according to which the part of capital which is constituted by capital in the narrow sense (or the goods used in the production of consumer goods to be sold in the market) is measured based on the market value of the firms’ equities. However, the method of calculation Piketty chooses does not seem to be crucial because the data that he provides on the ratio between the market value of corporations and their book value does not suggest that stocks of the developed countries’ companies have been systematically overvalued compared to the actual assets (p. 189).

There is a big puzzle related to Piketty’s calculations which arises from the question why the total value of wealth has been growing much faster than the national income. Let us set aside the issue of housing for a moment and focus on capital in the narrow sense.

From the standpoint of the market process theory, the fact that the total value of capital has been increasing translates into the conclusion that the prices of certain capital goods have been increasing. These capital goods are those that have actually been purchased and sold, and the increase in their prices, in the absence of capital destruction, means that there has been increased competition for those capital goods and that much of them have been reallocated. And, what is more important, the fact that the increases of the prices of those goods have been systematically outpacing the growth of the national income suggests that a lot of the reallocated capital has been malinvested.

But the crucial question that this reasoning leads to is how this substantial malinvestment could be compatible with the economic growth that has been observed. This is the most important question that needs to be answered and it can only be answered with the help of dynamic market process reasoning.

Consider the phenomenon of smartphones. They represent an important innovation which within a relatively short period of time has made essentially or nearly obsolete a lot of other consumer goods and their components. It is sufficient to mention the obvious examples fixed phones, portable music players, alarm clocks, point-and-shoot cameras, most video cameras, and GPS navigators. It is fairly plausible to assume that through this process they have freed up substantial amounts of capital for other uses.

However, the resources that are thus freed up do not get automatically reallocated to the new uses. Instead, innovators and entrepreneurs must come up with the ideas about such new uses. The process of innovation may take considerable amounts of time, especially with the increasing government regulation that discourages entrepreneurship and innovation.

At the same time the initial innovation – in this case, smartphones has freed up the money that the consumers would have spent on the things that smartphones have made obsolete. Thus, there will be a big incentive for entrepreneurs to try to discover such processes, even if it may be not easy to do that. At the same time, since the freed up money will tend to be channeled into the capital goods that have become cheaper as a result of the initial innovation, the malinvestments that arise will tend not to extinguish economic growth completely. This will of course only be the case if the process of intertemporal coordination is not distorted by the monetary policy which is often the case according to the Austrian Business Cycle Theory and based on the recurrent economic crises.

The idea that the excess increase of the total value of capital as calculated by Piketty actually represents malinvestment of resources freed up by successful innovation, if correct, casts doubt on Piketty’s thesis that this excess increase suggests growing inequality. Malinvestments do not make people wealthier, after all. It might suggest, though, that the existing government-created barriers to innovation must be minimized.

Finally, we may return to the issue of housing which is a major category of capital under Piketty’s definition the total value of which has become even higher than the total value of the national capital in some developed countries. According to Piketty’s data, it constitutes almost three fifths of the total value of capital of Great Britain, for example, and its ratio to the national income has grown rapidly since the 1970s, and especially since 1990. In France the ratio of the total value of housing to the total value of other capital is even higher – almost 2:1. In the US the total value of capital in the narrow sense slightly exceeds that of housing.

To start with, from the economic theory standpoint, housing is not part of capital. Capital goods are those goods which are produced and maintained to be used in the production of either other capital goods or final consumer goods. Residential houses, on the other hand, are for the most part durable consumer goods. I wrote for the most part because some people do use their living space for work or business, thus making such space partly a capital good. But it is doubtful that such uses generate a large part of the value of housing.

But the most important problem with housing is the assumption that the excessively fast growth of their total value is the result of endemic market forces whereas there are serious reasons to believe that this growth, especially in the European countries like the UK and France has been largely caused by supply-restricting regulations, especially zoning rules. As an illustration, recent research by Paul Cheshire in the South-Eastern England has demonstrated that more land in the Surrey County is devoted to golf courses than to housing. Add to this the regulations about the maximum height of the buildings and many others.

The mechanism of how the growth in housing prices may have been caused by regulation is not very complex. Although in countries like the UK and France population growth since 1950s has not been very dramatic, there has been a significant increase in welfare. It is very plausible to assume that welfare increases lead to an increased demand for housing space, and if the supply of housing is artificially restricted, it is no wonder that significant price increases would follow and persist. The rise of housing prices, although it does point to increasing inequality in this case, is probably not a symptom of an inherent contradiction of capitalism but of something that is opposite to it.

UPD: In his several criticisms of Piketty (see e.g. here) Robert Murphy correctly criticizes Piketty for confusing the return on capital with the rental price paid to the owners of capital goods. In my review I decided to use Piketty’s terms because my line of critique seems legit regardless of them.