Debunking Economics Part 4: Capital Controversies

In Chapter 7 of Steve Keen’s book, Debunking Economics, Keen goes over what is known as the Cambridge Capital Controversy (CCC). Out of all the debates between neoclassical and heterodox economists, the CCC was one of the most intense. The surprising part about the debate is that the neoclassical side actually admitted they were wrong. In Paul Samuelson’s article A Summing Up, he concluded that, “if all this causes headaches for those nostalgic for the old time parables of neoclassical writing, we must remind ourselves that scholars are not born to live an easy existence. We must respect, and appraise, the facts of life” (Samuelson 1966: 583). One could say that these debates didn’t really matter, which is a debatable question (although I’m convinced that they do), but that’s a much more complex topic and I won’t be covering it here.

In neoclassical economics, all commodities are produced by “factors of production”, which are normally reduced to just labor and capital. Like labour, capital is paid in proportion to its productivity (called the marginal productivity of capital or MPC). Profit maximizing firms will “hire” capital until up to point where its marginal contribution to output is equal to its cost (basically MR = MC). The cost of “hiring” capital is the rate of interest and its marginal contribution to output is the rate of profit.

The first problem is that MPC assumes that the other factor inputs are fixed (in this case labor) when capital is being used. Capital is the variable input while labor is the fixed input. But this scenario is absurd. Machinery (capital) is by far the least variable factor of production and if machinery is variable, then we would expect labor to also be variable.

Secondly, if we define an industry broadly enough, we run into a familiar problem from Chapter 5. At the level of the individual firm, economists assume that the rate of change in wages and profit is zero. A change in the firm’s output caused by hiring more capital doesn’t effect real wages or the rate of profit. This leads to the desired relationship of the MPC equals the rate of profit. And this is a reasonable approximation. However, when you broaden your definition of industry, a change in capital will certainly effect the wage rate and the rate of profit. The desired relationship of the MPC equals the rate of profit no longer exists.

Thirdly, there are major problems when economists try to aggregate capital. In order to measure something, we must use some sort of measuring stick, but the are some obvious problems when it comes to measuring capital. Capital includes a variety of heterogeneous objects (machines, buildings, brooms, blast furnaces, trucks, ships, power stations, etc…) and finding a single unit of measurement is near impossible. As a result, economists usually try to measure capital in terms of its price. However, the price of capital depends on its rate of profit, which varies as price changes. There is an obvious circularity here and the use of price as a unit of measurement for capital isn’t very useful.

Sraffa’s Critique

While Keen does a good job criticizing basic neoclassical production theory, the meat of this chapter involves an overview of Peirro Sraffa’s famous book, Production of Commodities by Means of Commodities. I find it odd that Keen didn’t reference Joan Robinson’s famous paper, The Production Function and the Theory of Capital, which most likely marks the beginning of the CCC. However, Sraffa’s book is also a great place to look, as it is arguably the most powerful critique against neoclassical capital theory. Before I begin, I must preface that this is by far the most difficult section in Keen’s book to follow. I’ll do my best to summarize Keen’s language, but I might make some mistakes along the way. I apologize in advance if I make any glaring errors.

Sraffa’s builds his models up carefully step by step, starting with a very simple model and eventually leading up to a more complex and fairly realistic model. In his first model, Sraffa built up an economy that was just able to reproduce itself  and there was no fixed capital. Instead all inputs were “circulating capital” and are used up in each round of production.

Industries

Wheat input (qrs)

Iron input (tons)

Pig input (pigs)

Total Outputs

Wheat

240

12

18

450 qrs

Iron

90

6

12

21 tons

Pigs

120

3

30

60 pigs

Total inputs

450

21

60

In this economy, Firm A needs a certain amount of wheat, iron, and pigs to produce commodity 1 (wheat), firm B needs a different combination to produce commodity 2 (iron), and firm C needs a different combination to produce commodity 3 (pigs). The total output of each sector equals the number of inputs used in all sectors, e.g. the output of the wheat industry (450) equals the inputs of wheats used in all the industries (240 + 90 + 120). The total inputs equals the total outputs.

The purpose of this model is to show that price was not determined by demand and supply, but rather determined by the “conditions of production”, i.e the amount of inputs needed to keep industry going. Using the example above, this meant that 240 times the price of wheat, plus 12 times the price of iron, plus 18 times the price of pigs, had to equal 450 times the price of wheat.

In Sraffa’s next model, he created an economy that produced a surplus: where one sector in the economy produces more output than total inputs used.

Industries

Wheat input

Iron input

Total output

Wheat

280

12

575

Iron

120

8

20

Total inputs

400

20

The purpose of this model was to incorporate a rate of profit. Because this is an equilibrium model, the rate of profit has to be uniform across all sectors, otherwise capitalist in sectors with a low rate of profit would move to sectors with a high rate of profit. For a uniform rate of profit r to apply, the prices in this economy must be such that the money value of inputs (multiplied by (1 + r)) is equal to the money value of outputs. So in this example, the price ratio of bushels of wheat to tons of iron is 15 to 1 and the uniform rate of profit is 25 percent (1).

In his third model, Sraffa explicitly incorporates labor with wages as an additional unknown. He notes that wages are an inverse function of profit (the higher wages are, the lower profit will have to be) as seen in the graph below.

Maximum R = 25%

Wage (% of surplus)

Profit rate (%)

0

25

10

23

20

20

30

18

40

15

50

13

60

10

70

8

80

5

90

3

100

0

He then proposed a new method of measuring capital, i.e measuring the value of the commodities used to produce capital, plus the value of the labor involved, times a rate of profit (to reflect a passage of time). If we repeat this process, we continue to reduce machinery inputs to the machinery and labor used to produce them. As we continue, we keep getting inputs of labor and declining, but never zero, units of residual machinery. Each input of labor is multiplied by the wage and by one plus the rate of profit raised to a power which reflects time. In mathematical terms, this “residual commodity” is equal to:

((labour input at time y * wages)*(1+rate of profit))^(time periods since time y) + commodity 

At some point during this process, the commodity variable will have a value that is so small that it can be negligible.

In the equation above, there are two competing elements, profits and wages (as shown in the graph above). As one rises, the other must fall.  This inverse relationship means that there is a peak value for capital somewhere in the middle. If one term (say wages) is too high, then that will overwhelm the other and the value of capital will decrease. This relationship creates an interesting phenomenon known as capital reswitching.

Consider two production techniques, one that uses more “direct labor” in the recent past and another that uses more “direct labor” in the far distant past. The latter would be akin to making wine in a barrel while the former produces wine of identical quality using advanced chemical processes. One production technique would be regarded as “capital intensive” (since a large amount of machinery is used) and the other would considered “time intensive” (or labor intensive). At a zero rate of profit, the cost of productions for both techniques is identical (the only cost incurred so far is the sum of wages). As profits rise from zero to a moderate rate, the “time intensive” procedure, which relies on fewer labor inputs, would be cheaper than using expensive machines from the “capital intensive “process. As rate of profit continues to grow, the compounding rate of profit on the “time intensive” procedure becomes enormous. Now the “capital intensive” process is less expensive and we would switch from the “time intensive” to the “capital intensive” means of production. However, as the rate of profit gets higher and higher, eventually reaching its maximum value (and wages fall to zero), the cost of wine would simply be the cost of its irreducible commodity components (e.g. grapes, etc..). The “time intensive” means of production is now more viable than the “capital intensive” and we would switch back.

This carries a number of implications:

1. The measured amount of capital depends on the rate of profit, not the other way around as neoclassical economists would claim. The rate of profit cannot be said to be the “marginal product of capital” and this puts a huge hole in the neoclassical economic theory of income distribution.

2. “Reswitching” destroys the simple relationship between the amount of capital employed and the rate of profit. Neoclassical economics teaches that the rate of profit for a unit of capital diminishes as more and more capital is employed (think diminishing returns). In mathematical terms, output is a concave but increasing function. Capital reswitching destroys this idea.

3. Contrary to the neoclassical picture, prices cannot be calculated without first knowing the distribution of wages and profits. Economists have the causality backwards.

Most of the debate on the CCC is extremely complicated and theoretical. Some even argue that it doesn’t really matter. However, I’m not convinced and this “criticism” comes across as a dodge. The CCC has real consequences not only on the way economics is taught at the undergraduate level, but also on the way economics is being done by thousands of real economists everyday.

Notes:

1. To find the rate of profit, you take the ration of total output over total input in terms of one commodity. We know that the price ratio is 15 bushels of wheat for one ton of iron. So we can do:

Total output/total input = (575 + (20 x 12))/(400 + (20 x 15))

= 875/700 = 1.25

The .25 is your rate of profit.

Relevant Links:

Debunking Economics, Part V: The Holy War Over Capital

The capital debates: A brief introduction

References:

Keen, Steve. Debunking Economics: The Naked Emperor Dethroned? London: Zed Book, 2011. Print.

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2 Comments

Filed under Economics, Home

2 responses to “Debunking Economics Part 4: Capital Controversies

  1. Blue Aurora

    Out of curiosity, Rousseau1214…how well-read are you on the literature about the Cambridge Capital Controversy?

    • I’m not as well read as I should be and I find much of the original debate difficult to follow. I have read Robinson’s paper and some of the early stuff from the Cambridge side, as well as some of the responses from Samuelson and Solow. I’ve also read quite a few historical surveys. But other than that, I haven’t read much.

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