A Refutation Of Austrian Capital Theory And Austrian Business Cycle Theory

1.0 Introduction

I have not posted about a non-fluke switch point in a while. This is an example from Bertram Schefold. I have examined perturbations and variations of this example before.

Here I present an example with tables exhibiting arithmetic. Is this any more transparent than examples presented with graphs?

I have been listening to some lectures on YouTube, especially Richard Wolff. I now have another hypothesis why mainstream economists have been promoting lies, ignorance, and nonsense for half a century: fear. The history of economics includes purge after purge after purge. Maybe many mainstream economists are cowed by their rulers.

2.0 Technology

Three processes are available for use in production. Each process is specified by coefficients of production (Table 1), when operated at an unit level. The person-years of labor employed, the bushels of corn used up in a process, and the number of new and old machines are specified. Outputs consist of bushels corn and new and old machines. Corn is both a consumer good and functions as circulating capital. Machines function as fixed capital. A machine's productivity varies with its age. An older machine requires less labor to operate, but more circulating capital.

Table 1: Coefficients of Production for The Technology

Input	Process
	(I)	(II)	(III)
Labor	1/10	43/40	1
Corn	1/16	1/16	1/4
New Machines	0	1	0
Old Machines	0	0	1
Outputs
Corn	0	1	1
New Machines	1	0	0
Old Machines	0	1	0

Suppose all three processes are run at unit level in parallel. At suppose at the start of the year, the firm has one new machine, one one-year old machine, and 3/8 bushels corn. The output of the first process is one new machine. The previously existing new machine is consumed in the second process, leaving an output of one one-year old machine. The third process uses up the one one-old year machine. So these processes reproduce the stock of new and old machines. But they also use up inputs of 3/8 bushels corn in producing a gross output of two bushels corn. Summing over all three processes, 2 7/40 person years of labor produce, with the capital stock, a net output of 1 5/8 bushels corn. The labor intensity of this technique is 87/65 person-years per bushel.

Assume free disposal for old machines. Another technique would be operated when the use of the machine is truncated after one year. In this case, one should consider the first and second processes being run in parallel at unit level, with a capital stock of one new machine and 1/8 bushels corn reproduced each year. Under this technique, 1 7/40 person years of labor are employed across the two processes. Net output is 7/8 bushels corn. The labor intensity is 47/35 person-years per bushel.

The more labor-intensive technique is the one with the truncated economic life of the machine. How many production cycles firms choose to run machines is an unambiguous physical measure in this example. And choosing to run the machine longer is a choice to adopt a less labor-intensive technique. Just as Eugen Böhm Bawerk says, a longer period of production, in some sense, is a more capital-intensive method. And that increase in the period of production results in greater output per worker. (I am not claiming that the number of production processes is the Austrian average period of production. I am merely noting how transparent the use of time is in this example.)

3.0 Some Accounting

One can easily see how a single firm would operate the last two processes in parallel, or only the process using the new machine, if the use of the machine is truncated. If such a firm was vertically integrated, they would also produce new machines with the first process. The firm can take the wage and the price of corn from the market, under various idealizations. For simplicity, I take a bushel corn as the numeraire. What prices would the accountants use to evaluate new and old machines?

3.1 At an Initial Wage

Consider a starting wage of 35/71 bushels per person-year and prices of machines shown in Table 2. For each process, the cost of capital inputs are the sum of the inputs of corn and machines of specified vintages, evaluated at the given prices. Wages are found from the labor input, evaluated at the given wage. Revenues are the sum of the outputs of corn and machines of specified vintages, evaluated at given prices. I assume wages are paid at the end of the year. So the rate of profits is the ratio of the difference between revenues and wages to the capital costs. With these prices, the owners are happy to operate all three processes. They make the same rate of processes in each, and prices do not signal that they should make any changes.

Table 2: Initial Prices

w = 35/71 ≈ 0.4930, p0 = 99/568 ≈ 0.1743, p1 = 1/284 ≈ 0.003521
	Capital Costs	Wages	Revenues	Rate of Profits
I	0.0625	0.04930	0.1743	100 percent
II	0.2368	0.5299	1.004	100 percent
III	0.2535	0.4930	1	100 percent

3.2 A Higher Wage

Now suppose the wage is 9,055/14,016 bushels per person-year. Table 3 shows accounting when the prices of new and old machines are unchanged. Notice that the rate of profits has fallen, with the rise in the wage, in all processes. But it has fallen to different levels, given that ratio of wages to the cost of capital originally varied among the processes. David Ricardo discusses this effect in the first chapter of his Principles of Political Economy and Taxation. Obviously, the price at which machines are entered into the firm's books must be changed to reflect the change in wages.

Table 3: Initial Prices with Raised Wage

w = 9,055/14,016 ≈ 0.6460, p0 ≈ 0.1743, p1 ≈ 0.003521
	Capital Costs	Wages	Revenues	Rate of Profits
I	0.0625	0.06460	0.1743	75.5 percent
II	0.2368	0.6945	1.004	30.5 percent
III	0.2535	0.6460	1	39.6 percent

Table 4 shows a set of prices such that the same rate of profits is obtained in all three processes. This is not the end of the story, though, The price of a one-year old machine is slightly negative. (My approach for perturbing reswitching examples can make this price more noticeably negative, but maybe I would end up with even more messy fractions.) Instead of decreasing the revenues for the second process from the output of old machines, the managers of the firm can simply throw the old machine away and enter a price of zero for it on its books.

Table 4: Raised Wage and Updated Prices of New and Old Machines

w = 9,055/14,016 ≈ 0.6460, p0 ≈ 0.1531, p1 ≈ -9.563 x 10-5
	Capital Costs	Wages	Revenues	Rate of Profits
I	0.0625	0.06460	0.08852	41.64 percent
II	0.2156	0.6945	0.3054	41.64 percent
III	0.2499	0.6460	0.3539	41.64 percent

Table 5 shows the result of truncating the use of machines. One must, however, set a new accounting price for new machines, as well. Without this adjustment, different rates of profits are obtained in the first two processes. Notice the rate of profits is indeed lower in the third process, which is not used by cost-minimizing firms.

Table 5: Raised Wage and Truncated Use of Machines

w = 9,055/14,016 ≈ 0.6460, p0 ≈ 0.15313, p1 = 0
	Capital Costs	Wages	Revenues	Rate of Profits
I	0.0625	0.06460	0.15313	41.64 percent
II	0.21563	0.6945	1	41.68 percent
III	0.25	0.6460	1	41.58 percent

Table 6 shows the final results of correct accounting, with increased wages. The rate of profits, r, is 5/12, halfway between 1/3 and 1/2. Those rates of profits are the switch points in this example. I have told this story as a matter of accounting for vertically integrated firms. But these are the only prices on the market consistent with a long period position with the postulated wage. How and whether market prices would converge to these prices of production, in a gravitational process (as in Adam Smith's metaphor) is not clear to me. I like the idea that Sraffa's book is about little more than accounting. This idea is not too far away from what Ajit Sinha has been arguing for a number of years.

Table 6: Raised Wage, Truncation, Updated Price of New Machines

w = 9,055/14,016 ≈ 0.6460, p0 = 1,431/9,344 ≈ 0.15315, p1 = 0
	Capital Costs	Wages	Revenues	Rate of Profits
I	0.0625	0.0646	0.15315	41.67 percent
II	0.21565	0.6945	1	41.67 percent
III	0.25	0.6460	1	41.58 percent

3.3 Summary

Table 7: Summary

Wage	Labor Intensity	Rate of Profits
35/71 ≈ 0.4930 bushels per person-yr.	87/65 ≈ 1.338 person-yrs. per bushel	100 percent
9,055/14,016 ≈ 0.6460 bushels per person-yr.	47/35 ≈ 1.343 person-yrs. per bushel	5/12 ≈ 41.7 percent

At a higher wage, firms want to run machines for one year, not two years. The economic life of machines is shortened from the physical life. And firms want to hire more workers to produce a net output.

Why might the wage rise and the rate of profits fall? In one theory, known to be nonsense, a shock might lead to labor be less abundant, as compared to capital. Perhaps people become more forward-looking and more willing to save, or the population falls for some reason. Wages rise, and firms take this as a signal to substitute capital for labor. But, in the example, a higher wage is associated with the adoption of a less capital-intensive technique and a rise in labor intensity. Somehow, if equilibrium is to be obtained, an increase in the labor force must be accompanied by a rise in wages.

Perhaps one can find a financial measure of capital, such as Hicks' average period of production, where a higher capital-intensity is always associated with a lower rate of profits around a switch point. But then one would have to grapple with the fact that more 'capital' does not always result in more output. Austrian school economists cannot seem to handle that their theory of 'malinvestment' is just incorrect.