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Notes
Hereafter, in the present rejoinder, when I write ‘my note’ or ‘my paper’ I refer to Fratini (2019).
Re-switching occurs when the same method of production of a certain commodity is optimal – i.e. profit-maximizing – for two different interest rate levels, but not for some level between them.
There are hundreds of papers devoted to the study of the causes and implications of the non-monotonic relation between the rate of interest and the net output per unit of labor. I do not want to bother the reader with a never-ending list of references. I have already mentioned Samuelson (1966), let me just add a couple of my favorite contributions: Burmeister (1980, ch. 4) and Mas-Colell (1989). Since Lewin and Cachanosky express surprise, or even skepticism, about this result, I would direct them to this literature.
In their comment, the two authors try to defend their position writing that the fall in the net output per unit of labor could be compensated by an increase in the total employment: ‘[t]he average product per worker may indeed fall with the boom as more workers are employed (at lower marginal products)’ (Lewin and Cachanosky 2019, emphasis in the original). However, this position is clearly inconsistent with their reconstruction of the working of the ABCT for the following two reasons. First, they explicitly state that ‘the distinctive aspect’ of the ABCT is that the boom is due to the increase in the degree of roundaboutness, here instead the boom would be caused by an increase in the employment of labor. Second, Lewin and Cachanosky write that, before the expansionary intervention of the Central Bank, the economy was in an equilibrium position and this means that the labor force available was fully employed – or, at least, there was no involuntary unemployment. Hence, the increase in the employment of labor is either impossible or, at the best, limited – in the latter event, the variation cannot be large enough to avoid a fall in the national net output. Therefore, although I assume a fixed employment of labor (full employment) in my note, my argument does not rigidly depend on this assumption.
Since perfect competition is assumed, firms are ‘price-takers’: from the point of view of each single firm, prices are exogenous variables. They can be seen as the prices cried by a Walrasian auctioneer, or even as the prices that firms expect will prevail on the market.
Moreover, as is known, relative price only (and not money prices) are relevant for firms’ decisions. This allowed us to express them in terms of a numéraire. Following Adam Smith, for the sake of simplicity, I decided to express prices in terms of ‘labor commanded’ (cf. Fratini 2019, footnote 11).
Once labor commanded is the unit of measure of value, the value of the wage rate is surely 1. This is the reason why the wage rate cannot vary in my model (cf. Lewin and Cachanosky 2019, footnote 6).
As for the description of the methods of production, I use a simplified version – ‘point-output’ instead of ‘flow-output’ – of the model introduced by Hicks in Capital and Time (Hicks 1973, ch. IV). In particular, 1 unit of output obtained in period 0 is produced by the employment of x1 units of labor in period −1; x2 in period −2, and x3 in period −3, with x = a, b.
Clearly, both the points of view – the beginning or the end of the process – give exactly the same result. One can easily move from the first to the second standpoint just by multiplying the numerator and denominator of the average period formula for the same factor of capitalization or discount.
As is explained in every Microeconomics textbook, referring to the long-run equilibrium of a perfect competitive economy, commodity prices correspond to their minimum unit costs of production (which include interest on invested capitals). This means that the maximum amount of profit for each firm is nil.
They write: ‘Profits will exist only in an uncertain world where entrepreneurs are sometimes able to see opportunities for the creation of value that make the expected revenues exceed the expected costs of a particular venture’ (Lewin and Cachanosky 2019).
Let us take an example. Imagine the cost of production of an umbrella is $ 5. There are two possible states at the moment the umbrella is delivered: ‘rain’, with probability 20%, and ‘sun’, with probability 80%. The price of an umbrella is $ 6 in the event of rain, and $ 4.75 in the event of sun. Even if firms expect $ 1 of profit for each umbrella sold on a rainy day, this does not mean that expected profit is strictly positive. In fact, for each umbrella, expected profit is 0.2 ∙ (6 − 5) + 0.8 ∙ (4.75 − 5) = 0.
Assuming constant returns to scale, according to the standard microeconomic argument, if expected profit was not nil, but strictly positive, then profit-maximizing firms would produce a greater quantity of umbrellas, the price would fall, and expected profit would fall as well. The only possible rest position of this mechanism is when expected profit is zero.
Maybe the authors are here confusing ‘marginal productivity’ with ‘marginal utility,’ but as far as marginal productivity is concerned, reference should be made to the theory of income distribution and not to the theory of value. If – for the sake of argument – we accept the marginalist idea that final outputs are produced by means of the three factors of production (labor, land, and capital), then the first-order conditions for the maximization of firms’ profit set the equality between the marginal products of the factors and their respective rates of remuneration (wage, rent, and interest rates). Hence, factor demand functions derive from these equalities. This is the role the marginal productivity of factors plays within the marginalist approach.
If production is understood as a circular process, then it does not have a precise beginning, but this is not a problem we wish to discuss here.
If all the inputs could be paid for at the end of the process, directly by revenues, then no investment of capital would be needed. For instance, it is known that wages paid ex-ante, before output is obtained, require an investment of capital, while postponed wages are paid out of revenues.
Incomes from capital are understood as a profit – namely a difference between revenues and costs – if they are not included in the costs of production – as in the classical and neo-Ricardian approach. By contrast, if they are included among the costs – as in the neo-classical theories, then they are an interest on the employment of capital and, in a competitive equilibrium, the difference between revenues and cost – firm’s profit – must be nil.
References
Burmeister, E. (1980). Capital theory and dynamics. Cambridge: Cambridge University Press.
Cachanosky, N., and Lewin, P. (2016) Financial foundations of Austrian business cycle theory. In S. Horwitz (Ed.), Studies in Austrian macroeconomics (advances in Austrian economics, vol. 20) (pp. 15–44). Bingley: Emerald Group Publishing.
Fratini, S. M. (2019). A note on re-switching, the average period of production and the Austrian business-cycle theory. Review of Austrian Economics. https://doi.org/10.1007/s11138-019-0432-0
Hicks, J. R. (1946). Value and capital (2nd ed.). Oxford: Clarendon Press.
Hicks, J. R. (1973). Capital and time. Oxford: Clarendon Press.
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Appendix: Capital in economic theory
Appendix: Capital in economic theory
In footnote 1 of their comment to my note, Lewin and Cachanosky wonder about my conception of capital. Hence, although this is irrelevant to my point (see section 2 above), I will spend some words on what capital is.
The notion of capital in economic theory is an old issue. Many contributions are available and it is almost impossible to add something new. Therefore, in the following lines, I will just try to provide a short synthesis of the existing literature.
The word ‘capital’ originates from the Latin word ‘caput,’ which means ‘head.’ It denotes either the most important element in a group (the capital city is the most important town in a country) or something that is at the beginning (a new sentence starts with a capital letter). In fact, in the capitalist mode of production, the investment of capital is at the beginning of each production process.Footnote 12
Focusing on a single production process, inputs must be employed before outputs are obtained (production takes time). Accordingly, if inputs are purchased when they are employed and outputs are sold when they are produced, then costs and revenues of the same process are not simultaneous, but the former typically precede the latter. Hence, costs cannot be financed directly with revenues. Capital is the amount of purchasing power that is invested in order to buy the inputs in advance, before revenues are obtained.Footnote 13 At a later date, revenues will allow producers to recover the capital invested with a net income (profit or interest, it depends on the approach adoptedFootnote 14).
This is the only possible concept of capital in the theory of production. Actually, this is the notion of capital we find in many different theoretical approaches, with the only relevant exception represented by the marginalist theory. In the marginalist theory, as is known, capital is not understood as something of the same nature as costs and revenues, but rather as something of the same kind as labor and land (factors of production). However, it is also well-known that the marginalist idea of capital as a factor of production did not work, but this is another story.
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Fratini, S.M. Re-switching and the Austrian business-cycle theory: A rejoinder. Rev Austrian Econ 32, 383–389 (2019). https://doi.org/10.1007/s11138-019-00467-8
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DOI: https://doi.org/10.1007/s11138-019-00467-8