Variations in the Economic Life of Machines

These posts demonstrate, in a model of fixed capital, that the cost-minimizing choice of the economic life of a machine need not conform to traditional Austrian and marginalist theory. The cost-minimizing choice of technique around a switch point might associate a shorter economic life of a machine with an increased capital intensity. This counter-intuitive variation of the economic life of a machine is independent of capital reversing and the re-switching of techniques, both of which are also illustrated in these posts.

These posts build on the Cambridge capital controversy (CCC). A lower rate of profits may be associated with a decreased value of capital per worker, a decreased ratio of the value of capital to output, and a decreased sustainable steady state of consumption per worker (Harcourt 1972). Capital is not a factor of production, and an equilibrium rate of profits, assuming competitive conditions, is generally not equal to the marginal product of capital (Harris 1973). The unfounded idea in the background is that, in a supply-and-demand explanation of prices and distribution, an increased relative supply of a factor of production supposedly drives its price down and incentivizes entrepreneurs to adopt techniques, out of a given technology, that use that factor more intensively. All sides to the CCC accepted that this theory lacks rigorous foundation:

"Such an unconventional behavior of the capital/output ratio is seen to be definitely possible. ... Moreover, this phenomenon can be called 'perverse' only in the sense that the conventional parables did not prepare us for it" (Samuelson 1996).

Han and Schefold (2006) and Zambelli (2018) have recently found some examples of such 'perverse' switch points, albeit not many, in empirical data obtained from national income and product accounts. Kurz (2021) raises some challenges to this empirical work.

Much of the discussion in the CCC focused on models with only circulating capital. Bidard (2004), Pasinetti (1980), and Schefold (1989) are canonical references in post Sraffian price theory to fixed capital. The economic life of a machine, in the general case of non-constant efficiency, varies with distribution. Steedman (2020) considers a model with an infinite number of alternative types of machines, each being the only basic commodity in the technique in which it used. Machines operate with constant physical efficiency, for possibly a different number of years in industry and agriculture. He finds that a machine with a shorter life can be adopted at a lower interest rate, independently of capital-reversing. In contrast, this article considers variation in the economic life of a single machine. The results established here and by Steedman can be seen as complementary.

The method of analysis is based on comparing stationary states, where prices of production prevail. These models are open, with distribution taken as exogenous. The numeric example is simple enough such that net output consists of a single consumption good, called 'corn'. Corn also functions as circulating capital, while a machine with a physical life of three years represents fixed capital. Both corn and new machines are basic commodities, in the sense of Sraffa. Although no attempt is made to represent production by a series of dated labor inputs, the economic life of the machine seems to be of interest for claims among economists developing capital theory along the lines of the Austrian school. Economists of this school have argued that a greater willingness to defer consumption leads to a greater supply of capital, a lower interest rate, and a greater period of production. In these posts, a greater period of production is identified with a longer economic life of a machine.

The application of perturbation analysis to the analysis of the choice of technique, to identify fluke cases, and to explore how switch points vary with technological change is relatively novel. A fluke case is such that almost any perturbation of model parameters disturbs its qualitative properties. Kurz and Salvadori (1995) is a classic textbook for the analysis of the choice of technique. Vienneau (2018, 2019, 2021, 2024a, and 2024b) extends this analysis to consider the effects of perturbing selected model parameters. In these posts, applying this approach to a single numeric example uncovers surprising variation in the economic life of a machine, including its non-monotonic variation with the rate of profits with neither capital-reversing nor the re-switching of techniques.

Harwick (2022) has noted that some followers of the Austrian school have recently tried to consider Austrian capital theory separately from business-cycle theory. Lewin and Cachanosky (2019) consider a financial measure of capital-intensity, namely the average duration of an investment project. Around any switch point, an increased Duration is associated with a lower interest rate. As emphasized by Fratini (2019), an increased capital intensity, in this sense, is associated with reduced net output per worker around a so-called 'perverse' switch point. Even so, any measure of capital intensity that always increases with a lower rate of profits around a switch point can be associated with a reduction in the economic life of a machine.

Capital-intensity is assessed in these posts by evaluating the price of inputs, either for a given net output or per worker. A reduction in the economic life of a machine is consistent with an increase in capital-intensity. This association between a shorter economic life and greater capital-intensity can arise around a switch point in which a smaller rate of profits results in the adoption of a more capital-intensive technique, with a consequent greater net output per worker. It can also arise around a 'perverse' switch point in which a less capital-intensive technique is adopted at a lower rate of profits. Neither type of switch point is a fluke case, as can be seen by contrasting such switch points with genuine fluke cases.