Heterogeneous unit labor costs and profit margins in an economy with vintage capital: an amended neo-Kaleckian model

Abstract

Post-Keynesian literature studying the impact of functional income distribution on economic activity and growth focuses on indirect demand effects (i.e., the consequences of real wage changes on aggregate demand components). The purpose of this article is to explore two points neglected by this literature. First, it ignores the direct supply effects corresponding to the impact of real wage changes on firms’ current profitability. Second, it does not explicitly take into account capital heterogeneity as a consequence of embodied technical progress. We, therefore, analyze the properties of a neo-Kaleckian model that includes both labor productivity differences between firms and the necessary condition of positive profits to engage in production. We show that the positive impact of real-wage increases on effective demand forces some firms to stop production because they become unprofitable. Moreover, the increase in effective demand can be impeded by the decrease in the capacity of profitable firms. Therefore, a recovery of economic activity through wage increases reaches its limits when profitable firms are at full capacity. The model also highlights the importance of technical competition and its role in firms’ behavior regarding capital replacement.

Keywords:

• Embodied technical progress
• heterogeneous capital stock
• income distribution
• labor costs
• neo-Kaleckian model

Jel codes:

• E12
• E20
• E23

Notes

1 See Taylor (2004), Hein (2014), Lavoie (2014) or Blecker and Setterfield (2019) for large surveys on this issue.

2 This strand of literature was developed from the seminal contributions of Rowthorn (1981) and Dutt (1984).

3 See the seminal contributions of Bhaduri and Marglin (1990) and Kurz (1991).

4 Beside the above references, see, for instance, McCombie and Thirlwall (1994) or Blecker (2011) regarding open economies, Stockhammer (2010) or Hein (2012) regarding financialization, Cassetti (2003) or Storm and Naastepad (2012) regarding technical progress, Cassetti (2003) again regarding conflicting claims and inflation, or Palley (2017) regarding personal income distribution.

5 Actually, Lavoie (2014, 293) notes this limitation of Kaleckian models but does not develop it, as he writes that “in general, higher real wages will not necessarily entail a reduction in production and employment, unless the real wage is so high that it is no longer profitable to produce; that is, unless the real wage is higher than labour productivity.”

6 According to the General Theory, a decrease in aggregate demand implies a decrease in the price level of goods, resulting in an endogenous increase in real wages that encourages profit-maximizing firms to reduce both production and employment (see Weintraub (1957) or Davidson and Smolensky (1964) among many others).

7 A positive mark-up rate ensures profitability if the price corresponds to a mark-up over the direct cost and if there are no indirect costs (mark-up pricing method). Things can be more complicated if there are indirect costs since a positive mark-up could be consistent with negative profitability). However, the mark-up then generally also applies to indirect costs, which ensures the firm’s profitability (full-cost or target-return pricing models). See Lavoie (2014, chapter 3).

8 Various authors have wondered whether direct unit costs can be assumed to be constant at the industry or aggregate level. However, they do not propose any explicit analysis. See, for instance, Davidson (1960, 53) and Lavoie (2014, 155–156). See also the growth model of Kaldor and Mirrlees (1962), which includes vintages of machines.

9 As stressed by an anonymous referee, this property is already at the heart of Steindl's analysis of the pattern of competition within an industry (Steindl 1952, 40–45). As a result, his analysis, which is essentially a narrative, is based on mechanisms and leads to conclusions that are close to those that we establish in a more formalized manner in this article.

See also Seppecher, Salle, and Lavoie (2018) for an agent-based model including the mark-up rate heterogeneity. In this article, however, labor productivity is assumed to be the same within every sector; heterogeneity results from firms setting both their mark-up and price.

10 See Steindl (1952, 45) and Perelman (2006). As highlighted by Lavoie (2014, 306), such arguments are already in Webb’s (1912) analysis of the implications of the minimum wage. See also Rowthorn (1981, 22), as he points that some specific variety of technical progress “encourages the replacement of old equipment by new, and leads to competitive investment amongst firms who are anxious to keep ahead in the race for profits.”

11 Taylor (1991) suggests the same kind of regime shift (i.e., a wage-led regime that becomes profit-led if the real wage exceeds a certain level). However, once again, the direct effect of real wages on production costs is neglected. Only indirect effects through aggregate demand are taken into account. In this model, the profit-led configuration emerges because of the combination of a positive propensity to save out of wages and an endogenous change in the sensibility of capital accumulation with regard to the rate of profit (the value of this parameter being assumed to increase with the level of real wages). Marglin and Bhaduri (1990) also investigate the possibility of regime shifts resulting from endogenous changes in some aggregate demand parameters.

12 See Lavoie and Stockhammer (2013), Hein (2014), Stockhammer (2017) or Lavoie (2017) for recent surveys.

13 See Cassetti (2003) and Lavoie (2014, chapter 8).

14 Indeed, capital is not heterogeneous if either the new equipment does not engender an increase in the level of labor productivity period after period (no technical progress) or firms do not accumulate (no investment).

15 See Cassetti (2003), Hein and Tarassow (2010) or Storm and Naastepad (2012) regarding the introduction of Kaldor-Verdoorn’s law in neo- and post-Kaleckian models.

16 However, as mentioned above, the extent of capital heterogeneity is assumed to be exogenous in this pioneering research.

17 Although Eichner (1976, 34–35) admits the possibility of rising marginal costs if the firm’s plants differ in efficiency, he quickly neglects this case, claiming that “the differences are not likely to be very great—or else the megacorp will certainly take steps to eliminate them” (35). Lately, Eichner (1986, 486) legitimatizes the choice in favor of a constant direct cost by arguing that it enables making a clear distinction between the shape of the firm’s cost curves in the absence of technical progress and the effect of technical progress alone on the firm’s costs curve. Yordon (1987) adds an argument as he criticizes Lee’s (1986) view, according to which “multiplant firms should exhibit increasing average direct costs because they should be able to achieve variations in total output by opening or closing plants, using those with lower costs for smaller outputs and those with higher costs for larger output” (Yordon 1987, 596). According to Yordon (1987), Lee’s argument must be rejected since it ignores both start-up, shutdown and transportation costs. On this question, see also Lavoie (2014, 154–156).

18 For example, if a firm’s plant faces losses, it can either definitely close, temporarily close, or engage in production depending both the firm’s strategy and whether the other plants of the firm make profits.

19 To legitimatize increasing marginal costs at the aggregate level, Davidson (1960, 52–53) refers to Reder (1952), who develops the following argument: “Suppose that all firms had marginal cost curves that were horizontal (up to capacity), but that the vertical intercepts of the marginal cost curves of some were higher than those of others; then, when the industry’s level of output was low, production might be predominantly by the low-cost firms, but as the industry’s output level expanded sharply under increased demand, these firms would be unable, in the short run, to expand output proportionately with demand, and the high-cost firms’ output share would rise. Thus, marginal cost in each industry (exclusive of any rents) would rise with output” (Reder 1952, 191–192).

20 Throughout the article, the subscript $x$ indicates that the variable takes a specific value for each firm according to the ranking of its equipment.

21 In other words, we are aware that the model is not fully consistent because we implicitly assume that $\underset{-}{y}$ and $\overline{y}$ change at the same pace over time, which will be correct at the model equilibrium but incorrect in a comparative statics analysis. Any shock in the model would cause a change in the value of the $\lambda$ parameter.

22 See, for instance, Cassetti (2003) and Lavoie (2014, chapter 8).

23 See Lavoie and Stockhammer (2013, 15–16).

24 See, for instance, the broad surveys in Hein (2014), Lavoie (2014) and Blecker and Setterfield (2019).

25 Bowles and Boyer (1990, fn. 6) suggest instead to relax the wage uniformity assumption if firms differ in their technology (which is not the case in their model).

26 Such an assumption is made in Lee (2015, 31), among others.

27 Steindl (1952, 44) proposed a very similar graph, although it ranks machines in order of increasing productivity.

28 In reality, some firms continue to produce even if their equipment generates losses because of the presence of a fixed cost or to keep their customers while hoping for better days. However, other firms shut down while profitability is still positive, allowing redirection of their resources towards more lucrative activities. Our aim here is not to discuss the level of profits or losses at which firms stop producing but rather to claim that such a level exists. Under our assumptions, this level corresponds to a zero mark-up rate.

29 We therefore depart from Reder (1952), who posits that high-cost firms produce only if demand has not been fully satisfied by lower-cost firms.

30 For their part, Bowles and Boyer (1990, 200) introduce a “reproducibility condition” in a model with homogeneous capital but an efficiency wage hypothesis. Consequently, a wage rise results in a decline in workers’ efforts that can engender losses for all firms because they are identical.

31 Therefore, both the analysis at the microeconomic level and the aggregation problems can be skipped.

32 This corresponds to the “naïve” formulation according to the expression used in Lavoie, Rodríguez, and Seccareccia (2004).

33 The positive influence of technical progress (related to $\lambda$) on capital scrapping was already introduced in Rowthorn’s (1981) seminal model.

34 We therefore do not take into account capital depreciation resulting from equipment wear and tear (see Rowthorn (1981) or Kurz (1991), who further assumes that wear and tear increases with the rate of capacity utilization). Our assumption is closer to that of Steindl (1979), who assumes that capital depreciation decreases with $u:$ firms delay depreciation when $u$ is high and hasten depreciation when $u$ is low. Indeed, unprofitable firms in our model face a zero rate of capacity utilization ($u_{\overline{x}}=0$).

35 According to Kalecki (1968, 269), “entrepreneurs scrutinize how a new investment ‘is doing’ in terms of profitability […]. An important element of how the new investment ‘is doing’ is the rise in productivity due to technical progress, which causes a transfer of profits from old to new equipment.” According to Eichner (1976, 88), “a megacorp will grow and prosper depending on how well it allocates the investment funds […]. It should also be noted that while the individual firm is constrained by […] the margin above costs […] implicit in the price level maintained by the various members of the industry, it is not so constrained with respect to the rate of investment. The rate of investment for the individual firm may diverge from the industry average […]. This greater degree of freedom on the investment side gives rise to the non-price competition so characteristic of oligopoly. Indeed, one can say that, under oligopolistic conditions, competition through investment will replace competition through price.” One may object that a megacorp is at the opposite of the assumption of single-equipment firms adopted in my model. However, this assumption has been adopted only to simplify the model resolution and does not question the framework, which remains that of an economy with imperfect competition.

36 The value of $\lambda$ would depend on $u,$ while $u$ depends on $\overline{x}$ and thus on $\lambda ,$ as we will show below.

37 While every capitalist obtains the same return on capital, each firm’s gross rate of profit depends on the ranking of its equipment, that is, ${\pi }_x{u}_x/\upsilon .$

38 We prefer equation (21) to the usual assumption according to which capitalists save a fraction of their net profit, $g^s=s\left(\pi u/\upsilon -\delta \right)$ (see Rowthorn (1981) and Lavoie (1992) among others). Indeed, the usual specification is not compatible with degrowth, because a negative value of $g^s$ goes hand in hand with a negative value of capitalists’ consumption, which does not make sense. This problem can be solved if capitalists offset the negative consumption out of profits by a positive consumption out of wealth (see Cahen-Fourot and Lavoie, 2016). Equation (21)(21) $$g^s=s\frac{\pi u}{\upsilon }-\delta$$(21) offers a simpler solution to this problem since capitalists’ consumption is positive provided a positive gross saving. In addition, degrowth is made compatible with a positive value of the net rate of profit.

39 Please note the distinction between $u^{*},$ the rate of utilization of the whole capacity in the economy (computed with respect to the capital stock at the beginning of the period) and the rate of capacity utilization of each firm, $u_x$ (with $u_x=0$ for unprofitable firms).

40 This occurs when the amount of saving out of gross profits is lower than the amount of capital scrapping. Note that the condition on the gross rate of profit is more binding on net accumulation ($g^{*}>0\iff \pi u/\upsilon >\delta /s$) than on net profit ($r^{*}>0\iff \pi u/\upsilon >\delta$). Accordingly, degrowing is compatible with a positive value of $r^{*}.$

41 See Steindl (1979), Rowthorn (1981), Lavoie (1992) and Cassetti (2006), among others. See Perelman (2006) about the neglect of replacement investment in Keynesian economics.

42 Let us remind that the decrease in $\overline{\theta }$ corresponds to an increase in the real wage in equation (5).

43 This relation between mark-up rates, capital scrapping and labor productivity was pointed out over a century ago in a less formal way by Webb (1912) and then by Steindl (1952). See also Perelman (2006).

44 In Bowles and Boyer (1990), the shift from the wage-led to the profit-led demand regime is due to the efficiency wage hypothesis. For a high level of employment, workers’ efforts are low (because the probability of securing an alternative job is high); therefore, a low rate of profit is observed. In this high-employment profit-squeeze regime, a wage rise results in a decrease in employment as the consequence of two complementary effects: the increase in workers’ efforts (at the expense of employment) and the decrease in aggregate demand stemming from the increase in the propensity to save because of profit restoration.

Bowles and Boyer (1990) do not analyze what happens if the goods market equilibrium meets what they call the “reproducibility condition” because a regime in which all firms face losses does not make sense. In our model, contrarily, some firms make profits as aggregate demand meets what we call the “profitability condition,” which is why this configuration must be analyzed.

45 Some results that can be expected from the endogenization of $\lambda$ will be briefly discussed in the following section.

46 As noted by an anonymous reviewer, our model partly replicates the outcomes of the French disequilibrium theory of Benassy and Malinvaud (see Malinvaud 1977). Indeed, a parallel can be made between the wage-led demand regime and Malinvaud “Keynesian unemployment” since, in both cases, the excess supply in the labor market results from the demand constraint in the goods market. Likewise, the profit-led demand regime corresponds to “Classical unemployment” since, in both cases, economic activity and employment are supply constrained: firms do not satisfy the excess in goods demand because of too high a level of real wages.

47 Such a situation could be drawn in a figure similar to Figure 4, assuming that ${\overline{x}}_B$ corresponds to the intersection between the $g^i$ and $g^s$ curves. In line with the previous footnote, it should be noted that this situation corresponds to Kahn's (1977) criticism of Malinvaud (1977): excess aggregate demand and “Classical unemployment” can only be temporary phenomena, as prices will rise if profitable firms are at full capacity.

48 Technical progress in new equipment corresponds to improvements in labor productivity between one generation of machines and the next generation.

49 Let us recall that the ranking is given by the value of $x,$ which is close to 0 for the most efficient firms and close to 1 for the least efficient firms. Consequently, the position of every firm in Figure 1 shifts to the right period after period.

50 This point is briefly discussed in Lavoie (2014, 127, 165). See also Perelman (2006).