Capitalism’s growth imperative: an examination of Binswanger and Gilányi

Abstract:

This paper examines Mathias Binswanger’s (2009) model of a growth imperative and Zsolt Gilányi’s (this issue) note on that model. The growth imperative in Binswanger’s model is established through a profit-loan linkage such that loans, as well as the economy as a whole, must grow at a suficiently high rate so that firms make positive profits. To come to this conclusion, Binswanger derives a particular steady-state rate of growth in which profits are zero, which he refers to as the zero profit growth rate. In his note, Gilányi derives his own minimum growth rate based on a constant money supply. Gilányi then compares the two minimum growth rates—Binswanger’s zero profit growth rate and his monetary growth rate—to determine which one is the binding constraint on the model. Upon comparison, Gilányi shows that his monetary constraint is always the binding constraint implying that the zero profit growth rate is redundant. This paper shows that after reformulating Binswanger’s model in order to make its equations stock-flow consistent, the resulting zero profit rate of growth is always the binding constraint. This zero profit rate of growth is thus not redundant as was the case in Binswanger’s model, and, on the contrary, it is Gilányi’s monetary constraint that is redundant in the reformulated model.

Key words::

• growth
• monetary circuit
• profits
• stock-flow consistency
• economic dynamics

Notes

¹Ricardo, for example, set up his counterfactual stationary state to emphasize the obstacles that regulated markets and technological inertia placed before capitalists in their ongoing pursuit to accumulate. But like those before him and the majority after him, he did not put forth an argument detailing why capitalism must grow.

²This last clause abstracts from Marx’s views on crisis and the related idea of a secular tendency for the rate of profit to fall as the accumulation process deepens.

³Given Marx’s insistence on capitalism’s necessity for growth, it is no surprise that in recent debates over so-called green capitalism or proposals for an ecologically sustainable stationary state it has been Marxists who have intervened in order to call attention to the inherent need for capitalism to grow. Among the many candidates on the topic, see Foster and Magdoff (2010) and Smith (2010, 2011).

⁴Of his numerous publications on the issue of the growth imperative, see Gordon (1980, 1987), and Gordon and Rosenthal (2003) in particular.

⁵Since Mathias Binswanger’s model is the focus of this paper, I will be referring to him just as Binswanger in what follows.

⁶Binswanger’s ZPGR is technically the steady-state rate of growth of loans corresponding to zero profits. But in the steady-state all variables must grow at the same rate, and so under these circumstances the economy’s rate of growth must equal the rate of growth of loans. For ease of exposition I will be referring to the growth rate of loans as simply the growth rate in what follows.

⁷An important consideration that should be taken into account in this newer body of work is the stock-flow consistency of the models since financial flows now have an explanatory role to play.

⁸Specifically, I have respecified the inconsistent equations of the model that are used to obtain the ZPGR. There are other issues with Binswanger’s model that I do not directly address, such as the failure to include a variable representing the money stock, the treatment of inventories, and a potential overdeterminancy problem once these other issues are addressed.

⁹See Keen (2009) and Wray (1993, 1996).

¹⁰See Rochon (2005) for a survey of the paradox of profits literature as well as the author’s solution.

¹¹As implicitly shown by Gilányi, Binswanger’s first equation that specifies consumption spending is unnecessary to derive the ZPGR, and so is disregarded in what follows.

¹²Binswanger does not introduce a variable to represent the money stock in his model, forcing loans to perform the dual role of the stock of loans outstanding and the stock of money. But the stock of existing loans and the stock of money are equivalent only under very special conditions due to the leakages and injections from and to circulation in the model. The nonequivalence of loans and the money stock is in fact fundamental to Gilányi’s minimum growth rate, which is examined in the final section.

¹³In what follows, by a quantity is meant a number of measurement multiplied by a unit of measurement (De Jong, 1967, p. 7). In economic models quantities are conventionally measured by real numbers, and most units of measurement can be derived from the following primary dimensions: money of account (e.g., dollars), per unit time, and a physical dimension (e.g., goods or labor). Thus, the unit of measurement (dimension) of a stock quantity in nominal terms is the money of account, while a flow quantity in nominal terms has dimension money of account per unit time.

¹⁴By conceptual dimension I just mean some quantity’s dimension, that is, its units of measurement. The qualifier, conceptual, is normally unnecessary, but a quantity’s dimension can become confounded once introduced into a discrete-time framework.

¹⁵Keen (2009) is explicit on this point.

¹⁶An equation is dimensionally homogeneous if both sides of the equation have the same dimension (De Jong, 1967, p. 23).

¹⁷Perhaps a more natural specification of Equations (3) and (4A) would substitute current period profits, Π_t, for last period’s profits. The ZPGR however is invariant to the time period chosen for profits in these two equations, provided profits in both equations have the same time period. Given this invariance and my interest in approximating the original model as closely as possible, I maintain Binswanger’s lagged profit variable in these two equations.

¹⁸Despite its consistency, there is a theoretical issue surrounding Equation (7), the equation that has the investment-goods sector always breaking even. Binswanger makes this assumption to simplify the model, but the theoretical consequences of his simplification are not discussed. Gennaro Zezza in his comments on a similarly formulated model writes that this “assumption cannot be maintained, since at the end of the production period the investment sector will have an increase in the stock of capital which must be accounted for.” Alternatively, if the assumption is maintained, then either it must be assumed that “the investment sector produces without using any investment goods” or that the “investment goods sector does not want to increase its stock of capital” (Zezza, 2003, p. 1). Moreover, Binswanger’s explanation of the growth imperative follows the tradition that sees production as being undertaken for its own sake and not for the sake of consumption. But in assuming a zero rate of profit in the investment-goods sector via Equation (7), why would anyone voluntarily choose to produce investment goods? It is clear then that there is much to gain and little to lose by aggregating production-sector firms in models formulated in this way.

¹⁹Equation (1) is omitted because it is unnecessary to derive the ZPGR. Regarding the equation numbers of the model, the respecified equations are denoted with the letter “A” following Binswanger’s equation number. The equations represented by a number only are Binswanger’s original equations.

²⁰Profits as shown in equation (13) are always less than Binswanger’s corresponding measure (p. 718). There are two reasons for the discrepancy. First, Binswanger uses last period’s wage-bill as the revelant real cost of production when he defines current profits (p. 714). In a growing economy last period’s wage-bill will be less than the current period’s because of the positive relation between the wage-bill in the consumption-goods sector and loans. Costs as calculated by Binswanger are therefore less than costs as calucated in equation (2A) above. The second reason for lower profits has to do with the respecified equations (4A) and (5A). By replacing the increase in loans, ΔL_t, for the stock of loans, L_t, in equations (4) and (5), both investment and the wage-bill in the consumption-goods sector are diminshed by cL_t−1 and (1 − c)L_t−1, respectively. As investment is equal to the investment-goods wage-bill by equation (7) and all wages are spent in the model, consumption spending—and therefore profits—are always lower in the respecified model than in Binswanger’s. A lower measure of current profits is part of the reason why the zero profit growth rate in this model is more restrictive than in Binswanger’s model. The numerical example at the end of this section illustrates the latter assertion.

²¹Graphs with each parameter taken as the independent variable, the other three parameters being held constant, are depicted in the Appendix below.

²²To see why this inequality determines the binding constraint it might be easier to negate it so that $$w_{0^{\mathrm{\prime }}}\le w_0^m$$. Ignoring the case of equality, if $$w_{0^{\mathrm{\prime }}}<w_0^m$$, then the rate of growth required to keep the money stock constant exceeds the rate of growth when profits are zero. That means at the rate of growth w₀ the money stock is declining, which is impossible if the economy were in a steady state. The formal justification for the claim that the money supply is declining at w₀ if $$w_{0^{\mathrm{\prime }}}<w_0^m$$ is that $$w_0^m$$ is a continuous function of b and z.

²³The left- and right-hand sides of the inequality do not have finite upper and lower bounds, respectively, because the interest rate has no finite upper bound. The absence of any upper restriction on z does not affect the result obtained though.

²⁴The graphs in the appendix with z and b as independent variables show that w₀ = 0 if either z = 0 or b = 1. But the graph with c as the independent variable does not show w₀′ tending to zero as c approaches one because both z and b are nonzero.

Additional information

Notes on contributors

Reeves Johnson

Reeves Johnson is a clinical professor in the Department of Economics at Loyola University Chicago.