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The paper proposes a general equilibrium model based on the classical assumption that the real wage rate is determined from outside the system of production. In this model, the Walrasian auctioneer in the labor market is replaced by a flexible accumulation rate. Several equilibrium concepts are introduced and studied.

Models of general equilibrium, based on agent optimization, rational expectations, and market clearing, play a key role in neoclassical economic theory. In such models it is supposed that prices provide economic agents with all necessary information about the economy that they need in order to make efficient use of the available resources. From this premise neoclassicals typically draw (perhaps, implicitly) the conclusion that the prices provide an exhaustible list of variables through which a state of economic equilibrium can be established. This deduction looks plausible from a normative point of view: indeed, well-known theorems read that under more or less restrictive assumptions an equilibrium exists and, moreover, is Pareto-optimal. From a positive point of view the conclusion is less unambiguous, since the logical possibility of establishing equilibrium through varying prices does not imply the relevance of this possibility. One of the features of real economies that catches eye is that labor markets do not behave like competitive commodity markets, where prices fall or even plunge when supply exceeds demand. The failure of pay rates to fall is termed wage stickiness, downward wage rigidity, or simply wage rigidity, and has puzzled economists for years. Wage rigidity is central to intense controversy between Keynesian and neoclassical macroeconomists over whether government economic policy should be used to stabilize aggregate income and employment. Keynesians claim that wage rigidity is confirmed by statistical evidence that pay rates almost never fall. They say that labor markets do not automatically adjust to eliminate excess unemployment and that joblessness is a grave misfortune forced on people, most of whom want to work, even at wages lower than those earned previously. Neoclassicals believe that wage rigidity is an illusion, that wages and salaries are flexible, and that labor markets always clear. Central tenets of those beliefs are that the existing rate of unemployment is the optimal outcome of market forces and should not or cannot be affected by government policy. The view is that during recessions pay rates fall below reservation levels, or the minimum at which people are willing to work. This decline causes employees to leave their jobs and become unemployed. Neoclassicists also assert that anyone can find some job quickly and that people remain unemployed because they seek for higher pay than available to them. There are compelling reasons for wages to display much less flexibility than would be observed in Walrasian auction markets. Because wages are observed to be sticky, the assumption that at any point in time wages are a datum seems to be a more realistic basis on which to model the economy. Little is known about which theories are correct or under what conditions. The three theories that have been advanced to account for sticky wages are generally referred to as the implicit contracts theory, the efficiency wage hypothesis and the insiders–outsiders approach. Two points should now be made. First, it is worth noting that Keynes himself assumed that nominal wages are ‘sticky’ downwards. He postulated that workers would accept a decrease in their real wages caused by a general increase in the price level, but would resist direct efforts to cut their wages. At the same time, two of the three mentioned approaches, the efficiency wage models and the implicit contracts theory, explain why the real wage rate (but not nominal wages) is rigid. Secondly, changes in aggregate demand in Keynesian models are met with changes in quantities only in the short-run; over time, however, as output constraints become binding, adjustment occurs through prices. Keynesians will agree with the assertion that in the long-run nominal and real wages are flexible. The conventional economic wisdom says that the real wage rigidity is not compatible with market clearance in the labor market. Since labor market clearance looks more satisfactory in the long run than in the short run, two possible conclusions can be drawn. Either in the long run the impersonal Walrasian auctioneer takes care of the labor market more successfully than in the short run or there exists a non-Walrasian mechanism of labor market clearance. Most economists would perhaps be inclined to make the first conclusion. The main objective of this paper is to introduce one of possible non-Walrasian mechanisms. To do this, a dynamic general equilibrium model in which the real wage rate is considered as a datum is constructed and studied. Recall that one of the most important differences between the classical and neoclassical schools of economic thought lies at their approaches to the distribution of income between wages and profits, in particular, to the formation of the real wage rate. A neoclassical economist considers the real wage rate as an endogenous variable in a general equilibrium model and would agree with the assertion that labor is simply one of the factors of production, and therefore, the price of this factor is established at the level that provides the equilibration of the demand for labor and labor supply. Contrary to the supply-and-demand approach, in the theoretical approach to distribution of classical economists, the real wage rate and the rate of profit are not symmetrically and simultaneously determined on the basis of the relative scarcity of labor and capital. Within the classical approach, one of the two distributive variables is explained independently from both the social product and the other distributive variable and is considered as a parameter; the other one is considered as an endogenous variable determined as a residual. Piero Sraffa, a ‘pioneer’ of the modern classical theory, argued that the rate of profit is “determined from outside the system of production, in particular by the money rate of interest” (Sraffa, 1960, p. 33)). At the same time, the founders of the classical economic thought, Adam Smith and David Ricardo, considered the real wage as independent in the relation between the real wage rate and the profit rate, maintaining that its normal rate is determined by the level of subsistence. It was generally recognized by them that population might fail to grow as much as employment, thereby enhancing workers’ bargaining position and that wages can be above their minimum, even for long periods of time, and ‘subsistence’ itself can change as a result. In modern times it is not reasonable to interpret the assumption that the real wage rate is exogenously given in terms of subsistence. It is better to mention historical, social and institutional circumstances and human values. For example, we can read in a paper of a modern student of the labor market: I conclude that wage rigidity stems from the very interest in humane values that seems so incompatible with layoffs. My findings support none of the existing economic theories of wage rigidity, except those that emphasize the impact of pay cuts on morale (Bewley, 1998, p. 460). The real wage rate, in the view of classical works, has little effect on the level of employment. One of the modern proponents of the classical school of economic thought writes: It should be emphasized here that attempts to explain the emergence of institutions or norms which render wages ‘sticky’ tend not to be very convincing when a high elasticity of employment to wages is affirmed, as traditionally done by neoclassical economists…. By contrast, in the classical approach a fall in the real wage rate cannot be expected to bring about an increase in employment, but would only cause a fall in workers’ income. This may help explain why wage norms or institutions tend to emerge as a safeguard for the working class, and also to preserve social stability (Stirati, 1999, p. 1242). Since Bewley does not pretend to be a classical economist, it is especially interesting to notice that his point of view looks closely analogous to the classical one: The issue of wage rigidity should not be confused with the questions of why unemployment exists at all and why it increases during recessions…. Wage rigidity does not necessarily help explain unemployment increases, for it is not clear that wage flexibility would prevent or even diminish them. Though a single firm might employ more workers if it cuts wages, it does not follow that the same is true for all firms together (Bewley, 1998, p. 460). The model proposed in this paper is very much in the spirit of the classical tradition of economic thought though there is always some reluctance within classical economists to use the terms equilibrium or general equilibrium (exceptions to this can be found in Burgstaller, 1994, Duménil and Lévy, 1993 and Walsh and Gram, 1980). In this model the Walrasian auctioneer is replaced by a flexible accumulation rate which is supposed to respond to a situation in the labor market so that excess demand (supply) in the labor market will lead to a reduction (an increase) in the accumulation rate and in the level of production. We consider not only long-period positions, whereas classical authors traditionally emphasize the importance of the long-period approach in their studies and only recently they started to elaborate models with classical features that deviate from this approach, in particular, in connection with exhaustible resources, (see, e.g. Kurz and Salvadori, 1995, chapter 12; Kurz and Salvadori, 1997 and Kurz and Salvadori, 2000). One of the aims of this paper is to show that the classical approach is logically compatible with a general equilibrium framework not only in a long-period framework. Among the aims of the paper is also the desire to stress once again that classical economic theory cannot be considered as a particular case of neoclassical theory as neoclassicals try to prove sometimes (see, e.g. Burmeister, 1984 and Hahn, 1982). It should be emphasized that the model developed in this paper is essentially intertemporal; it would be difficult to construct its atemporal version. To start with, let us recall two one-sector models which usually are labeled as classical, the conventional wage model with unlimited supply of labor (see, e.g. Marglin, 1984 and Foley and Michl, 1999) and Pasinetti (1962) version of the Cambridge model of growth and distribution. In both models it is assumed that the capitalists’ saving rate sc>0, is higher than that of workers, sw≥0. The production sector is described by the Leontief production function y=min{a0x, a1l}, where x is the capital stock, l is the input of labor, y is the output of the only commodity in the economy, which can be used interchangeably as a consumption good or as investment to add to the capital stock. If sw is sufficiently smaller than sc, the Cambridge equation hold in equilibrium: g=scr, where r is the rate of profit and g is the growth rate. In its turn, the profit rate is connected with the real wage rate by the equation r=a0(a1−w)/a1 (it is supposed here that wages are paid ex post and there is no depreciation of the capital stock). Thus, given the capitalists’ saving rate, there is a negative relationship between the real wage and growth rates. The divergence between the two models is in the assumption on whether the capitalists’ saving rate or the real wage is considered as exogenous. In the conventional wage model the real wage rate is considered as an exogenously given; the growth rate is determined endogenously. Labor supply is supposed to be of infinite elasticity. Even if the assumption that the elasticity of labor supply is infinite would not look entirely satisfactory for some economists, it is admissible as a first logical step of consideration in the light of a Marxian reserve army or the Lewis (1954) model. In the Cambridge model, the real wage rate can be determined in each period so as to equate the demand for labor to a given supply of labor, which grows at an exogenously given rate, g, independent of the wage. The economy reaches equilibrium through the impact of profits on the accumulation of capital. If the real wage rate were lower (higher) than the equilibrium level, then profits would be higher (lower), and the capital stock would grow more rapidly (slowly) than the labor force, creating an upward (downward) pressure on the real wage rate. At first glance the assumption that the real wage rate is given would contradict the assumption that the labor market clears. However, these two assumptions are in contradiction only if we consider saving rates as exogenously given. At the same time the assumption that the capitalists’ saving rate is determined exogenously does not look evident. This assumption is reasonable only under the presumption that capitalists are mere consumers in the neoclassical sense, that there is no distinction between capitalists and entrepreneurs, and that all savings automatically invested in real capital. If we make a distinction between capitalists and entrepreneurs, it does not look unreasonable to assume that the capitalists’ saving rate is determined endogenously by investment rate decided by entrepreneurs. Let us suppose that there is an excess supply in the labor market. If the real wage rate is rigid, this will naturally be interpreted by entrepreneurs as an indication of the possibility to increase the level of production (under the assumption that there is no problem with effective demand) and will lead in the long run to an increase in the capitalists’ saving rate. Symmetrically, excess demand in the labor market will lead to a reduction in the capitalists’ saving rate and in the level of production. If we make the assumption that the capitalists’ saving rate is determined endogenously, then there will be no contradiction between a given level of the real wage rate and the labor market clearance. This assumption is in full accordance with the classical tradition. The fundamental concern of the economic thought of Smith and Ricardo was with the allocation of (surplus) output so as to attain the greatest possible growth of the economy. They regarded the capitalist mode of production as the most advantages for the creation of wealth just because the class of industrial capitalists, as a whole, saved the surplus they extracted as profits and devoted it to capital accumulation, while the landlords, as a class, spent the surplus which they extracted as rent on high living. Without going into details, note that our model share a number of traits with general equilibrium models with fixed prices, in which equilibria are allowed to be determined by non-Walrasian mechanisms (see, e.g. Benassy, 1982 and Drèze, 1975), but unlike those models, our approach is not suitable for studying short-run economic fluctuations. The assumptions that the real wage rate is given exogenously and that the accumulation rate is determined endogenously are far from being entirely satisfactory since, in particular, the impact of labor market conditions, especially the number of unemployed or underemployed, are ignored. However, as the starting point for constructing dynamic general equilibrium models, these assumptions are not much more heroic than the traditional neoclassical assumption that the real wage rate is perfectly flexible. The rest of the paper is organized as follows. Section 2 introduces the model and its main assumptions. In Section 3 we introduce and discuss the notions of equilibrium, quasi-equilibrium and pseudo-equilibrium paths. The notions of equilibrium and quasi-equilibrium paths require that in every time period the real wage rate be equal to some exogenously given benchmark level. The difference between them is that the notion of equilibrium path requires market clearance not only in all commodity markets but also in the labor market, whereas the notion of quasi-equilibrium path admits unemployment of labor. As for the notion of pseudo-equilibrium path, it requires market clearance in the labor market but admits the possibility for the real wage rate to be lower than its benchmark level in time periods when the accumulation rate achieves its upper bound. The existence theorems for quasi- and pseudo-equilibrium paths are formulated in Section 4. Also it is shown that under some reasonable assumptions quasi-equilibrium paths exhibit full employment of labor in some time periods and the real wage rate on a pseudo-equilibrium paths will be equal in some time periods to its benchmark level. A stationary version of the model is considered in Section 5. The existence of steady-state quasi- and pseudo-equilibria is proved. Also it is shown that any steady-state quasi- or pseudo-equilibrium is a steady-state equilibrium and, therefore, steady-state equilibria exist. Two examples are constructed in Section 6. The first example shows that there exist pseudo-equilibrium paths on which periods when the real wage rate is equal to its benchmark level alternate with periods when the real wage rate is lower. The second example shows that periods of full employment on a quasi-equilibrium path can alternate with periods of positive unemployment. In Section 7 asymptotic properties of (quasi-)equilibrium paths in the case of a generalized Leontief technology are studied. First results on convergence of intertemporal equilibria towards steady states were proved by Bewley (1982). Our approach is close to the approach developed by Dana et al., 1989a and Dana et al., 1989b. It is closely related to the theory of stability of production prices (for a survey, see Boggio, 1992). We show that (quasi-)equilibrium prices are formed in accordance with a full-cost rule and converge in ratios to prices of production. As for quasi-equilibrium quantities, their relative stability is shown only for quasi-equilibrium paths with permanent unemployment. Section 8 contains concluding remarks. All proofs are relegated to Section 9. The following traditional notation is used: for x, y∈View the MathML source+n, x≤y means xi≤yi (i=1,…, n); x≪y means xi<yi (i=1,…, n); xy=View the MathML source, ∣∣x∣∣=∑i=1n|xi|.

The conventional economic wisdom says that the classical assumption that the real wage is determined from outside the system of production is not compatible with market clearance in the labor market. In this paper, we have made an attempt to challenge this view. To do this, we have constructed an intertemporal general equilibrium model in which the Walrasian auctioneer in the labor market is replaced by a flexible accumulation rate, proposed several equilibrium concepts and proved existence theorems. In particular, it has been shown that though the accumulation rate's flexibility cannot assure full employment at every time, steady-state full-employment equilibria exist. Also it has been noted that if the technology set is a generalized Leontieff one, steady-state equilibrium prices are prices of production and under some assumptions they are relatively stable. The distinctive feature of the model introduced in this paper is the abandonment of the orthodox view on how the society divides its income between consumption and investment, which is closely connected with the nature of intertemporal choice of consumers. In this paper, we have adhered to the view that within some limits capitalists save whatever is needed to finance the investment that entrepreneurs decide. Elsewhere (Borissov, 2002a and Borissov, 2002b) we propose models which are based on different assumptions on the intertemporal choice of consumers and though these assumptions are much closer to neoclassical ones than assumptions accepted in this paper, the results are very much in the classical spirit. It is hoped that scrutinizing the nature of intertemporal choice will be fruitful for further development of the classical approach to economic theory and bridging the long-standing gulf between the classical and neoclassical camps.