دستمزدها و رشد بهره وری در یک انحصار پویا

This paper studies the intertemporal problem of a monopolistic firm that engages in productivity enhancing innovations to reduce labor costs. The optimal innovation policy is not monotone and the rate of productivity growth is the highest when the firm's size is in some intermediate range. As long as its initial productivity is not too low, the firm eventually reaches a steady state where the rate of productivity growth is identical to the rate of wage growth. Productivity dependent wage differentials do not affect productivity growth in the steady state; they increase, however, the firm's long-run equilibrium cost level.

This paper studies the impact of labor costs on the incentives for process innovations. It considers the intertemporal problem of a firm that engages in productivity enhancing innovations to reduce its labor costs. While the firm acts as a monopoly in the output market, it takes the current competitive wage in the labor market as given. At each point in time, the wage rate and the firm's productivity determine its unit labor cost. Through investments in process innovations it can raise productivity and thus reduce its cost at subsequent dates. This generates a dynamic optimization problem because innovation affects future labor costs and the incentives for innovation depend on the evolution of these costs. We formulate this problem as an infinite horizon optimization program. In this way we can study the long-run evolution of productivity growth. At each point in time, the optimal innovation policy is determined by the firm's current unit labor cost. We show that this policy is not monotone but has an inverted U-shape: the optimal innovation rate is higher for intermediate values of the firm's unit labor cost than for low or high values. Since the firm's output and employment decrease with its cost, the empirical implication is that the relation between innovation and the firm's size, as measured by its output or employment, is not monotone. In fact, on an optimal path with output increasing over time, there may be an initial phase of accelerating productivity growth, which is followed by a phase of decelerating productivity growth. The long-run prediction of our analysis is that productivity growth converges towards the rate of wage growth in all firms that survive in the long-run. Indeed, we show that increasing wages will not drive the firm out of the market as long as the initial level of its labor cost is not too high. In this case the rate of productivity growth approaches the rate of wage growth under the optimal innovation policy. Eventually, the firm reaches a steady state where these two rates coincide so that its unit labor cost remains constant over time. Interestingly, this steady state is independent of the level of wages; it only depends on their growth rate. The level of wages determines only whether the optimal policy tends towards the steady state or whether the firm will go extinct in the long-run. In our model it is the evolution of wages that stimulates productivity enhancing innovations at the firm level. Our cost-push argument addresses the interaction between labor market conditions and the innovative performance of industries and countries. This interaction is the subject of a number of empirical studies both at the macroeconomic (see e.g. Gordon, 1987) and the microeconomic level (see e.g. Doms et al., 1997, Chennells and van Reenen, 1997, Mohnen et al., 1986 and Van Reenen, 1996). An important issue in this context is the relation between unionization and firms’ R&D investment and innovation activities, which has been the subject of a relatively small number of theoretical and empirical studies. Theoretical studies by Baldwin, 1983, Grout, 1984 and van der Ploeg, 1987 show that unionization is associated with underinvestment. In the absence of legally binding contracts, once a firm has incurred the sunk costs of investment, its union pushes for higher wages in order to capture a share of the quasi-rents created by the firm's innovation. Due to the union's hold-up behavior, the firm's incentives to innovate are decreasing with the union's bargaining power1. This underinvestment result may, however, not hold if unionized firms are competing in the market and invest strategically to increase their market shares and profits: Tauman and Weiss (1987) show that a unionized firm, competing with a non-unionized rival, may overinvest in R&D under plausible conditions. Ulph and Ulph, 1994, Ulph and Ulph, 1998 and Ulph and Ulph, 2001 show that overinvestment may be observed in a unionized duopoly where firms are involved in a patent race for a single cost-reducing innovation. We address the issue of rent sharing in Section 5, where we endogenize the firm's wage rate by introducing productivity dependent wage differentials. These may reflect the employees’ bargaining power within the firm. In contrast with the static hold-up problem our dynamic analysis reveals that rent sharing has some quite different long-run effects. Indeed, the firm's steady state rate of innovation is independent of the degree of rent sharing. This is so because in the steady state the rate of productivity growth equals the rate of wage growth and the ratio of the firm's wage to the competitive wage remains constant over time. Our model thus indicates that unionization does not influence the firm's long-run innovation behavior. The higher the degree of rent sharing, however, the higher is the firm's long-run equilibrium cost level and the lower is its output. Yet, employment at each date after the steady state has been reached is independent of the degree of rent sharing. This is so because rent sharing has two exactly counterbalancing effects on employment: on the one hand, it reduces the firm's steady state output; on the other hand it also lowers the long-run level of labor productivity. While the output effect tends to decrease employment, this is offset by the increase in employment due to the productivity effect. The empirical evidence of the impact of unionization on productivity enhancing activities is mixed and, to a large extent, inconclusive. Studies for USA show that unionization is associated with significantly less investment in physical capital (Bronars and Deere, 1993 and Hirsch, 1990); significantly less innovation (Acs and Audretsch, 1987a, Acs and Audretsch, 1987b, Acs and Audretsch, 1988 and Hirsch and Link, 1984); significantly less investment in R&D (Connolly et al., 1986, Addison and Hirsch, 1989 and Bronars et al., 1994); but significantly more investment in employer-related training (Tan et al., 1992). The empirical evidence from UK is more inconclusive. A few studies identify a positive, but not necessarily significant, impact of unions on investment (Machin and Wadhwani, 1991 and Latreille, 1992), while others identify a negative impact (Denny and Nickell, 1992). Unionism may, however, be related with a higher probability of receiving formal training (Booth, 1992 and Tan et al., 1992). More recent studies also report mixed evidence on the relation between union power and productivity enhancing activities (Addison and Wagner, 1994, Menezes-Filho et al., 1997 and Menezes-Filho et al., 1998)2. This paper complements our study in Bester and Petrakis (1998) of the relation between wages and productivity growth in a competitive industry with free entry and exit where the last period's best technology is freely available to any firm3. Also in the competitive framework it is the growth rate of wages that determines the industry's long-run behavior. There are, however, some important differences between the competitive case and the present model. First, under perfect competition the individual firm does not face a truly dynamic optimization problem to determine its optimal innovation policy. This is so because free entry and exit, and free availability of last period's best technology imply that a firm's future profits are zero, independently of its innovation decision. Second, and more importantly, under perfect competition and free entry and exit, the individual firm does not have to consider the impact of its production cost on the output price. Therefore, in Bester and Petrakis (1998) there is a positive relation between the incentive for innovation and the current cost level. This is no longer the case in the present monopoly model or, more generally, under imperfect competition. Instead, under the optimal policy the relation between R&D investment and current cost has an inverted U-shape: when the monopoly's cost are relatively low, there is little incentive to reduce these costs even further. Also relatively high costs, however, reduce the gains from cost reduction because of the low output associated with a high monopoly price. As a result, the monopoly's highest innovation effort occurs for some intermediate level of labor costs and its adjustment path towards the steady state may not be monotone. In our model the firm's output and employment are both negatively related to its unit labor cost. Thus, if we view output or employment as a measure of firm size, an empirical implication of our analysis is that the relation between innovation and firm size is not monotone. Instead this relation has an inverse U-shape as the rate of productivity growth is highest when the firm's size is in some intermediate range. These findings are in line with Machin and Wadhwani (1991), who report that “initially, an increase in size is associated with higher investment, though, eventually, size appears to be a disadvantage”. In contrast, most of the literature considers the R&D–firm size relationship as monotonic. For example, Cohen and Klepper, 1992 and Cohen and Klepper, 1996 provide an explanation for an inverse relationship between R&D productivity and firm size. Klette and Griliches (2000) present a model of firm growth in which R&D investment is proportional to sales. Some empirical studies give evidence for a positive relation between R&D and firm size in selected industries (e.g. Grabowski, 1968 and Mansfield, 1964). Others find that firm size barely matters for R&D or that the relation may even be negative (e.g. Acs and Audretsch, 1988, Pavitt et al., 1987 and Scherer, 1980). Moreover, Acs and Audretsch, 1987a and Acs and Audretsch, 1987b indicate that a large or a small firm may have the relative innovative advantage, depending on a number of industry features, such as the degree of concentration and unionization, the capital intensity, the proportion of skilled labor, etc. This kind of studies, however, typically measures the firms’ innovative activity without distinguishing between process and product innovations. Therefore, it is worth emphasizing that our theoretical findings only refer to productivity enhancing innovations. This paper is organized as follows. Section 2 describes the firm's infinite horizon optimization problem. The steady state solutions of this problem are derived in Section 3. Section 4 analyses the adjustment dynamics of the optimal innovation policy. The impact of productivity dependent wage differentials is studied in Section 5. Section 6 presents conclusions. The proofs of Lemma 1 and Proposition 1 and Proposition 2 are relegated to Appendix A.

Modern industrialized countries are characterized by rapid technical progress accompanied with substantial increases in real wages. We have shown that, in a dynamic monopolistic industry, the firm optimally invests each period in productivity enhancing innovations to counterbalance increasing wages. Our analysis presents a dynamic cost-push argument of productivity growth. This argument is in the same sprit as Kleinknecht (1998) who emphasizes that labor market rigidities may have positive dynamic efficiency effects because they create stronger incentives to increase labor productivity. In our model higher current labor costs create stronger incentives for process innovations. Unless the wage level is too high, the monopolist's rate of productivity growth monotonically approaches the growth rate of wages and eventually the firm reaches a steady state where its unit cost of labor remains constant over time. Interestingly, long-run productivity growth only depends on the growth rate of wages and is thus independent of the initial level of wages. While the monopolist's unit labor cost as well as its output in the long-run depend only on the growth rate of wages, the long-run levels of labor productivity and employment depend on the level of wages. We have also analyzed the case where the rents stemming from productivity enhancing innovations are shared between the monopolist and its workers. Surprisingly, also in this case the long-run productivity growth only depends on the growth rate of wages and is independent of the share of profits over which the workers have claims (measured e.g. by the union's power). Hence, unionization does not influence long-run productivity growth, despite the fact that it depresses the short-run incentives for innovation. The union's bargaining power, however, determines the monopolist's long-run unit cost of labor and thus its output level: in the steady state its unit cost of labor is the higher and its output is the lower, the higher the union's power is. Nonetheless, long-run employment may actually be positively related to the union's bargaining power. This is so because unionization has a negative impact on labor productivity and reduces the sensitivity of the firm-specific wage towards changes in the market wage rate. Our model could be extended to consider dynamic imperfectly competitive markets. In an intertemporal model where at each date firms compete in prices or quantities it will be interesting to analyze how strategic interactions between the firms affect productivity growth in the short-run and in the long-run. Stimulated by the work of Schumpeter (1947), a large part of the literature on R&D relates the pace of innovative activity to market structure. An imperfect competition version of our model could combine this approach with our cost-push argument.