Strategic Intrafirm Innovation Adoption and Diffusion

Abstract

1. Introduction This paper addresses two empirical observations that are common in the extensive literature on innovation diffusion. First, a firm usually adopts an innovation over time, not instantaneously. That is, there are intrafirm diffusions (Mansfield 1968; Nasbeth and Ray 1974; Romeo 1975; Stoneman 1981, 1983). Second, the time path of an intrafirm diffusion has a predictable shape. Diffusion curves plot the extent of adoption against time, and are generally S-shaped. That is, they are initially convex, reach an inflection point, and then are concave thereafter. Often they are also skewed in that they are initially convex for less than half of the length of the diffusion. This skewing can be so severe that the diffusion curve is essentially concave (Davies 1979; Stoneman 1983). Given the voluminous literature on innovation diffusion, it is surprising that intrafirm diffusions have not received more attention. With few exceptions (noted below), the theoretical literature assumes adoption is a discrete choice variable, and so occurs instantaneously. Moreover, empirical studies typically assume adoption occurs at the date of first use of the innovation by the firm. To the extent intrafirm diffusions occur, these studies clearly overestimate the speed at which the innovation is put into use, and thus the speed at which its benefits accrue to the firm and society. Intrafirm diffusions are especially common in the case of capital-embodied, new process innovations, because adoption involves adjustment costs as well as acquisition costs. In a seminal study, Mansfield (1968) found that the time interval between 10 and 90% usage of diesel locomotives ranged from three to more than 14 years for firms in the U.S. railroad industry. More recent examples abound. Most readers have undoubtedly experienced, at least once, the adoption of new computer equipment in their workplace. From my own experience, not all users are upgraded to the new equipment within a day, a week, or even a month. Hence, in this paper I analyze the intrafirm diffusion of a new process innovation in a differential game model of an oligopoly. The model's predictions are consistent with the empirical regularities noted above. First, an intrafirm diffusion occurs in equilibrium because the marginal cost of adoption is increasing in the rate of adoption. It is not optimal to adopt instantaneously, just as it is not optimal to adjust to the desired level of a stock instantaneously, when adjustment costs are increasing at the margin. Second, the equilibrium intrafirm diffusion curve is either S-shaped or concave. Moreover, this diffusion curve is more likely to be Sshaped the more competitive the industry, the larger the marginal cost of adoption or the preinnovation unit cost of production, or the smaller the demand. The analysis also shows a firm's diffusion is longer, and so the extent of its adoption at any date is lower the more competitive the industry, the larger the marginal cost of adoption or the pre-innovation unit cost of production, or the smaller the demand. That is, a diffusion is longer the smaller the incentive to adopt (whether due to lower flow profit or higher adoption flow cost). One surprising result is that an increase in the unit cost reduction from the innovation has an ambiguous effect on the intrafirm diffusion. The reason is that there are two conflicting effects. First, as is obvious, a larger cost reduction allows each firm to earn a larger flow profit at every date from the same rate of adoption. However, a more subtle effect is that it also allows the firm to earn the same flow of profit with a slower rate of adoption, and so lower adoption costs. That is, the firms also have an incentive to spread out the diffusion over a longer period of time to save on adoption costs. These results are important for two reasons. First, they show that diffusion curves are more likely to have an S-shape for longer diffusions. …