Multiplant firms and innovation adoption and diffusion.

• Author: Jensen, Richard A.

1. Introduction

   One empirical regularity associated with the adoption of new technology is that large firms tend to adopt sooner than small firms (e.g., see Davies 1979; Mansfield 1968; Mansfield et al. 1982; Stoneman 1983, 1995; or Hoppe 2002). The usual explanation, of course, is that large firms expect a greater return from adoption than small firms. However, large firms do not always adopt first, as can be seen from the diffusion of several new processes in the U.S. steel industry: the basic oxygen furnace and continuous casting (Adams and Mueller 1982) and thin-slab casting (Ghemawat 1993, 1995). This article develops a new theoretical model of innovation adoption and diffusion that explains why large firms tend to adopt first but admits conditions under which small firms adopt first.

   The analysis focuses on the adoption of an innovation of uncertain profitability when a firm's size is measured by the number of plants it operates. As is well known, one reason for operating multiple plants is production costs that are increasing at the margin. Another reason is the existence of economies of multiplant operations, cost savings that result solely from the operation of multiple plants. Theoretical and empirical support for these economies is mixed. Theoretically, the operation of multiple plants can allow savings in nonproduction costs, such as transportation, distribution, and inventory. It can also allow economies of massed reserves, cost savings associated with retaining proportionately fewer spare parts, backup machines, and repair persons in reserve. Information sharing between plants can reduce production and adoption costs. However, multiplant operation can also result in greater information costs. Van Zandt and Radner (2001) show that, because information processing takes time, computational constraints limit the amount of information that can be used in reaching a decision. This informational crowding-out effect can result in decreasing returns to size, or diseconomies of multiplant operation.

   In a seminal, wide-ranging study, Scherer et al. (1975) find little empirical evidence in support of multiplant economies. Moreover, when these economies do exist, they involve savings in nonproduction costs. More recently, in their comparative study of the performance of light water nuclear reactor power plants in the United States and France, Lester and McCabe (1993) do find empirical support for production cost savings due to information sharing about learning-by-doing between plants. In his study of the adoption of thin-slab casting in the steel industry, Ghemawat (1995, 1997) finds that Nucor achieved cost savings due to information sharing between plants regarding both construction and production costs. However, he attributes these multiplant economies to specific aspects of Nucor's organizational structure, and observes that other steel firms with different organizational structures did not achieve these same cost savings.

   Given these conflicting results, the analysis in this article assumes that, if there are multiplant economies, they take the form of savings in nonproductinn costs. In this case, a large firm need not have a greater incentive to adopt first. Its increase in profit from the adoption of a success in all its plants is certainly greater. However, the existence of nonproduction cost economies can reduce the incentive of a large firm to adopt first. Suppose there are two firms, a large firm with two plants and a small firm with one plant. Also suppose that, when the innovation is first installed in a plant, the adopter must shut down that plant for a finite amount of time in order to learn if the innovation is a success or not. This shut-down time can be considered as an experimental period during which the firm trains workers, produces and tests prototypes, attempts to overcome any problems associated with the use of the new technology, or makes any necessary changes in its existing organization. Thus, the opportunity cost of the first adoption of the innovation includes a "learning cost" in the form of profit foregone during this experimental period in which the firm attempts to adopt. This learning cost can be greater for a large firm if there are multiplant economies because the nonproduction cost savings from multiplant operation are lost, or at least reduced, when the firm shuts down one of its plants to adopt. That is, the profit lost when that plant is shut down exceeds the profit from production in either plant, and thus can exceed the profit lost by the small firm when it shuts down its plant to adopt.

   A two-period model of a duopoly faced with an exogenous innovation is analyzed. Adoption requires converting a plant to the new technology, which can succeed or fail to reduce production costs. Conversion is instantaneous and costless, but the first adoption does not reveal immediately if the innovation is a success. An initial adopter must spend a period experimenting with the new technology to learn about it. Its true nature is revealed to all at the end of this learning period. If it is a success, any remaining plants are converted and production begins immediately. If not, any converted plants are reconverted to the old technology.

   This initial learning cost provides an incentive to wait and learn about the innovation from the rival's adoption (see Adams and Mueller [1982] for examples in the U.S. steel industry). This incentive to free ride on rival adoption implies the subgame perfect Nash equilibrium in pure strategies must be either no adoption or a diffusion. In fact, for some probabilities of success, a diffusion is the unique subgame perfect Nash equilibrium. Joint adoption occurs only if both firms randomize in equilibrium, and in this case, a diffusion led by the large firm or the small firm is also possible. If there are no economies of multiplant operations, then the large firm leads the diffusion because the greater return from adoption of a success dominates. However, if there are such economies and the large firm's resulting learning cost disadvantage dominates, then the small firm leads the diffusion.

   By now there is a large theoretical literature on innovation adoption and diffusion. (1) These studies typically assume that firms are identical, and the exceptions do not focus on differences in the size of the firm. (2) A noteworthy exception is David (1969), who analyzes a capital-embodied new process with lower variable cost but higher fixed cost. He shows that a diffusion occurs if wages rise over time relative to capital costs (notice this is similar to Fellner's (1951) argument that a diffusion occurs as the cost of maintaining a plant with old technology rises over time). Large firms adopt sooner because larger output means larger labor savings. Most empirical studies simply conjecture large firms adopt first because they expect to earn more from adoption. For example, Davies (1979) assumes a firm adopts if the expected time to pay off the adoption cost is less than a critical pay-off period. Thus, large firms adopt sooner because their higher profits allow them to pay off the adoption cost sooner. More recently, Ghemawat (1993) shows that large firms are first adopters of new processes with large enough minimum optimal scales, but small firms are first adopters of new processes with low enough minimum optimal scales. The analysis herein differs in that a large firm may be the first adopter of a new technology with a zero minimum optimal scale.

   The results of the analysis also contribute to the literature on multiplant firms. The most closely related studies are those that analyze exit in industries where demand and profit are steadily declining over time and find that small firm size is an advantage in this environment. Ghemawat and Nalebuff (1985) show that, given capacity constraints such that firms must produce at a fixed capacity or shut down, a large firm exits before a small firm. When firms have different numbers of equal-sized plants, Whinston (1988) shows that the largest firms shut down plants first. The analysis herein is complementary because it focuses on a case where profit increases, in expectation, but a firm must shut down a plant to adopt initially. Because the large firm adopts first if there are no economies of multiplant operation, this analysis indicates that the results of these exit studies might differ if they were extended to allow for multiplant economies.

   The next section introduces the two-stage adoption model and discusses the Nash equilibria in the period-two subgames. Section 3 derives initial subgame perfect adoption behavior and the conditions under which each firm leads the diffusion. An algebraic example with linear demand and quadratic cost is also provided. Section 4 concludes and discusses the implications of relaxing several of the key assumptions. Proofs are relegated to an Appendix.

2. A Model of Cost-Reducing Technology

   Consider a two-period model of a duopoly faced with an exogenously developed innovation. The new technology can succeed or fail in that it may or may not reduce marginal cost at all output levels.

   When it appears, each firm's common knowledge estimate of the probability of success is p [member of] [0, 1]. The large firm L has two plants and the small firm S has one plant. The innovation is adopted by converting a plant to the new technology. That is, the innovation must be a new machine, technique, or process that can be grafted onto existing plants. Conversion at any date is instantaneous and costless, but the first adoption by either firm does not immediately reveal if the innovation succeeds or fails. After...