A Model of the Linked Adoption of Complementary Technologies

Margaret H. Smith
Department of Economics
Pomona College
Claremont CA 91711
mhwang@pomona.edu
telephone : 909.607.7897
fax : 909.621.8576

Abstract

This paper presents a dynamic feedback model of the technology diffusion process in which each firm’s technology adoption decisions maximize the net present value of its anticipated cash flow, taking into account the direct cost savings, the number of linked firms expected to adopt complementary technologies, and anticipated changes in adoption costs. The adoption of complementary technologies need not be simultaneous, but linked technologies can induce a rapid industrial regime shift without explicit coordination or planning.

Key words: technology diffusion, complementary technologies, innovation

J.E.L. classification: O31, L10

* I am grateful to the editor and referee for their insightful comments and helpful suggestions.

Introduction

An important research question is how technological changes are adopted and diffuse through industries. For technologies that link industries together, the technology-adoption process should be studied not just at the industry level, but at the supply-chain level. For example, when information technologies link upstream manufacturers and downstream retailers, the adoption decisions affect each other’s decisions. Because of this symbiotic relationship, linked technology shifts may occur rapidly without explicit coordination.

Most technology diffusion studies examine single technologies, exploring why and how innovations diffuse across firms within a single industry. These studies variously examine how adoption decisions are affected by firm- and market-specific conditions, rival precedence, learning, ownership structure and other factors (Oster 1982; Hannan and McDowell 1984, 1987; Rose and Joskow 1990; Karshenas and Stoneman, 1993).

While the impact of a buyer’s market power on technology adoption by suppliers has been examined (e.g., Quirmbach 1986), the linkage between the technology adoption decisions of customers and suppliers has not been studied much. Models of information technology adoption that focus on industry characteristics (such as number of previous adopters or market concentration) or firm characteristics (such as size and profitability) miss the crucial fact that technologies that link the supply chain together may create cross-industry complementarities so that the adoption decisions of firms in one industry (e.g., retailers) affect the adoption decisions of firms in another industry (e.g., wholesalers).

Such linkages are, for example, critical in explaining rapid regime shifts in the apparel retail supply chain, where the adoption of the complementary technologies of barcode labels, barcode scanners, and electronic data interchange occurred in lockstep fashion. As retailers began to adopt barcode scanners to speed up the checkout process, suppliers began to adopt barcode labels for their shipped products and move toward electronic means of communicating with and taking orders from their buyers. Explicit coordination in the apparel retail supply chain was not required to induce a rapid regime shift because the initial economic incentives for unilateral adoption subsequently triggered a bandwagon effect on other firms (Hwang and Weil, 2002). As a feedback loop developed, more firms adopted the complementary technologies. The current paper presents a model of this ratchet-up process of the adoption of linked technologies.

In this model, each firm maximizes the net present value of the anticipated cash flow by taking into account the cost savings, adoption of matching technologies by linked firms, and changes in adoption costs. The initial adopters have sufficient incentives even if their customers or suppliers do not yet demand or have not yet adopted matching technologies. After the initial adoptions, the payoff spillovers from technological complementarities create a bandwagon effect.

The traditional complementarities story focuses on a single firm and is not well-suited to explain such an asynchronous industrial regime shift. For example, Milgrom and Roberts (1990, 1995) provide a comparative-statics analysis of manufacturing complementarities. Their model implies that complementarities “make it relatively unprofitable to adopt only one part of the modern manufacturing strategy. The theory suggests that we should not see an extended period of time during which one component of the strategy is in place and the other components have barely begun to be put into place” (1990, p. 524). This argument suggests that, with perfect foresight, cross-firm complementarities will lead to simultaneous all-or-nothing technology adoption. Technology diffusion in my model may well involve asynchronous adoption.

A Model

A manufacturing firm supplying a growing number of retail customers using modern retail practices faces a dynamic investment decision. The firm must weigh the benefits from immediately entering into relationships with modern retailers against the costs of such relations, including anticipated changes in the cost of adopting modern technology. Retail firms must make analogous decisions.

The adoption of complementary technologies by linked firms will reduce the operating costs of both firms. One example is that the adoption of electronic data interchange (EDI) by a clothing retailer will its reduce order processing costs, and will also speed up the frequency and improve the accuracy of demand information received by the suppliers, which reduces the supplier’s order processing costs. A second example is the adoption of barcode scanners by retailers. Barcode scanners speed up the recording of sales and improve the efficiency of check-outs for the retailer, and they also lower the wholesalers’ delivery costs because these retailers can process the received goods more quickly and accurately.

There are many ways to model adoption decisions in which firms maximize profits by waiting to adopt. For example, if a firm expects to expand over time, the present value of the cost savings might be predicted to be larger in the future than they are today. Alternatively, the adoption cost might be predicted to be smaller in the future than today because of technological innovations, increased competition, or economies of scale. A third possibility is that in an uncertain world, there is an option value to waiting to make investments that are costly to reverse (Jensen, 1982; Pindyck, 1988; Dixit, 1989). Even if benefits are not certain to increase and costs are not certain to decline, uncertainty about the dynamic paths of either may be sufficient to warrant postponing the adoption of new technologies.

Here, I will assume that the present values of the cost savings are constant and that adoption costs are declining at known rates. Anticipated changes in the present value of the cost savings can be handled with somewhat more complicated equations; uncertainty about future benefits and costs can be analyzed with dynamic programming. Neither generalization is needed to make the basic point that complementarities can cause an uncoordinated rapid (but not necessarily simultaneous) diffusion of linked technologies.

Consider a group of firms and suppose that the cost for Firm i of adopting a new technology at time T_i is

where ai is the continuously compounded rate of decline of its adoption cost. Ignoring complementarities with other firms, the present value of the cost savings from adopting its new technology at time T_i is a constant amount V_i > 0. If a linked Firm j adopts a technology at time T_j that benefits Firm i, the present value of the benefit to Firm i of Firm j’s adoption is C_i[j] Ž 0 at time max[T_i, T_j], the time when both technologies are in place.

Perfect Foreknowledge

I initially assume perfect foreknowledge, so that each firm anticipates perfectly when other firms will adopt. The net present value for Firm i of adopting its technology at time T_i is

(1)

where the linked firms have been separated into those who adopt before and after T_i.

The effect of delaying adoption is measured by the first derivative of Equation (1):

(2)

The cost of delaying is the postponement of the cost savings; the benefit is the postponement of the adoption cost plus the decline in the adoption cost.

If Firm i adopts immediately, the net present value is

(3)

and the first derivative is

The first derivative is nonpositive if and only if

(4)

If K_i[0] is in fact less than K_i*, then substitution into Equation (3) shows that P_i[0] > 0 and substitution into Equation (2) shows that P'[T_i] < 0 for all values of T_i > 0. Therefore, Firm i should adopt immediately if its current adoption cost is less than the threshold K_i*, since its net present value is positive and will be reduced by delaying adoption.

If Equation (4) does not hold, the first derivative is currently positive and Firm i maximizes present value by adopting when the first derivative given by Equation (2) is equal to zero:

(5)

The adoption cost at the time of adoption is

Thus, Firm i should adopt its new technology as soon as its adoption cost falls to the threshold K_i* given in Equation (4).

No Foreknowledge

So far, I have assumed that each firm has perfect foresight about other firms’ plans. Let’s consider the opposite case. Suppose, that a firm has no foreknowledge: it does not know that another firm will adopt a new technology until it has actually done so. Equation (1) for the perceived value of adopting then becomes

(1a)

since the firm only considers complementary technologies that are already in place (T_j < T_i).

The marginal effect on net present value of delaying adoption is

(2a)

If Firm i adopts its technology immediately, the net present value is

(3a)

and the first derivative is

Using the same reasoning as before, Firm i should adopt immediately if the following condition holds:

(4a)

If Firm i does not adopt immediately, it will maximize present value by adopting when the first derivative given by Equation (2a) is equal to zero:

(5a)

Because they lack foresight, firms do not anticipate each other’s plans. They consequently have a lower threshold for the cost of adoption and adopt later than if they had perfect foreknowledge. In fact, we could even have an impasse where two firms that would adopt simultaneously if they knew of each other plans delay adoption until the adoption cost falls sufficiently to persuade one of the firms that it is worthwhile to adopt even if the other firm does not. Once the first mover adopts, the other firm quickly follows suit.

No Complementarities

If the new technologies are not complementary, then C_i[j] = 0 and Equation (4), the condition for immediate adoption, becomes

(4b)

If Firm i does not adopt immediately, the adoption time given by Equation [5] becomes

(4a)

As with the case of no foresight, firms have a lower threshold for the cost of adoption and adopt later if there are no complementarities. The firm’s time to adoption can be substantially higher than when there are complementarities.

Illustrative Calculations

This model can be parameterized to provide numerical examples. I will show the equations for wholesalers; the retailer equations have the same structure, with possibly different parameter values. There are n wholesale firms with the initial cost of adopting the technology uniformly distributed between minK and maxK:

The present value of the annual cost saving without complementarities is set to give adoption times (in the absence of complementarities) that are uniformly distributed from minT to maxT:

Solving Equation (5b) for V_i:

The complementary benefit to wholesale firm i from retail firm j’s adoption of a new technology will be described by this equation,

(6)

where the summation is over the retail firms whose technologies benefit wholesale Firm i. This parameterization assumes that each wholesaler’s cost savings will be increased by 100g percent if all linked retailers adopt the complementary technology, and that each retailer’s contribution to the wholesaler’s cost savings is proportional to that retailer’s own cost savings relative to all linked retailers’ own cost savings.

Suppose for example, that the present value to wholesale Firm i of adopting its new technology is V_i = 100, the present value to 10 linked retail firms of adopting their new technologies is V_j = 100, and that the complementary parameter is g = 0.5. The complementary benefit to the wholesale firm of any single retailer’s adoption is 5:

If all 10 linked retailers adopt the complementary technology, the complementary benefit to the wholesale firm is 50.

The baseline case uses the parameter values shown in Table 1. As in the apparel industry, a small number of large retailers (with large adoption costs) buy products from a large number of small wholesalers (with smaller adoption costs). For convenience, the other parameters are the same for wholesalers and retailers. The same results would apply in an industry in which a large number of small retailers (with small adoption costs) buy products from a small number of large wholesalers (with larger adoption costs): simply exchange the wholesale and retail labels.

Figure 1 shows the time profile of the wholesaler and retailer adoptions. Table 2 shows the number of years for half of the firms and all of the firms to adopt. As shown, even though there is no explicit coordination between wholesalers and retailers, adoption times are reduced substantially by the complementarities that link technologies.

For a sensitivity analysis, we can make ceteris paribus changes in the parameter values while maintaining the baseline distributions across firms of initial technology costs K_i[0] and own cost savings V_i. Thus, except for the parameter changes, the adoption times (in the absence of complementarities) are still uniformly distributed from minT to maxT. The results in Table 2 are sensible. The anticipation of a faster rate of decline a in the cost of technology delays adoption by making it more appealing to wait for the lower cost. A higher discount rate r speeds up adoption because the present cost savings are more valuable relative to the lower cost realized by delaying adoption. Larger complementarities g increase the benefits from adopting and thereby induce faster adoption.

Implications

This paper presents a theoretical model of a ratchet-up process of technology adoption where linked technologies induce a rapid regime shift without explicit coordination or planning. A feedback loop that stimulates a ratchet-up effect encourages advances on the manufacturing side when retailers adopt new technologies, and vice versa. In contrast, if retailers were not adopting better technologies, manufacturers would have less incentive to adopt better manufacturing techniques. The ratchet-up effect also implies that firms will sort partners over time as manufacturing firms with more information technologies match up with retailers who are also using more information technologies and thus demanding more rapid replenishment of their orders.

If all firms in an industry were identical and equally well informed, they would all adopt simultaneously. Heterogeneous firms will adopt at different times. The potential cost savings are a function of many factors, some unique to a firm and some common to many firms. The unique factors include the firm’s size, product variety, product mix, and the usage of other complementary technologies. The common factors include the number of customers that have adopted the matching technology and the prices of complementary goods and services. The cost savings are expected to be larger for large firms with greater product variety that use more complementary technologies. Larger firm size implies that new technologies will affect a larger set of products and that there will be larger economies of scale and scope and lower average fixed costs for a given technology adoption. Two potential sources of cost savings are lower stockouts and lower markdowns. Cost savings are also expected to be greater if more firms in the matching downstream or upstream industry have adopted matching technologies and if the prices for complementary goods and services fall.

The first movers adopt first because their cost savings from adopting are sufficiently high, even when no firms in the matching downstream or upstream industry have adopted. For other firms, the cost savings are not high enough until firms in the matching industry have adopted, increasing the cost savings and reducing the adoption threshold in Equation (4). This generates a pattern of more and more firms adopting as the ratchet-up effect kicks in with complementary technologies reducing cost thresholds.

Perfect foresight speeds adoption. Although there are advantages to disclosing plans to linked firms, there are disadvantages to disclosing plans to competitors. One way to have perfect foresight is for wholesale and retail firms to be vertically integrated. Another avenue would be government policies that encourage coordination between wholesalers and retailers. Government subsidies or tax credits can also be used to break impasses where firms delay adoption until other firms adopt.

References

Dixit, Avinash (1989). “Entry and Exit Decisions under Uncertainty.” Journal of Political Economy 97: 620-638.

Hannan, Timothy, and John M. McDowell (1987). “Rival Precedence and the Dynamics of Technology Adoption: An Empirical Analysis,” Economica 54: 155-171.

Hwang, Margaret, and David Weil (2002). “Ratcheting Up: Linked Technologies Induce Rapid Regime Shift,” Working paper.

Jensen, Richard “Adoption and Diffusion of an Innovation of Uncertain Profitability.” Journal of Economic Theory 27 (1982): 182-193.

Karshenas, Massoud, and Paul L. Stoneman (1993). “Rank, Stock, Order, and Epidemic Effects in the Diffusion of New Process Technologies,” Rand Journal of Economics 24: 503-528.

Milgrom, Paul and John Roberts (1990). “The Economics of Modern Manufacturing,” American Economic Review, 80: 511-528.

Milgrom, Paul, and John Roberts (1995). “Complementarities and Fit: Strategy, Structure, and Organizational Change in Manufacturing,” Journal of Accounting and Economics 19: 179-208.

Oster, Sharon (1982). “The Diffusion of Innovation Among Steel Firms,” Bell Journal of Economics 13: 45- 56.

Quirmbach, Herman C. (1986). “The Diffusion of New Technology and the Market For an Innovation,” Rand Journal of Economics 17: 33-47.

Pindyck, Robert S. (1988). “Irreversible Investment, Capacity Choice, and the Value of the Firm.” American Economic Review 78: 969-985.

Rose, Nancy L., and Paul L. Joskow (1990). “The Diffusion of New Technologies: Evidence from the Electric Utility Industry,” Rand Journal of Economics 21:354-373.

Table 1 Baseline Numerical Parameters

Table 2 Number of Years for Half and All of the Firms to Adopt

Figure 1 Adoption Times