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An efficiency explanation for why firms second source.

Firms facing research costs and demand uncertainty may engage in second-sourcing, in which potential suppliers agree to pool production facilities. I show how sellers and buyers both can benefit from the practice. Second-sourcing allows firms to meet a wider range of possible rates of demand and often to supply a given rate of demand at a lower total cost than under non-cooperation. Buyers benefit through a reduced probability of stock-outs and frequently a lower purchase price. Semiconductor industry data are found to be consistent with the paper's predictions.

I. INTRODUCTION

The practice of second-sourcing is frequently observed among firms facing technological and demand uncertainty. Second-sourcing encompasses agreements between buyers and sellers requiring that a firm license its proprietary technology to rivals, as well as agreements among potential suppliers to pool production facilities. The first type of agreement is often explained as guaranteeing buyers "a secure supply at a fair price." In this type of second-sourcing agreement, control over production and pricing decisions resides with each supplier. The second arrangement, where the owner of the production technology controls production and pricing, has largely been overlooked by the literature despite its adoption by firms in a wide range of technologically dynamic industries, including semiconductors, robotics and biotechnology. A primary motivation for this second form of secondsourcing, I will argue, is to achieve a more efficient matching between the industry's productive capacity and market demand. This paper indicates how second-sourcing of this form may benefit both purchasers and suppliers and identifies the conditions making second-sourcing profitable for firms.

The existing literature has offered two explanations for second-sourcing. According to the first explanation, second-sourcing is sought by prospective buyers. Purchasers may require that a developer license alternative suppliers to force revelation of private cost information in the contract bidding process, or to discipline the eventual supplier(s)' pricing behavior. Examples of this line of reasoning are found in Riordan and Sappington [1989], Anton and Yao [1987], Demski, Sappington and Spiller [1987], and Rob [1986]. If this motivation is correct, however, it is sufficient for firms to compete at the contract bidding stage (Demsetz [1968]). In contrast, we often observe competition at the production stage with active second-sourcing, and a large number of licensed alternative suppliers in a single industry (see section V). This explanation's exclusive focus on the gains to buyers from second-sourcing also is inconsistent with Swann's [1987] observation that "many manufacturers ... have actually sought second sources."

The literature's alternative explanation suggests that second-sourcing may be preferred by producers. Farrell and Gallini [1988] and Shepard [1987] show how a monopoly supplier can use second-sourcing as a commitment not to raise price or lower product quality in the future, either of which would debase the value of sunk investments made by prospective purchasers. If credible, this commitment may stimulate industry demand sufficiently to yield higher profits for the former monopolist, despite increased product market competition. An important shortcoming of this second explanation is its apparent incongruity with the existence of five, six or more second-sourced suppliers in a single industry. Shepard [1987], for example, shows that a single licensed alternate supplier will provide the monopolist with its desired credible commitment to future price and quality.

This paper suggests an alternative explanation that is consistent with observed trends in second-sourcing. I depart from the existing literature's focus upon principal-agent problems to analyze secondsourcing in a market flamework. The paper indicates why sellers may secondsource voluntarily, explains why multiple second-sources will be preferred, and shows how both sides in the agreement may benefit.

The argument may be summarized briefly as follows. Consider an industry operating in an environment requiring extensive research and development facing demand uncertainty. Each firm's decision about how much to invest in research and production inputs (plant capacity) will depend upon its expectation of the probability of winning the development race, and upon its expectation of future downstream demand. Acting independently, firms will "over-invest" in research because of the usual common pool problem. Additionally, under plausible expectational and cost assumptions, the firm that wins the development race will have insufficient internal production capacity to satisfy expected demand. Conversely, losing firms will be left with idle production capacity. Under a variety of cost and demand conditions to be specified, each firm can expect to earn higher profits if producers agree collectively and in advance to second-source unsatisfied demand using production facilities of the losers from the development race. Second-sourcing allows firms to ignore firm-specific development risk and to operate with greater flexibility under non-diversifiable industry demand uncertainty. With secondsourcing, the firm winning the development race is able to meet a wider range of possible demands with a lower average level of excess capacity, a lower average level of excess demand and, as result, frequently a lower average cost of production. Second-sourcing also may alleviate the common pool problem in research patent races. Finally, the benefits of this more efficient form of industry organization will accrue, at least in part, to buyers in the form of a reduced incidence of stock-outs and frequently a lower average cost for their purchases.

The paper is organized as follows. Section II presents a relatively simple model of competition under technological and demand uncertainty to serve as a framework for analysis. Firms' research and development and capacity investment decisions under non-cooperation are discussed in section III. Section IV outlines firms' decisions in the presence of secondsourcing agreements and identifies the conditions under which firms will tend to find second-sourcing profitable. Section V provides an application of the theory to the semiconductor industry. In section VI, I identify the benefits received by purchasers from second-sourcing and contrast their relative importance with the opportunism argument stressed in the existing literature. Section VII briefly considers several alternatives to second-sourcing: joint research ventures, separation of firms' design and production activities, and horizontal merger. Finally, section VIII contains some concluding remarks.

II. THE MODEL

In this section, I describe a relatively simple model of competition focusing on product development and demand uncertainty. The appendix provides the formal statement of the model and details of its solution. I confine the text's discussion to the central issues. Competition occurs in three separate stages in the stylized model: research, capacity acquisition and production. The model's timing is summarized in Figure 1. Suppose that a group of downstream producers require a certain input and they find it more efficient to contract out its development and production than to perform these activities inhouse. The number of (identical) potential suppliers for this factor of production, n, is taken as given throughout the analysis.

In period one, upstream firms compete in a race to develop the product and its production technology. As in Lee and Wilde [1980], firms will invest at a constant rate xi during the research stage until a discovery is made by one firm in the industry. Firms' probability of winning the development race and their total expected research investment are functions of their own and their (n-1) competitors' research spending (see the appendix).

In period two, prior to knowing the outcome of the development race, firms select a stock ki of an essential production input in anticipation of the subsequent production stage.[1] This essential input might be special production facilities, specially trained production workers, or some other key intermediate input. For concreteness, I will refer to it as "plant capacity" to underscore the fact that the input's stock places an upper bound on the upstream firm's output rate. I will assume that the winning firm must rely solely upon its own period-two capacity investments. The opportunity to renovate capacity from earlier product cycles is ruled out. This assumption is most reasonable in industries such as semiconductors, robotics, and biotechnology where product innovations are accompanied by substantial changes in firms' manufacturing technologies and production facilities. The firm also is assumed unable to supplement its capacity after the pre-production stage through additional investment or purchases of rivals' capacity in the spot market in the absence of second-sourcing agreements.

The implication of these assumptions is that firms will base their capacity investment decision on two variables: the probability of their winning the development race and their expectation of demand by downstream buyers. This implication, and the paper's qualitative conclusions, would remain robust if these simplifying assumptions about capacity acquisition were relaxed. Provided that firms find it profitable to pre-commit to some capacity investments in the current product cycle, or provided that firms cannot reach their desired level of capacity through exclusive reliance upon spot markets, second-sourcing will offer suppliers the advantages to be discussed below.[2]

Uncertainty surrounding industry demand when firms make their research and capacity investment decisions is introduced in a relatively simple manner. Following Sharkey [1977], I assume that there are an uncertain number of potential buyers, each willing to purchase one unit of the input at a price not exceeding r dollars. I will denote the actual number of buyers (units sold) by q, where q is distributed uniformly over the interval [b,B]. Again, as Sharkey [1977] indicates, this simplifying assumption may be relaxed without

significant consequence.

The third and final stage of competition, the production era, begins once one firm is successful in the development race. Only the patent winner will advance to the production stage in period three. The winning firm is assumed able to protect its property rights fully, either by keeping the innovation secret or through patent protection. Alternatively, reverse-engineering or inventing around a patent may be prohibitively costly, either in terms of financial resources or delay costs. This strong assumption of private research results highlights the fact that even if innovations are fully appropriable, firms may wish to second-source production. Thus, I demonstrate that others' reliance upon incomplete appropriability of research results to explain second-sourcing is unnecessary (eg. Swann [1987], Rosenblum [1985]).[3] Realized industry demand q also becomes known in the third period, and the firm that won the development race chooses its rate of production.4 While the winning firm acts as a monopoly supplier in this period, its output rate is potentially constrained by its installed capacity ki.

Finally, firms' production stage costs are assumed to have three components: fixed, variable and avoidable costs. A firm's fixed costs in the production stage arise from building plant capacity and are given by a linear function of its capacity (k.sub.i): F =f+ [gk.sub.i]. Variable costs are given by a constant marginal cost of production equal to c. Avoidable costs are those incurred only when a plant is active. These setup costs are a function solely of the firm's capacity and may be avoided by shutting down production altogether. The firm's avoidable cost is [hk.sub.i]., and this establishes a minimum scale of production activity given by [hk.sub.i]/(r-c).[5] The firm's total costs are thus {(f+[gk.sub..i] + cq + [hk.sub.i]} when q [equal to or less than] hki/(r-c) and simply (f+[gk.sub.i]) when realized demand falls below the firm's minimum requirements.[6]

III. A BENCHMARK: NON-COOPERATION

To provide a benchmark for comparison, this section considers firms' research and capacity investment choices under the assumption of non-cooperative behavior throughout the product cycle. In choosing its optimal output and research and capacity investments, the firm solves a threestage maximization problem in reverse order. In period three, the winning firm will select its output rate to maximize profits subject to its capacity constraint. Given the structure of the firm's costs and industry demand, the monopoly supplier will produce either zero, q or ki units. In the pre-production stage, firms will act as Cournot-Nash competitors.

In period two, each potential supplier selects a capacity level [k.sub.i] to maximize its expected profits, given its research investment choice xi in period one. Because firms are assumed identical, each will select the same research budget, and therefore the probability of any firm winning the development race will be exactly (1/n). Each firm's expected profit function in period two, therefore, will be a function only of its capacity choice (see equation (A.6)). The [i.sup.th] firm's optimal capacity choice in the non-cooperative equilibrium, ki, is found by maximizing this expected profit function, yielding

[THIS FORMULA HAS BEEN OMITTED]

In the absence of second-sourcing agreements, the firm's internal capacity also will equal total industry capacity K.

The result in (1) A implies that the firm's optimal capacity [k.sub.i] will be less than the maximum rate of industry demand B, unless the marginal costs of building and operating capacity are both zero (g=h=O). Thus, in general firms will find it optimal to choose a capacity that may leave some demand unsatisfied. The firm incurs a risk of not being able to recoup fully its fixed capacity costs should it lose the development race or should downstream demand be lower than expected. The firm weighs this cost against the opportunity cost of having insufficient internal capacity to satisfy downstream demand should it win the patent race. Under non-cooperation, this calculus leads the firm to select a capacity level that precludes production at the profit-maximizing rate in high demand states (q> [K.sub.i]).7 Equation (1) also indicates that the expected fraction of demand that will be left unsatisfied by the winning firm depends positively upon the marginal cost of building capacity (g), the marginal capacity use charge (h), the number of potential suppliers (n) and the extent of industry demand uncertainty[8] and is inversely related to the product's markup over variable costs (r-c).

In period one, firms select research budgets by maximizing their expected profit function (A.5) under the assumption that capacity is chosen optimally in the subsequent period. Equation (A.8) defines the implicit solution to this maximization problem. An important implication is that firms will find it optimal to operate in a region of decreasing returns from research in the non-cooperative equilibrium (see the appendix). The relevant concern in a firm's research investment decision is the impact of research and development outlays on its average probability of winning the patent race. At the industry level, by contrast, the value of research expenditures is measured by their impact on firms' marginal probabilities of success. This divergence between private and social productivities of research is usually termed the common pool problem. Lee and Wilde [1980] show that in this general class of models, unrestricted entry into the industry will lead to too many researching firms, too much aggregate research investment and premature discovery of the innovation on average, relative to the cooperative solution. In contrast to firms' plant capacity decisions, then, excessive resources are devoted to research and development from the industry-wide standpoint,

IV. THE SECOND-SOURCING OPTION

Firms' research and capacity investment decisions are altered by secondsourcing opportunities in ways which reduce resource waste. Cooperation will be limited to the production stage, with firms continuing to make independent research and capacity choices in periods one and two? Under the terms of firms' secondsourcing agreements, the firm that wins the development race is able to rent former competitors' idle capacity at a pre-arranged price should realized demand exceed its internal plant capacity. Firms will enter into second-sourcing agreements with each competitor prior to the start of the product cycle, allowing them to adjust optimally their individual research and capacity investments in periods one and two in anticipation of second-sourcing opportunities at the production stage. (Section V provides empirical support for this timing assumption for the semiconductor industry.) This provides two direct benefits to potential suppliers.

First, firms' ability to rent or lease capacity in period three will allow them to ignore the effects of firm-specific research risk when selecting their optimal plant capacities.[10] Under the second-sourcing arrangement, firms losing the research race will recover some portion of their sunk investments by leasing idle capacity when the winner has insufficient internal capacity. This reduces the cost to losers of holding idle capacity. The winning firm also avoids the cost of firm-specific research risk with second-sourcing by facing a lower opportunity cost of having insufficient internal capacity at the production stage.

Second, second-sourcing will allow firms to operate with greater flexibility under demand uncertainty. Under secondsourcing, firms each select a smaller optimal plant size but, in many cases, the net effect is to increase aggregate capacity available for production in the industry because the winner has access to former competitors' plant facilities. The reduction in individual plant size allows the winning firm to match more closely realized demand with available internal and second-sourced capacity. The increase in aggregate capacity allows this firm to satisfy a larger range of potential rates of demand.

As in the non-cooperative equilibrium, firms will solve their three-stage profitmaximization problem recursively. In period three, the patent holder will select its profit-maximizing rate of output q which is bounded now by aggregate industry capacity K, not the firm's internal capacity ki. The firm will exhaust first its own plant's capacity and then meet residual demand with second-sourced capacity. In period two, each firm selects its capacity investment to maximize expected profits, given its research investment choice in period one. As in section III, the fact that firms are identical implies that each has probability (1/n) of winning the patent race. Thus, as before, the firm's expected profits in period two are solely a function of its capacity choice ki. The firm's expected profit function is given in equations (A.9) and (A.10).

The/th firm's optimal capacity choice under second-sourcing, kL is found by maximizing its expected profits, yielding Total industry capacity available for use by the patent holder is n-times each firm's individual capacity, or

[THIS FORMULA HAS BEEN OMITTED]

Comparing (1) and (2) indicates that optimal firm-level capacity decreases when firms agree to second-source (see equations (A.13) and (A.14) in the appendix). Second-sourcing reduces both the winning firm's opportunity cost of having insufficient internal capacity in the production stage, and lowers the losing firms' opportunity cost of holding idle capacity after the development race. The appendix explains that we may focus upon the first effect when considering the impact of second-sourcing on firms' capacity choices. That the winning firm now can acquire additional capacity in period three thus leads it to select a smaller optimal plant size in the pre-production stage.

The absolute reduction in firm-level capacity from second-sourcing will be larger the more firms there are in the industry, the greater is the demand uncertainty faced by firms,[11] and the higher is the marginal capacity building cost in period two. Intuitively, each of these factors increases the incentive of firms to rely on second-sourced rather than internal capacity. Further, the reduction in firm-level capacity will be greatest in cases of low product markups over variable costs and relatively high avoidable plant operating costs. Both factors lower the opportunity cost of having insufficient internal capacity in the production stage relative to the opportunity cost of having idle excess capacity.

The reduction in individual plant size under second-sourcing allows the winning firm to meet a given rate of industry demand with a lower average level of excess capacity and a lower average level of excess demand (see also Sharkey [1977]). By making the firm's plant capacity more finely divisible, second-sourcing allows the patent holder to match more closely available capacity and realized demand. The firm's increased flexibility in accommodating uncertain demand represents an increase in the efficiency of its operation.

Total industry capacity available for production may rise or fall under secondsourcing. Aggregate available capacity is given by equation (1) in the non-cooperative equilibrium and by equation (3) with second-sourcing. The ability of the winning firm to employ otherwise idle capacity from its competitors tends to increase aggregate capacity available for production. The reduction in each firm's capacity, however, tends to offset this. Equations (A.15) and (A.16) reveal that a necessary and sufficient condition for second-sourcing to increase aggregate installed capacit is that

2h < (r-c).

Thus, aggregate capacity rises in cases of relatively low marginal capacity-use fees and relatively high markups over variable costs. This result coincides with the earlier observation that these conditions will be associated with only a modest reduction in firm-level capacity investment. Comparative statics also show that if aggregate capacity does rise under second-sourcing, the increase will be largest when there are relatively few firms in the industry, when the marginal capacity-building cost is relatively low, and when there is relatively little demand uncertainty. If total industry capacity does rise under second-sourcing, the winning firm will find itself able to accommodate a wider range of potential rates of demand. This is the second benefit to suppliers from second-sourcing.

Next, consider the impact of secondsourcing on firms' expected profits, given by equations (A.6) and (A.10) evaluated at the optimal firm and industry level capacities in the two equilibria. The impact of industry demand uncertainty and firms' plant construction costs on the relative profitability of second-sourcing is non-linear. At one extreme, if there is very little demand uncertainty and if capacity building costs are negligible, there is clearly little to be gained from cooperation. At the other extreme, if demand is highly variable and if capacity commitment costs are very high, the dampening firm-level effect on capacity will be so acute as to virtually eliminate the second|sourcing incentive. An "intermediate" level of demand uncertainty and "moderate" marginal capacity commitment cost are conducive to secondsourcing. Several specific implications can be drawn.

First, in the special case in which firms face no plant setup cost, expected profits rise unambiguously with second-sourcing. When avoidable costs are zero, there is no minimum efficient scale of operations. Hence, there is no penalty for operating many small plants instead of a smaller number of large plants. Moreover, in this situation it can be shown that with the second-sourcing option firms will scale back their internal capacity investments at a rate that leaves aggregate capacity available for production exactly the same in the two equilibria. The source of the increase in firms' expected profits in this case therefore lies entirely in savings on capacity building costs. A similar argument applies to situations in which the marginal capacity-use charge is small relative to the product's markup over variable costs and the marginal cost of building capacity. The theory therefore predicts that second-sourcing will be relatively attractive to firms in industries with low avoidable costs or, equivalently, with small minimum efficient scales of operation.

Second, and more generally, firms' expected profits will increase under secondsourcing in those cases where aggregate capacity available for production increases. The intuition is as follows. Industry-wide capacity will increase whenever individual firms' capacities decline by less than n percent. The benefit to firms from second-sourcing in these cases comes not from savings on plant investment (holding constant total industry capacity), but rather from the increase in aggregate capacity that allows the winning firm to satisfy a wider range of possible demands. Increases in firms' expected profits under second-sourcing thus will be positively correlated with increases in available industry capacity. The conditions under which this latter result will occur were noted in equation (4): a high markup over variable costs relative to the marginal capacity-use charge. Furthermore, also as noted earlier, if aggregate capacity does rise, the increase will be largest when there are few firms in the industry, when the marginal capacity-building cost is relatively low, and when there is relatively little demand uncertainty. In these cases, second-sourcing will tend to be relatively more profitable than non-cooperation.

The expected profitability of secondsourcing depends also upon firms' ability to enforce the terms of their cooperative agreement. As in any cooperative agreement among potential competitors, there exists the possibility of opportunistic behavior after the second-sourcing agreement is negotiated. Second-source suppliers could debase the patent holder's reputational stock by lowering product quality, and firms on either side could force renegotiation of the pre-agreed capacity rental price. If third-party enforcement of the agreement is prohibitively costly or untimely, firms must rely upon self-enforcement through market mechanisms. Telser [1987] derives sufficient conditions for a self-enforcing agreement by comparing firms' expected profit streams with continued cooperation and with chiseling. An important implication of that analysis is that we are more likely to observe stable, on-going second-sourcing agreements in industries where the same firms compete over time in successive product cycles.

Finally, consider firms' research investment decisions. The optimality condition, given by equation (A.12) in the appendix, is identical in form to that in section III defining the firm's optimal research choice under the assumption of non-cooperation throughout the product cycle. Firms' research choices in the two equilibria, therefore, will differ only if the expected gain from being first in the development race differs. Intuitively, it can be shown that if second-sourcing is individually more profitable for firms than non-cooperation in the production stage, and if firms therefore adopt this contractual arrangement, then each will unambiguously devote greater resources to the development race in the second-sourcing equilibrium.[12] The result of this increased research activity will be an earlier expected discovery date for the innovation.

An important question to ask is whether the increased pace of research activity with second-sourcing alleviates or aggravates the industry's common pool. The existence of a common pool problem in the non-cooperative equilibrium depended upon the winning firm's ability to appropriate fully the profit attributable to its innovation. This requires the winning firm to protect its exclusive control over the innovation's use and an ability to perfectly price discriminate in the output market. The current model's assumptions ensure that both of these requirements are satisfied in both the non-cooperative and second-sourcing equilibria. This implies that second-sourcing will aggravate the common pool problem. The cost of this social inefficiency must be subtracted from any efficiency gains that secondsourcing creates by realigning firms' capacity and output choices.

By contrast, if the winning firm were unable to appropriate fully the social value of its patent, the Nash equilibrium could be characterized by under-researching relative to the social optimum. In this case, by promoting greater research effort, second-sourcing could move firms closer to the social optimum. Which of these outcomes is the more likely in any given industry could be established by empirical evidence on the ability of firms to keep secret their research discoveries, the cost to competitors of reverse-engineering or inventing around a patent, and the ability of patent holders to discriminate among customer groups.

Levin et al. [1987, 809-10] report that in a wide range of research-intensive industries firms' success in protecting the secrecy of their product and process innovations is transitory. They report also that imitating firms' costs of duplicating an innovation most typically are 25 to 50 percent less than the innovator's development cost. Finally, the firm's ability to perfectly price discriminate is limited by the costs of acquiring complete information about individual demand schedules, avoiding antitrust scrutiny, and preventing substitution or resale. Together, these imply that an innovator is unlikely to capture the full social value of its patent in the non-cooperative equilibrium, which may lead to under-researching. If secondsourcing raises the expected profitability of downstream production, the resulting increase in firms' research investments may, over some range, move total industry research expenditures closer to the socially efficient level.

V. AN APPLICATION OF THE THEORY TO SEMICONDUCTORS

The theory's empirical relevance is illustrated well in the semiconductor industry. Advances in semiconductor product designs are linked to significant changes in firms' production techniques and, importantly, in the production environment. Semiconductors are manufactured in facilities known as clean rooms with stringent environmental standards designed to reduce damage to the silicon wafers from contaminants in the air or chemical solutions used in the production process. Advances in product design are tied closely to improvements in plant environment: shrinking integrated circuitry has been made possible only by corresponding improvements in plant environmental control. Semiconductor producers typically have found construction of new clean room facilities with more stringent filtration and purification systems to be less costly than conversion of plants used in earlier chip generations.

Consistent with the model's timing assumptions, firms usually begin construction of new plant capacity before the outcome of the patent race is known. Firms' pre-investment in production capacity is explained by the sizable financial costs associated with production delays, the industry's short product cycle, and the relative ease of installing the actual production equipment after plant capacity is built. A consequence of this timing is that firms make plant capacity investments based on their expected probability of winning the patent race and on their expectation of downstream demand. Because of the costs imposed by research uncertainty and the low salvage value of their plant investments should they not be successful at the research stage, microprocessor producers often have found themselves with insufficient internal capacity to satisfy downstream demand.[13]

Idle capacity held by firms that lost the development race is typically the cheapest and most readily available source of additional production capacity for the winner. Under the terms of a second-sourcing agreement, the patent holder supplies duplicates of the design templates or "photo masks" to other firms (Swann [1987]). The original developer and its second-sources then jointly produce under the developer's trademark for the downstream market. Consistent with the model's timing assumptions, second| sourcing agreements typically are made prior to the completion of the product development stage. Some agreements span several product generations and are entered into by firms prior to the start of research activity (for examples, see Haklisch [1986, 60-63]). More detailed discussions of the operation of second-sourcing agreements in the semiconductor industry can be found in Swann [1987; 1986; 1985], Haklisch [1986], United Nations Centre on Transnational Corporations [1986)] and Rosenblum [1985].[14]

Between 1974 and 1985, second-sourcing increased rapidly among semiconductor producers. Tables I and II summarize trends in the industry. During this period, the number of companies producing only their own integrated circuit designs fell by one-half, while the number of firms acting as second-sources either exclusively or for some chip designs rose more than tenfold. The number of second-sourced products also has risen much faster than the number of sole-sourced designs. For example, between 1974 and 1982, the number of second-sourced chips rose by a factor of forty while the number of singlesourced designs increased only one-tenth as quickly. The proportion of original designs with second-sources has risen from one-quarter to three-quarters over the twelve-year period. The average number of second-sources per chip design also has risen steadily, from one in 1974 to 3.6 in 1985.

These trends are consistent with the theory's predictions about when secondsourcing will be relatively more profitable. First, the period 1975 to 1980 was characterized by significant merger and acquisition activity in the U.S. semiconductor industry, and the rate of new entry declined substantially.[15] Both factors contributed to a significant reduction in the number of major integrated circuit producers, which the theory predicts should make second-sourcing more attractive to firms. The largest increase in second-sourcing activity in fact took place during the period 1975-1980.

Second, the theory predicts that the (expected) profitability of second-sourcing will be positively related to the size of the product's markup over variable costs. During the period 1974-1985, the semiconductor industry's average gross markup rate (the value of industry shipments minus material costs and total employee compensation divided by shipments value) rose fairly monotonically from 30 percent to 38 percent.[16] Again, this coincided with a continual increase in secondsourcing activity.

Third, if one breaks down the data in Tables I and II more finely, one finds that 8-bit and 16-bit microprocessors have been second-sourced much more frequently and extensively than were the earlier 4-bit generation of integrated circuits (Swann [1987, 247-49]). The 4-bit generation was produced primarily for use by a small number of original equipment manufacturers. By contrast, the market for 8- and 16-bit microprocessors was characterized by a large number of original equipment manufacturers, each purchasing smaller quantities. Other factors held constant, a reduction in average customer size coupled with an increase in the number of customers will reduce the aggregate demand variability faced by a supplying firm. The theory predicts that this will tend to increase the profitability of second-sourcing. Again, this change in the composition of demand during the late 1970s coincided with the observed increase in second-sourcing activity.

Finally, section IV indicated that a second-sourcing agreement is more likely to be self-enforcing if the same firms remain in the industry over several product cycles. Lazlo [1985, 14-15] indicates that the identity of the major American and Japanese semiconductor producers remained extremely stable during the 1970s and early 1980s. Haklisch [1986] also identifies a large number of multi-year and multiproduct-generation second-sourcing agreements. Firms frequently also have entered into reciprocal second-sourcing agreements for patented chip designs requiring different production technologies. Haklisch [1986] and Suby [1985] cite agreements between AMI and Mostek, Mostek and Advanced Micro Devices, and Intel and Advanced Micro Devices as examples of reciprocal agreements. Both multi-year and reciprocal second-sourcing agreements are conducive to self-enforcement as required for stability.

VI. SECOND-SOURCING FROM THE STANDPOINT OF BUYERS

Section IV established how potential suppliers may benefit from the option to second-source, but what are the benefits to purchasers? The existing literature stresses how second-sourcing might prevent opportunism by a monopoly seller. In contrast, I focus upon two efficiencies stemming from second-sourcing arrangements. First, second-sourcing can reduce the stock-out risk faced by downstream firms. Second, it can lower the average cost of production and, in turn, the market price of the product.

Section III established that in the noncooperative equilibrium firms individually will select plant sizes that fall short of the maximum possible rate of industry demand. Downstream buyers therefore face a stock-out risk in high demand states. This uncertainty imposes a direct cost upon purchasers who either must locate substitute inputs or else fail to satisfy fully their own final demand should a stock-out occur. Section IV identified the conditions under which second-sourcing will increase the industry's total installed production capacity. In those situations, second-sourcing will reduce the fraction of potentially unsatisfied industry demand by supplementing the patent holder's internal capacity.

Second-sourcing also can benefit purchasers by lowering the average cost of producing the good.[17] Whereas secondsourcing's impact on industry aggregate capacity was relevant to the issue of stockouts, the relevant consideration here is how firms can use second-sourcing to match more efficiently individual plants' capacities with realized industry demand. This more efficient matching will translate into a lower average cost of production in most states of demand.

In the non-cooperative equilibrium, the winning firm's average cost of production is[18]

[THIS FORMULA HAS BEEN OMITTED]

Thus, industry average cost decreases up to the firm's capacity constraint. With second-sourcing, the firm's average cost of production is[18]

[THIS FORMULA HAS BEEN OMITTED]

for q [less than or equal to] K* =[nk*.sub.i]. As such, the winning firm will operate each active plant at full capacity before bringing on-line the next plant. At each multiple of [k*.sub.i] in demand, industry average cost jumps by [hk*.sub.i]/q dollars as the firm incurs an additional plant setup cost.

The potential total cost saving with second-sourcing is then given by subtracting (6) from (5) and multiplying through by industry demand q to yield

[THIS FORMULA HAS BEEN OMITTED]

The first term in (7) corresponds to the industry's potential savings in plant construction and setup costs and is unambiguously positive (see equation (A.14)). Recalling section IV's results, this term will tend to be larger the more firms there are in the industry, the greater is the demand uncertainty faced by firms, the higher are the marginal capacity building and avoidable plant costs, and the smaller is the product's markup over its variable costs. Acting against the reduction in total industry supply cost is the second term in (7), the cost penalty associated with operating multiple plants of smaller scale. If individual plant size exceeds realized industry demand in the second-sourcing equilibrium, that is q < [k.sub.i], the second term in (7) disappears. In this situation, the patent holder will satisfy all demand internally, and it will do so at a lower average cost than it could have in the non-cooperative equilibrium. Although it acts as a monopolist and does not second-source production, the firm has economized on capacity acquisition and avoidable plant setup expenditures, leading to a lower average cost.

When realized demand exceeds individual plant size, q > [k.sub.i], average production costs will be lower with second-sourcing provided that the reduction in plant size when moving from the non-cooperative equilibrium, (k^.sub.i] -[k*.sub.i)], does not fall below a critical value, Bh/(g+h). [19] Intuitively, with a large number of relatively small plants at its disposal, the winning firm will be able to match realized demand more efficiently with on-stream capacities. A larger number of small plants, in lieu of a single large plant, will be able to meet the range of possible demands with a lower average level of excess capacity, a lower average level of excess demand and, therefore, most frequently at a lower average cost of production. Under most specifications of industry demand, this lower average cost will yield a lower average purchase price for buyers.

The existing literature has focused on preclusion of post-contractual opportunism by a monopoly seller as the source of purchasers' (or sellers') benefit from second-sourcing. Earlier, it was argued that opportunism could be overcome either by ensuring competition at the contract bidding stage prior to production or, as in Shepard [1987], with a single licensed alternate supplier.[20] For at least the semiconductor industry, this opportunism explanation appears inconsistent with the evidence. Table II indicates that since 1980 most microprocessor designs have had three or more second-sourced producers. In many cases, the number of secondsources has been significantly higher. For example, Intel's 8086, Motorola's 6800 and Zilog's Z8000 and Z80 microprocessors all had five licensed second-sources. Motorola's 6802 and 68000 chips each had six alternative licensed suppliers, and Intel's 8080 microprocessor had eight licensed second-sources.[21] Table II also indicates that the average number of second-sources per design has risen steadily over time.

This multiplicity of second-sources would be redundant if purchasers sought only to avoid post-contractual opportunism. Moreover, if as Farrell and Gallini [1988] and Shepard [1987] argue, it is the monopoly developer who seeks the commitment against opportunism, the excessive product market competition created by redundant second-sources will be costly to firms. By contrast, the explanation offered here focuses upon the advantage of flexibility in meeting varying rates of demand afforded by establishing second-sourcing contracts with a relatively large number of competitors. The fact that most semiconductor products have relied upon a large number of second|sourced suppliers provides indirect evidence that stock-out and cost-reduction motives may be more important empirically than preclusion of opportunism.

VII. ALTERNATIVES TO SECOND-SOURCING

The preceding sections have shown how firms may use second-sourcing to reduce the costs of operating under research and demand uncertainty. Other organizational arrangements may offer similar advantages to firms, however, and I will briefly discuss three: joint research ventures, separation of design and production activities, and horizontal merger. One alternative industry organization is for firms to cooperate at the research stage. Joint research ventures allow firms to pool firm-specific research risk, eliminating the common pool problem and leading to the efficient rate of research investment from the industry's standpoint. A joint research venture also implies that control over capacity-utilization decisions will reside with individual firms rather than with the single patent holder as under secondsourcing. If capacity utilization decisions are made independently by each firm, the average cost of production will be higher than if a single firm decides which plants should be active and which should remain idle.22 Fewer plants will be active in the second-sourcing equilibrium for any given rate of demand, economizing on avoidable plant costs. Thus, while a joint research venture can lead to a more efficient allocation of resources in the development stage than will a second-sourcing agreement, this must be balanced against the more efficient allocation of resources at the production stage under secondsourcing.

Another alternative to second-sourcing is for firms to separate research and development from production activities. Under this industry organization, some firms would specialize in product and process technology design while others would be dedicated solely to producing licensed designs. In this way, firms' capacity investment decisions could be separated from research uncertainty. Separation of research and production functions characterizes some industries where product design changes occur regularly.[23] For some products, however, firms may not wish to specialize vertically. Where product quality is easier to assure by monitoring the production process rather than actual output, vertical integration may be preferred to specialization. Monitoring of production facilities often will be easier when manufacturing occurs in-house. Such is the case in the semiconductor industry where quality control is performed primarily by monitoring continually the plant's production environment and processes. Also, vertical integration may be preferred to specialization when capacitysupplying firms have the potential to behave opportunistically. This potential will be greatest in industries where capacity investment lag times are long relative to the duration of the product cycle, where product imitation by competitors can occur relatively quickly, and where production facilities are product specific. The semiconductor industry provides a good illustration of these three characteristics.[24]

Finally, firms may desire more formal, extensive forms of cooperation such as horizontal merger when operating in an uncertain environment, yet they may face legal constraints on the set of available organizational arrangements. Horizontal mergers are subject to antitrust scrutiny by the Department of Justice, and those involving foreign firms are now subject to a heightened antitrust standard and additional political uncertainty under the Exon-Florio Amendment.[25] By contrast, the current legal attitude towards secondsourcing is fairly liberal.[26] In this case, firms may select second-sourcing as a second-best alternative. Legal and political obstacles to more extensive forms of cooperation may explain partially the large and increasing number of second-sourcing agreements between American and Japanese semiconductor producers.

VIII. CONCLUSIONS

Second-sourcing can benefit both suppliers and purchasers in industries where firms pre-commit to certain pre-production decisions before research and development and demand uncertainty are fully resolved. By analyzing second-sourcing in a market setting rather than within the usual principal-agent flamework, I reach results that differ significantly from the existing literature. Second-sourcing allows firms to avoid firm-specific research risk and to operate with greater flexibility under non-diversifiable industry demand uncertainty. With second-sourcing, the winning firm is able to meet a wider range of possible rates of demand and to supply a given rate of demand frequently at a lower total cost than under non-cooperation. Firms' enhanced efficiency in turn benefits buyers by reducing the probability of stock-outs and lowering the average cost of production in most circumstances. In some situations, second-sourcing also may alleviate the common pool problem in firms' research investment decisions.

[FORMULA[S] HAVE BEEN OMITTED]

Evidence from the semiconductor industry offers support for the theory's predictions about when firms are more likely to adopt second-sourcing agreements. To date, empirical industrial organization economists have paid relatively little attention to second-sourcing, despite the many settings in which this organizational arrangement is observed. Robotics and biotechnology are two important examples of other industries in which firms often rely on second-sourcing. What these examples have in common with the semiconductor industry is the concurrence of continual product and process technology innovations that can lead to mismatchings between a firm's production capacity and its realized demand when some capacity must be committed to in advance. This paper's predictions could be tested further by studying a variety of case studies of such industries. Detailed empirical analysis of second-sourcing in different industry settings would be a valuable complement to the theoretical issues treated in this paper.

APPENDIX

This appendix provides the formal details underlying the model and its solution as developed in the text.

The Model

The patent race considered in the paper follows Lee and Wilde [1980]. Firms invest in research during period one at the constant rate of xi dollars until one firm makes a discovery. By incurring the continual flow cost x the ith firm (i- 1,...,n) "purchases" a random variable T(X.sub.i) that represents its uncertain discovery date for the innovation. Firm i's innovation discovery date is distributed exponentially according to the probabilistic relationship

(1.1) Prob{Tau(X.sub.i) [equal to or less than]

t} = 1 -exp{-v(x.sub.i)t},

where v(x.sub.i) is its instantaneous probability of discovery, which is an increasing function of [x.sub.i]. Following Lee and Wilde [1980] and others, I impose the following properties on the function v(xi) to ensure that, while there may be an initial range of increasing returns to scale in research and development technology, eventually diminishing returns set in: (i) v({})- 0- lim v'(x) as x-->[infinite], (ii) v"(x)> or < 0 as x < or > x*, and (iii) v(x)Ix > or < v'(x) as x > or < x[infinite]. The expected duration of a given firm i's research phase equals v(xi)'1, and the winning firm's expected discovery date is given by

[THIS FORMULA HAS BEEN OMITTED]

The probability of the [i.sup.th] firm winning the development race equals the ratio of these terms,

[THIS FORMULA HAS BEEN OMITTED]

Finally, assuming no discounting, firm i's total expected research investment is given by

[THIS FORMULA HAS BEEN OMITTED]

(see Lee and Wilde [1980]).

Industry demand is given by the random variable q which is distributed uniformly over the region [b,B]. The density function for the distribution of market demand [Omega (q)] is thus

[THIS FORMULA HAS BEEN OMITTED]

The common reservation price among potential purchasers is r. The firm incurs sunk capacity acquisition costs of (f+[gk.sub.i]) and an avoidable cost of hki when its plant of size [k.sub.i] is active. This latter cost establishes a minimum scale of production equal to [hk.sub.i]/(r-c). The firm's constant marginal production cost equals c. The firm's total costs therefore are given by

[THIS FORMULA HAS BEEN OMITTED]

Upon simplification this condition requires that

A necessary condition, therefore, for the firm's expected profits to be non-negative is that

This implies that the firm will operate in a region of decreasing returns from research and development. This is the essence of the common pool problem.

The Second-Sourcing Equilibrium. When secondsourcing is permitted in the production stage, firm i's expected profits in period one are

[THIS FORMULA HAS BEEN OMITTED]

In period two, the firm's expected profit function is identical in form after making the substitution of 1/n for v(x.sub.i)/[Sigma v](x.sub.j]) and xi for [x.sub.i] for all i. The expected profit function is explained as follows. With probability v(xi)/[Sigma].(X.sub.j]) = (1/n), the/th firm wins the development race. If realized demand q lies in the interval [hk.sub.i]/(r-c),ki], the firm satisfies all buyers internally and need not exercise its call option to second-source production to its former competitors. In this case, the firm's revenues net of variable and avoidable costs are (r-c)q - [hk.sub.i]. If realized demand falls in the range [ki, [Sigma k.sub. j], the winning firm first exhausts its own capacity and then second-sources the remaining (q-ki) units of demand by renting idle capacity from former competitors at a unit price [Lambda]. In this case, the firm's net revenues from its internal capacity are (r-c-h)ki and those from its secondsourced production (after subtracting capacity rental fees) are (r-c-Lambda)(q-ki) -h[q/ki]ki where [.] denotes the greatest integer function, i.e., [x] = (greatest integer [equal to or less than] x).[28] Finally, if demand exceeds total installed capacity in the industry, q > [Sigma k.sub.j], the winning firm again second-sources and then produces at aggregate industry capacity. In this case, the firm's net revenues from its own capacity are (r-c-h)[k.sub.i] and those from its second-sourced production, after subtracting capacity rental fees, are (r-c-h-[lambda],)([Sigma - k.sub.i]).

Should some other firm (j) win the development race, an event with probability (1- v(x.sub.i)/[Sigma v](x.sub..j])) = (1-1/n), the losing firm is capacity need not remain idle. Should realized demand exceed the winner's capacity [k.sub.j], its (n-1) former competitors can lease some fraction of their plant facilities to allow firm j to satisfy its excess demand. If demand falls in the region [k/, Sigma k.sub.i], I assume that second-sourced demand is allocated among the (n-1) losing firms by a random mechanism. Thus, each losing firm's expected second-sourcing receipts equal [Lambda](q-k.sub.)/(n-1). In the event that demand exceeds total industry capacity, all of the capacity of the (n-1) losing firms is fully employed. Each of these firms' second-sourcing receipts therefore are [Lambda. k.sub.i]. Finally, firms' total expected profits are then simply a probability weighted average of all of the above terms, less capacity acquisition costs, less expected research investments.

Equation (A.9) can be simplified by noting that total receipts must equal total payments for second-sourced capacity in the industry. Moreover, in the symmetric equilibrium, expected net receipts are exactly zero for each firm. Capacity rental fees represent only an ex-post redistribution of wealth among firms. Importantly, then, the rental price of capacity [Lambda] is not a determinant of the relative profitability of second-sourcing over sole-sourcing. To see this, let Ks be the aggregate second-sourced capacity. If a firm wins the development race, its total second-sourcing payments to the (n-1) losers are then [Lambda K.sup.S]. In the symmetric equilibrium it makes this payment with probability 1/n, so that its total expected payment is [Lambda K.sup.s]/n. A losing firm receives 1/(n-1) of the second-sourcing payments, or [Lambda K.sup.S](n-1) dollars. It receives this payment with probability (n-1)/n, yielding an expected receipt of [Lambda K.sup. S]/(n-1)'(n-1)/n or [Lambda K.sup.S]/n dollars. This is exactly equal to each firm's expected payment.29 The practical implication of this is that when studying the impact of second-sourcing on firms' optimal capacity decisions, we need only consider the perspective of the firm winning the development race.

Consolidating (A.9) yields

[THIS FORMULA HAS BEEN OMITTED]

Let W(ki) denote the expression given in the large parentheses in (A.10). It is the reward to being the first to introduce the new input, given that second-sourcing is permitted. Following (A.5), equation (A.10) may be rewritten as

[THIS FORMULA HAS BEEN OMITTED]

Firm i's optimal research investment rate [x*.sub.i] is derived by maximizing (A.11) with respect to xi for a given optimal plant capacity choice [k*.sub.i]. The firm's research and development choice is defined implicitly by the condition

[THIS FORMULA HAS BEEN OMITTED]

The firm's optimal capacity investment is found by maximizing (A.11) by choice of ki and recalling that in the symmetric equilibrium

[THIS FORMULA HAS BEEN OMITTED]

The derivation requires also using an approximation for the greatest integer function of [x] =x - 0.5 and evaluating this term at its mean value over the interval [ki,Y. kj]. The resulting expression is given by equation (2) in the text.

Firm Capacity With and Without Second-Sourcing. Under non-cooperation, each firm i's capacity is given by equation (1) in the text. Under second-sourcing, it is given by equation (2). Subtracting yields

[THIS FORMULA HAS BEEN OMITTED]

Rewriting the denominators of each expression gives

[THIS FORMULA HAS BEEN OMITTED]

The numerators in the two terms in (A.14) are identical. For all n > 1 and h > 0, the first term's denominator exceeds that of the second term. It follows that [k*.sub.i] < [K.sub.i] unambiguously.

Industry Capacity With and Without Second-Sourcing. With non-cooperation, industry capacity is given by equation (1) in the text. Under secondsourcing, it is given by equation (3). Subtracting yields

[THIS FORMULA HAS BEEN OMITTED]

Upon rearranging and collecting terms, a necessary and sufficient condition for industry capacity to rise with second-sourcing is that

(A.6) 2H < (r-c).

Aggregate capacity therefore rises for relatively low capacity-use charges and large markups over variable costs. The intuition is supplied in the text.

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