Outsourcing innovation in a durable good monopoly.

Lee, Sanghoon

I. Introduction

If you buy a notebook computer or a personal digital assistant (PDA) today, the chances are that it is designed by a company that you have never heard before. The list of products does not stop here. In consumer electronics alone, an increasing number of products such as MP3 players, digital cameras, and mobile phones are designed through outsourcing but sold under top brands. The trend seems to be spreading to other sectors, too.

Although outsourcing in general has been the subject of considerable interest recently, outsourcing product innovation has not been paid much attention in the literature. A notable exception is Aghion and Tirole (1994), which adopts an incomplete-contract approach to analyze the make-or-buy decision in the production of innovation. Their analysis focuses on the development of innovation and hence abstracts away from the pricing or marketing of innovation so developed. But pricing and product development are inter-related problems, especially in durable-good markets where such a practice seems to be most pronounced. This article attempts to find a role of outsourcing from the interaction between the two problems.

Consider a durable-good monopolist who has the capability to improve the quality of its product. The firm may develop an improved product in house or may outsource the development to a contractor. Assuming that contracts are incomplete, outsourcing involves a hold-up problem, which leads to insufficient investment in product development. Meanwhile, the monopolist seller faces a well-known dynamic pricing constraint inherent in durable-good sales. This means that a durable good must be sold at a price below its intrinsic value. Otherwise, consumers would not make a purchase because they expect that their purchase will become economically obsolete once the monopolist introduces an improved product. In relation to the development decision, however, the pricing constraint becomes the source of a commitment problem for the monopolist (Waldman (1996), Fishman and Rob (2000)). Although frequent product improvements will suppress the sales price hence the profits, the monopolist has an incentive to speed up the development once the sales of the current product has been made to the consumers. Consequently, the monopolist will have an overinvestment problem if the development is done in house.

It is not difficult to see then why outsourcing may be preferred over vertical integration. Although the hold-up problem associated with outsourcing has a negative effect of reducing the investment in product improvement, the inefficiency in investment also relaxes the pricing constraint and hence has a positive effect of boosting the sales of the original product. Which of the two forms of organization gets selected will depend on the relative size of the two effects.

Outsourcing is a useful strategic option for the monopolist but its welfare effect is in general ambiguous. On the one hand, outsourcing reduces social welfare because it causes inefficiency in product improvement. On the other hand, it may improve the monopolist's profitability and hence provide an added incentive to develop the original product. This implies that outsourcing must be socially wasteful if it is adopted when the original product can be developed profitably in house. If the profits under vertical integration are not sufficient to cover the development cost, however, outsourcing may be the only way to bring out a valuable innovation to market. Despite its inefficiency in subsequent product improvement, outsourcing improves social welfare in this case.

The model predicts that relatively less significant improvements are outsourced while more significant ones are made in house. When the value of improvement is relatively small, the sales of the original product must be more important than the sales of an improved product. Outsourcing must be the better alternative in this case because generating hold-up will have more positive than negative effect on profits. The case for vertical integration will be the exact opposite, i.e., it should be the preferred mode of organization when the improvement has a relatively large value. Although the validity of this claim needs to be verified by rigorous empirical evidence, a casual observation suggests that it is consistent with actual practice. (2) Such a prediction, however, does not follow easily from a standard hold-up model, which focuses only on the incentive for product improvement.

In management literature, "core competence" argument has been commonly used as an explanation for outsourcing. In the context of research and development, it suggests that firms can raise profitability by performing only "core" R&D and outsourcing non-core R&D activities. In a nutshell, the argument emphasizes potential gains from specialization associated with outsourcing. (3) The framework developed in this article, however, provides a different interpretation of this popular idea. Once the development of an original product is identified as core and the development of an improved product as non-core R&D, the current analysis suggests that outsourcing non-core R&D, which helps the sales of the pioneering innovation, will increase the profitability of core R&D. This implies that gains from outsourcing may not come from a better capability for core R&D as commonly believed but from a better return on the investment in such activities.

This article takes a view that outsourcing may be adopted not because of its intrinsic benefits or cost advantages relative to vertical integration but precisely because of the hold-up problem that it entails. (4) In the analysis, outsourcing plays a "strategic" role in the sense that it mitigates the commitment problem faced by the monopolist. Although in a quite different setting, Chen (2005) considers such a strategic effect of outsourcing or vertical disintegration. The idea is that a vertically integrated firm may divest its upstream division in order to make a commitment not to discriminate against its downstream competitors. The audiences for commitment are the rival firms in the downstream market. In this article, consumers are the audience for the monopolist's commitment.

The rest of the article is organized as follows. Section 2 introduces the basic model. The main result is presented in section 3 in which the strategic role of outsourcing is identified and a comparison is made between the two modes of organization. Section 4 examines possible alternatives to outsourcing such as rental and buyback schemes. Also, the incentive for pioneering innovation is discussed by extending the basic model. Concluding remarks follow in section 5.

II. Basic Model

There is a firm, the "pioneer", with a technology to produce a durable good, and a continuum of identical consumers. Each consumer has a unit demand of the good, i.e., buys either zero or one unit but not more. The per-period utility of a representative consumer is given by u = v - p, where v(p) denotes the quality (price) of the good. It is assumed that a consumer chooses to buy when he feels indifferent between buying and not buying the good. The size of the consumers is normalized to 1. The quality of the good is [v.sub.I] > 0 initially but it may be improved to [v.sub.I] + [v.sub.II] (> [v.sub.I]) by investing in research and development. The improvement cannot be marketed separately from the original product and must be combined with the pioneer's input to make a final product. For simplicity, the pioneer's input is assumed to be costless although it is essential in the production.

The improvement occurs with a probability q [member of] [0, 1 ], which depends on the level of investment e [greater than or equal to] 0 spent on the development project. The relationship between the two is governed by a function q = q(e) where q"(x) < 0 < q'(x), q(0) = 0, [lim.sub.e[right arrow][infinity]] q(e) = 1, and [lim.sub.e[right arrow]0] q'(e) = [infinity]. It is assumed that neither the level of investment nor the amount of improvement can be verified in court. Except for the development cost, there is no other cost associated with producing or selling the good.

There are two different ways to organize the production of the improvement: the pioneer may develop an improved product in-house (vertical integration) or it may set up a separate firm, an "outsourcee", to do the job (vertical disintegration or outsourcing). An alternative interpretation of the second option is that the pioneer hires an outside "contractor" for the development. Suppose that using the pioneer's technology is essential for the development, and also that the market for outsourcing is competitive. Then, the pioneer must be able to extract the entire surplus from the development project, for instance, by auctioning off the contract. From the pioneer's perspective, therefore, outsourcing becomes equivalent to setting up its own spin-off.

The model has two periods and each period is composed of either one or two stages depending on the mode of organization. The first period starts with a stage in which the pioneer sells the original product. In the next stage, investment for product improvement is made. The decision maker at this stage becomes the pioneer (outsourcee) if the development is done under vertical integration (outsourcing). In the second period, improvement materializes with probability q(e). The pioneer sells the improved product, if any, in case of vertical integration. In outsourcing, a bargaining takes place between the pioneer and the outsourcee before the sales are made. The bargaining is modeled in a reduced form in which the pioneer gets an exogenously given share [lambda] [member of] (0, 1) while the outsourcee receives the remaining 1 - [lambda] of the sales revenue. Payoffs are discounted between the two periods but there is no discounting within a period. Let [delta] [member of] (0, 1) be the common discount factor.

III. Analysis

1. Social Optimum

For a benchmark, it is helpful to consider the socially optimal allocation first. The social welfare is defined as the sum of consumers' and producers' surplus. Since production is costless, the consumption/production decision is trivial: the highest-quality product should be produced and distributed to every consumer. The only non-trivial decision becomes how much investment to make for the improvement. The planner's problem is then given by

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where W(e) denotes the social welfare as a function of the investment level e.

In the first period, the original product is consumed and the investment is made for product improvement. The social surplus therefore equals [v.sub.I]- e. In the second period, the improvement materializes with probability q(e), which results in the consumption worth [v.sub.I] + [v.sub.II]. Otherwise, the original product must be used by the consumers. The discounted expected surplus thus becomes [delta]{q(e)( [v.sub.I] + [v.sub.II]) + (1 - q(e))[v.sub.I]}.

Under the assumptions on q(x), the problem is well-defined. The solution exists given the continuity of W(x), and the fact that W(0) > 0 and [lim.sub.e[right arrow][infinity]] W(e) = - [infinity]. The uniqueness follows from the strict concavity of the objective function, i.e., W"(e) = [delta]q"(e)[v.sub.II] < 0. Moreover, the assumption [lim.sub.e[right arrow]0] q'(e) = [infinity] implies that the solution must be in the interior. Let [e.sup.so] be the socially optimal investment level. Then the first-order condition for the maximization problem is given by

-1 + [delta]q'([e.sup.so])[v.sub.II] = 0.

The condition simply shows that the marginal cost of investment (= 1) must be equal to its marginal benefit (= [delta]q'([e.sup.so]) [v.sub.II]) at the optimum. Since q(x) is strictly concave, the optimal investment level [e.sup.so] must be strictly increasing in the size of the product improvement [v.sub.II].

2. Vertical Integration

An assumption, which will be maintained throughout this article, is that the product is sold through a simple sales contract. Renting, for instance, is not allowed as well as more sophisticated sales methods such as buybacks. The effects and limitations of these pricing methods will be discussed after the main analysis. To find the Subgame Perfect Equilibrium of the game, one needs to proceed backwards starting from the last stage of the game.

Second period, sales stage

At the last stage, the integrated firm sets a price for its second-period sales. The price may depend on two things: the amount of the first-period sales and whether there was a product improvement or not. Let x [member of] [0, 1] be the sales in the first period. Also, define s to be a binary variable that takes a value 1 if there is product improvement and 0 otherwise. The price in the second period then becomes a function [p.sub.2] = [p.sub.2](x, s). Let [p.sup.int.sub.2](x, s) be the optimal second-period price and [R.sup.int.sub.2](x, s) be the corresponding revenue of the integrated firm.

When there is no product improvement in the second period, the firm's choice becomes trivial: the optimal strategy must be to charge [v.sub.I] to whoever wants to buy the original product. This implies that [p.sup.int.sub.2](x, 0) = [v.sub.I] and the corresponding revenue [R.sup.int.sub.2](x, 0) is given by (1 - x)[v.sub.I].

When there is an improvement instead, the firm may set i) [p.sub.2](x, 1) = [v.sub.II] to supply all consumers, or ii) [p.sub.2](x, 1) = [v.sub.I] + [v.sub.II] and sell only to those who did not make a purchase in the first period. The corresponding revenues become [v.sub.II] for the first strategy, and (1 - x)([v.sub.I] + [v.sub.II]) for the second strategy. Targeting all consumers must be optimal if [v.sub.II] [greater than or equal to] (1 - x)([v.sub.I] + [v.sub.II]) or x [greater than or equal to] [v.sub.I]/[v.sub.I] + [v.sub.II]. The optimal price and the corresponding revenue in this case are then summarized as follows:

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First period, investment stage

At the second stage of the first period, the integrated firm decides the level of investment taking the first-period sales as given. The optimal investment is then determined by solving the following interim profit maximization problem:

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where [[DELTA].sup.int](x) [equivalent to] [R.sup.int.sub.2](x, 1) - [R.sup.int.sub.2](x, 0). One can easily verify that the problem is well-defined and has an interior solution. Let [e.sup.int](x) be the optimal investment level. The first-order condition is then given by

-1 + [delta]q'([e.sup.int](x))[[DELTA].sup.int](x) = 0

Notice that [[DELTA].sup.int](1) = [v.sub.II] = ([v.sub.I] + [v.sub.II]) - [v.sub.I] = [[DELTA].sup.int](0). This implies that the first-order condition will coincide with that of the social planner's either if x = 0 or x = 1. Let [e.sup.int] [equivalent to] [e.sup.int](0) = [e.sup.int](1).

First period, sales stage

At the first stage of the game, the price of the original product is set by the firm and purchase decision is made by the consumers. Let [p.sub.1] be the price offered by the integrated firm. Before accepting an offer made by the firm, a rational consumer must think about not just how much benefit he will get from the product but also how long he will actually use the product. This is because the original product will become economically obsolete once an improved product is introduced in the next period. Recall that the probability of an improvement is determined by the firm's investment but the investment is in turn determined by the first-period sales. This implies that the consumers' expectation regarding the first-period sales becomes a crucial determinant of their purchasing decision.

Let [x.sup.e] be this expectation formed by a representative consumer. A consumer then should buy in the first period if

[v.sub.I]-[p.sub.1]+[delta][v.sub.I] [greater than or equal to] [delta]q([e.sup.int]([x.sup.e])){[v.sub.I] + [v.sub.II] - [p.sup.int.sub.2]([x.sup.e], 1)}

The left-hand side of the inequality equals the payoff from purchasing the product in the first period. A consumer's utility in the first period is given by [v.sub.I] - [p.sub.1]. If there is no product improvement in the second period, each consumer will use the original product and hence get the utility of [v.sub.I]. If there is an improvement, on the other hand, a new product will be sold at [p.sup.int.sub.2]([x.sup.e], 1). A consumer may buy a new product in this case, the utility from which will be [v.sub.I] + [V.sub.II] - [p.sup.int.sub.2]([x.sup.e], 1). But this is at most [v.sub.I] because [p.sup.int.sub.2](x, 1) takes either one of the two values [v.sub.II] and [v.sub.I] + [v.sub.II]. Regardless of product improvement, therefore, the consumer's utility in the second period is fixed at [v.sub.I].

The payoff from delaying the purchase is given by the right-hand side of the inequality. The first-period utility is zero since there is no purchase and hence no consumption. In the second period, an improvement is made with probability q([e.sup.int]([x.sup.e])). If there is a product improvement, buying the improved product is optimal for the consumers because the resulting utility [v.sub.I] + [v.sub.II] - [p.sup.int.sub.2]([x.sup.e], 1) is always non-negative. When there is no improvement, which arises with probability 1 - q([e.sup.int]([x.sup.e])), the original product will be sold at [p.sup.int.sub.2](x, 0) = [v.sub.I]. Each consumer should buy one and get the utility of zero.

The integrated firm takes the consumers' expectation as given and maximizes its profits. Given that each consumer will make a purchase as long as the previous inequality condition holds, the firm should charge the maximum price that satisfies the condition, if it chooses to sell at all in the first period. This gives the optimal selling price for the firm in the first period:

[p.sub.1] = (1 + [delta])[v.sub.I] - [delta]q([e.sup.int]([x.sup.e]))

{[v.sub.I] + [v.sub.II] - [p.sup.int.sub.2]([x.sup.e], 1)}.

The price depends on the consumers' expectation of the first-period sales. Without any restrictions on the consumers' expectation, however, this may lead to rather unreasonable predictions about the outcome of the game. For instance, it may happen that each consumer makes a purchase believing that no one else is going to buy the product. Given that consumers have identical preferences, this implies that every consumer will buy the product in equilibrium contradicting their own expectation. One way to get around this problem is to focus on "rational-expectations" equilibria (Fishman and Rob (2000)), in which the consumers form a correct expectation in equilibrium. In the remainder of this article, "equilibrium" refers to such a rational-expectations equilibrium of the game.

A possibility that is not examined explicitly at this point is that the firm may skip the first-period market and supply only in the second period. The following lemma establishes however that this does not occur in equilibrium.

Lemma 1. In equilibrium, x = 1.

Let [p.sup.int.sub.1] be the equilibrium price set by the firm in the first period. Given that the consumers form a correct expectation in equilibrium, it must be that x = [x.sup.e] = 1. But this implies

[p.sup.int.sub.1] = (1 [delta])[v.sub.I] - [delta]q([e.sup.int](1)){[v.sub.I] + [v.sub.II] - [p.sup.int.sub.2](1, 1)} = [v.sub.I] + [delta]{1 - q([e.sup.int])} [v.sub.I]

The equilibrium profits of the integrated firm [[PI].sup.int] then can be written as

[[PI].sup.int] = [p.sup.int.sub.1] - [e.sup.int] + [delta]{q([e.sup.int])[[DELTA].sup.int](1)+ [R.sup.int.sub.2](1,0)}

= (1 + [delta])[v.sub.I] - [e.sup.int] + [delta]q([e.sup.int])([v.sub.II] - [v.sub.I])

Examining the expression for [p.sup.int.sub.1] reveals that the firm cannot extract the full surplus out of the consumers in its first-period sales. The consumers know that an improved product may be introduced in the next period, in which case it will be offered at a price below its intrinsic value, i.e., [p.sup.int.sub.2](1, 1) = [v.sub.II] < [v.sub.I] + [v.sub.II]. This means that the firm must give a "discount" to the consumers in the first period, if it wants to make any sales at all.

As the firm supplies the entire market in the first period, the equilibrium level of investment becomes efficient, i.e., [e.sup.int](1) = [e.sup.int] = [e.sup.so]. This should not be surprising because the firm appropriates exactly its social benefit [v.sub.II] by selling an improved product in the second period.

Commitment Case

Although the equilibrium investment is socially optimal, it is not what the firm would choose if it had the ability to commit to an investment level before the first-period sales. To see this, suppose an imaginary case where the firm can make such a commitment. The optimal investment for the firm is then determined by solving the following problem:

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The difference now is that the firm takes into account the effect on the first-period sales as well as the effect on the probability of improvement when it makes a decision on its investment. Given that the sign of [v.sub.II]-[v.sub.I] is indeterminate, one cannot exclude the possibility of a boundary solution. Let [e.sup.com] be the optimal investment level. The first-order condition is then given by

-1 + [delta]q'([e.sup.com)([v.sub.II] - [v.sub.I]) [less than or equal to] 0

One can easily verify that the condition must hold with equality if [v.sub.II] - [v.sub.I] > 0. Otherwise, it holds as a strict inequality and the optimal investment becomes zero. In either case, the investment level is smaller than the equilibrium level under vertical integration. Given that increasing the probability of improvement suppresses the sales-price in the first period, the firm must invest less in the commitment case than it does in equilibrium.

3. Outsourcing

Instead of developing an improved product in-house, the pioneer may outsource the job to a contractor. Given that the investment for product development is relationship-specific and nonverifiable, outsourcing will lead to an insufficient investment. In standard hold-up models, underinvestment is a "problem" that needs to avoided or possibly corrected through various measures. In the current context, however, the very inefficiency may actually benefit the pioneer because investment under vertical integration turns out to be excessive from the pioneer's point of view.

Research has shown that not all bilateral relationships with specific and non-verifiable investment lead to inefficiency. Several contractual solutions have been suggested indeed under various assumptions (Aghion et al. (1994), Edlin and Reichelstein (1996), Noldeke and Schmidt (1995)). But the kind of investment considered here--the one that benefits only the investor's trading partner--is known to be particularly problematic (Che and Hausch (1999)). Instead of examining all contractual possibilities in detail, this article takes the fact that contracts are incomplete as given. An outsourcee is thus assumed to make the investment decision solely based on its expectation of a future order by the pioneer. Once an improvement has been made, it becomes observable to both parties. The terms of trade will then be determined by a costless bargaining between the two parties. (5)

Second period, sales stage

The equilibrium under outsourcing is once again found by backward induction. At the last stage of the game, the pioneer sets its sales price and the consumers make their purchase decisions. Given that its share of the sales revenue is already determined in the previous bargaining stage, the optimal sales price chosen by the pioneer must be the same as the one under vertical integration. Let [p.sup.out.sub.2](x, 1) ([p.sup.out.sub.2](x, 0)) be the second-period price under outsourcing with (without) a product improvement. Then it follows that [p.sup.out.sub.2](x, 1) = [p.sup.int.sub.2](x, 1) and [p.sup.out.sub.2](x, 0) = [p.sup.int.sub.2](x, 0).

Second period, bargaining stage

The second-period bargaining is modeled as a generalized Nash bargaining game. Let [lambda] [member of] (0, 1) be the pioneer's bargaining share. Without any product improvement, there is no trade to be made between the pioneer and the outsourcee. The original product will be sold by the pioneer and the outsourcee will earn nothing. Let [R.sup.out.sub.2](x, 0) be the pioneer's and [r.sup.out.sub.2](x, 0) be the outsourcee's payoff in this case. This implies that [R.sup.out.sub.2](x, 0) = (1 - x)[v.sub.I] and [r.sup.out.sub.2](x, 0) = 0.

Consider next the case where there has been a product improvement. If an agreement is reached between the two parties, the improvement can be turned into a product and sold to the consumers. The corresponding sales revenue must be max{[v.sub.II], (1 - x)([v.sub.I] + [v.sub.II])}, which is the same as the one under vertical integration (=[R.sup.int.sub.2](x, 1)). When there is no agreement, the improvement cannot be produced and the pioneer must sell the original product. The pioneer (outsourcee) then will get [R.sup.out.sub.2](x, 0) ([r.sup.out.sub.2](x, 0)) respectively. The two parties thus gain by [R.sup.int.sub.2](x, 1) - {Rout(x, 0) + [r.sup.out.sub.2](x,] 0)} when they reach an agreement. Generalized Nash bargaining then gives [lambda] of the gains to the pioneer and the remaining 1 - [lambda] to the outsourcee. Let [R.sup.out.sub.2] (x, 1) be the pioneer's and [r.sup.out.sub.2](x, 1) be the outsourcee's payoff when there is a product improvement. Then it follows that

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First period, investment stage

At the investment stage in the first period, the outsourcee decides on its investment taking the first-period sales as given. Let [[PI].sup.s](e) be the profits of the outsourcee. The outsourcee's problem is then given by

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where [[DELTA].sup.out](x) [equivalent to] [r.sup.out.sub.2](x, 1) - [r.sup.out.sub.2](x, 0). It is straightforward to check that the problem is well-defined. Let [e.sup.out](x) be the optimal investment level chosen by the outsourcee. At an interior solution, the first-order condition becomes

-1 + [delta]q'([e.sup.out](x))[[DELTA].sup.out](x) = 0

One can easily verify that [[DELTA].sub.int](1) = [[DELTA].sub.int](0) = (1-[lambda])[v.sub.II]. This implies that [e.sup.out](1) = [e.sup.out](0). Let [e.sup.out] [equivalent to] [e.sup.out](1) = [e.sup.out](0).

First period, sales stage

The problem of the first-period sales is virtually the same as in vertical integration. The only modification is that now both firms expect that the probability of future improvement will be determined by the outsourcee's investment not by the pioneer's. The pioneer must sell in the first period as before. The optimal sales price [p.sup.out.sub.1] is again obtained from the consumer indifference condition, which gives

[p.sup.out.sub.1] = (1 + [delta])[v.sub.I] - [delta]q([e.sup.out](1)){[v.sub.I] + [v.sub.II] -[p.sup.out.sub.2](1, 1)} = [v.sub.I] + [delta]{1 - q([e.sup.out])}[v.sub.I]

where the first equality follows from [p.sup.out.sub.2](1, 1) = [p.sup.int.sub.2](1, 1) = [v.sub.II] Let [[PI].sup.b] ([[PI].sup.s]) be the equilibrium profits of the pioneer (outsourcee). Then it follows that

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To compare the allocations under vertical integration and outsourcing, notice first that the two modes of organization result in the same allocation in terms of production and consumption. The only difference arises in the level of investment and hence the probability of product improvement in the second period. The equilibrium investment under vertical integration is determined by the first order condition of the pioneer, which is reduced to

-1 + [delta]q'([e.sup.int])[v.sub.II] = 0.

The first-order condition of the outsourcee, on the other hand, is given by

-1 + [delta]q'([e.sup.out])(1 - [lambda])[v.sub.II] = 0.

The difference between the two conditions comes from the fact that the marginal benefit of investment under outsourcing is smaller than the marginal benefit under vertical integration. Since the investment under vertical integration is socially optimal, this implies that [e.sup.out] < [e.sup.int] = [e.sup.so]. This should not be surprising given that the outsourcee appropriates only a fraction the surplus but bears the entire cost associated with product improvement. In other words, outsourcing leads to the usual underinvestment problem associated with hold-up.

Whether vertical integration or outsourcing will be adopted by the pioneer will depend on which of the two modes of organization generates higher profits. Let [[PI].sup.out] be the joint profits of the pioneer and the outsourcee under outsourcing:

[[PI].sup.out] [equivalent to] [[PI].sup.b] + [[PI].sup.s] = (1 + [delta])[v.sub.I] - [e.sup.out] + [delta]q([e.sup.out])([v.sub.II] - [v.sub.I])

Then outsourcing will dominate vertical integration if and only if [[PI].sup.out] [greater than or equal to] [[PI].sup.int]. The following proposition shows when this will be the case.

Proposition 1. There exists a [[bar.v].sub.I] [member of] (0, [v.sub.II]) such that [[PI].sup.out] [greater than or equal to] [[PI].sup.int] if and only if [v.sub.I] [greater than or equal to] [[bar.v].sub.I].

Outsourcing should be preferred if the value of the pioneering innovation (= [v.sub.I]) is relatively large compared to that of the improvement (= [v.sub.II]). To put it another way, relatively less important improvements are outsourced while more important ones are developed in house. The result follows from the double-edged sword nature of the holdup problem in outsourcing. On the one hand, it reduces the incentive to invest for improvement, which has a negative effect on the sales in the second period. But the very inefficiency in investment also has a positive effect because it raises the first-period sales by relaxing the dynamic pricing constraint. Outsourcing will be adopted, therefore, when the first-period sales is more important than the second-period sales.

Given that the advantage (or disadvantage) of outsourcing depends on the severity of the holdup problem it entails, a natural questions is whether assigning more bargaining power to the pioneer will increase or decrease the joint profits of the two parties. It turns out that the relationship is in general non-monotonic. The following proposition summarizes this finding.

Proposition 2. If [v.sub.I] - [v.sub.II] [greater than or equal to] 0, [[PI].sup.out] is monotonically increasing in[lambda]. If [v.sub.I] < [v.sub.II], [[PI].sup.out] is increasing in [lambda] for [lambda] [member of] (0, [v.sub.I]/[v.sub.II]) but decreasing in [lambda] for [member of] ([v.sub.I]/[v.sub.II], 1).

An increase in the pioneer's bargaining share reduces the outsourcee's incentive to invest hence lowers the level of equilibrium investment. When the value of the pioneering innovation exceeds that of the improvement, any second-period gains due to an increased probability of product improvement will be more than offset by the corresponding losses in the first-period sales. Less investment, therefore, is always preferable, which implies that the joint profits must increase with the pioneer's bargaining share. If the improvement is more valuable than the original innovation, however, the conclusion may be reversed. As investment results in net gains in the sales revenue, the pioneer's desired level of investment becomes positive. There are two cases to consider. If the equilibrium investment is above the commitment level, the joint profits will increase with the pioneer's bargaining share. This is because reducing investment will move the equilibrium closer to the commitment solution. If the investment is below the commitment level instead, a decrease in investment will move the equilibrium further away from the commitment solution. In this case, the joint profits will decrease if the pioneer's bargaining share increases.

IV. Discussion

1. Renting and Price Discrimination

The commitment problem associated with vertical integration can be resolved either if the pioneer rents the product or if it gives a discriminatory price-discount to its previous customers (Waldman (1996), Fishman and Rob (2000)). By renting the product, the pioneer can extract the full surplus from the consumers by charging each period [v.sub.I] for the original product and [v.sub.I] + [v.sub.II] for an improved product. The objective function of the pioneer then coincides with that of the planner. Consequently, the equilibrium investment becomes socially optimal.

Virtually the same outcome can be achieved if the pioneer buys back the original product when a product improvement has been made in the second period. The original product may be bought back at [v.sub.I] while the improved product can be sold at [v.sub.I] + [v.sub.II]. Given the prices, consumers with the original product will sell the unit they have and buy an improved product. Effectively, therefore, the consumers pay only the price difference [v.sub.II]. Those who did not buy in the first period will pay the price of [v.sub.I] + [v.sub.II]. In any case, consumers get zero surplus from the trades regardless of their previous purchase history. In the first period, the pioneer may offer the original product at (1 + [delta])[v.sub.I]. By accepting this offer, a consumer just breaks even, i.e., gets zero surplus for two periods. In contrast to the simple pricing case, delaying purchase does not help in this case because a consumer then has to pay the full price for an improved product. As the consumers become indifferent, the offer will be accepted in equilibrium.

Although these methods have been used in practice, their applicability is limited by several factors. Let alone the well-known moral hazard problem in the maintenance of rented products, rental-only policy by a durable-good monopolist is illegal under the current antitrust law. Buying back used products, on the other hand, may have its own commitment problem. This point can be illustrated easily in a slightly modified version of the basic model. Suppose now that the pioneer may buy back its products in the second period but incurs a small cost by doing so. In such a situation, however, it is not difficult to see that the buyback scheme will simply break down. This is because the pioneer will have no incentive to actually buy back the used products once all the consumers have made their purchase in the first period. In this case, the pioneer will do better by simply selling the improved product at [v.sub.II]: it will give the same net revenue [v.sub.II] but no additional cost associated with buybacks. Expecting this, however, consumers will not pay the full price (1 + [delta])[v.sub.I] in the first period because they can delay the purchase and take advantage of the low price in the second period. If the pioneer can make a contractual commitment to a future buyback, the problem may go away. Given that buyback involves material cost, however, such a contract is likely to be renegotiated away, i.e., the pioneer and the consumers will voluntarily nullify the original contract and agree to a simple sales contract instead. When these concerns are important, therefore, one may expect that strategic outsourcing will be an attractive alternative for the pioneer. (6)

2. Incentive for Pioneering Innovation

Investment for product improvement is insufficient under outsourcing while it is socially optimal under vertical integration. Given that production and consumption are efficient in either mode of organization, this implies that vertical integration dominates outsourcing in terms of social welfare. The reasoning, however, is based on an assumption that the original product has been already developed by the pioneer. The conclusion may not hold when the pioneer's choice to develop the original product is endogenized.

A simple extension of the basic model can illustrate this point. Suppose that the original product has not been developed yet. But the pioneer has an "idea" for the product, which can be developed into a production technology by spending a fixed cost K > 0. The analysis in the previous section then suggests that the pioneering innovation will be introduced if

max[[[PI].sup.int], [[PI].sup.out]] - K [greater than or equal to] 0

If outsourcing is prohibited instead, the condition will become

[[PI].sub.int] - K [greater than or equal to] 0

The latter condition is more restrictive than the former, which means that some pioneering innovations will be introduced only if outsourcing is allowed. This implies that the overall effect of banning (or allowing) outsourcing becomes ambiguous in general. Since outsourcing causes inefficiency in product improvement, banning outsourcing will improve social welfare as long as the pioneering innovation can be introduced profitably under vertical integration. Outsourcing must be allowed, however, if the pioneering innovation becomes profitable only under outsourcing, and hence cannot be brought to market under vertical integration.

In management, core competence has been frequently used as an explanation for outsourcing. The idea is that a firm should focus on a few activities (the "core") that it does (or should do) particularly well (the "competence") in order to be a successful competitor. By shedding non-core activities, it is argued, a firm can enhance its capabilities for core activities while saving costs on non-core activities. In the context of product innovation, it has been argued that the core becomes the "mission-critical" R&D that generates key intellectual properties while other "commodity work" may be regarded as non-core R&D. (7)

In the current model, one may identify the development of the original product as the core, and the subsequent product improvement as the non-core activity. What the previous analysis shows is that outsourcing non-core R&D may increase the profitability of the core R&D. The reason was that outsourcing helps the sales of the "core" product, the gains from which may outweigh the losses in subsequent product development. One can argue, therefore, that outsourcing non-core R&D may help not necessarily because it enhances the capability for core R&D as commonly believed, but because it raises the return on the investment in such an R&D. The framework developed in this article thus provides a new perspective on this popular core competence idea.

V. Concluding Remarks

A durable-good monopolist's decision to outsource its product improvement is analyzed. When contracts are incomplete, outsourcing generates a hold-up problem, which leads to underinvestment in product improvement. But the very inefficiency in investment also relaxes the monopolist's pricing constraint and hence helps the sales of its pioneering innovation. For less significant improvements, outsourcing is shown to outperform vertical integration as its strategic gains outweigh the losses in product improvement. The incentive for pioneering innovation is also discussed.

This article investigates the strategic motive for outsourcing in durable-good monopolies. To focus on the interaction between the hold-up and the commitment problem, the analysis is kept to a very stylized setting with a single pioneering innovation and a corresponding improvement opportunity. Surely, actual process of product innovation is much more complicated than what this article describes. Incorporating more details into the model will not only add realism to the analysis but may also produce some useful insights. An aspect that is absent in the current analysis, for instance, is that the pioneer ends up breeding its own competitor when it outsources product improvement. This imposes additional cost on the pioneer in addition to the efficiency loss associated with hold-up. A possible extension may examine the outsourcing decision in such a situation and also its welfare implications. Another direction of future research might be to consider the case of multi-product monopoly. The issue there will be the effect of complementarities at the level of production and/or consumption. It would be interesting to see how these modifications will affect the basic conclusions of this article.

Appendix

Proof of Lemma 1

Given that the consumers have identical preferences, it must be that either x = 0 or x = 1 in equilibrium. Suppose to the contrary that x = 0 Since equilibrium requires that the consumers have the correct expectation, the actual sales must be equal to the expected sales, i.e., x = [x.sup.e] = 0. The equilibrium profit of the integrated firm is then given by

-[e.sup.int](0) + [delta]{q([e.sup.int](0))[[DELTA].sup.int](0) + [R.sup.int.sub.2](0, 0)} = [delta][v.sub.I] - [e.sup.int] + [delta]q([e.sup.int])[v.sub.II].

But the firm can certainly do better than this by selling the product instead. Notice that, given the expectation [x.sup.e] = 0, each consumer will accept an offer as long as the price [p.sub.1] does not exceed (1 + [delta])[v.sub.I] - [delta]q ([e.sup.int](0)){[v.sub.I] + [v.sub.II] - [p.sup.int.sub.2](0, 1)} = (1 + 6)[v.sub.I]. But this implies that the firm can make up to

(1 + [delta])[v.sub.I] - [e.sup.int] + [delta][q([e.sup.int])[[DELTA].sup.int](1) + [R.sup.int.sub.2](1, 0)] = (1 + [delta])[v.sub.I] - [e.sup.int] + [delta]q([e.sup.int])[v.sub.II].

by selling the product in the first period, which is definitely greater than the equilibrium profit. The firm cannot be maximizing its profit therefore if it does not sell in the first period. Q.E.D.

Proof of Proposition 1

By recognizing the dependence of [[PI].sup.out] and [[PI].sup.int] on [v.sub.I], one can define the difference D([v.sub.I]) [equivalent to] [[PI].sup.out]([v.sub.I]) -[[PI].sup.int]([v.sub.I]) as a function of [v.sub.I]. Then D([v.sub.I]) > 0 for [v.sub.I] > [v.sub.II]. This is because D([v.sub.I]) = [e.sup.int] - [e.sup.out] + [delta]{q([e.sup.out]) - q([e.sub.int])}([v.sub.II]- [v.sub.I]) > 0 given that [e.sup.int] > [e.sup.out] and {q([e.sup.out]) - q([e.sub.int])}([v.sub.II] - [v.sub.I]) > 0. For [v.sub.I] [less than or equal to] [v.sub.II], notice first that D([v.sub.II]) = [e.sup.int] - [e.sup.out] > 0 and D'(x) = -[delta]{q([e.sup.out]) - q([e.sup.int])} > 0. Also, strict concavity of q(x) implies q'([e.sup.int]) = 1/[delta][v.sub.II] < q([e.sup.int]) - q ([e.sup.out])/[e.sup.int] - [e.sup.out] where the equality follows from the first-order condition under vertical integration. But this implies that

D(O) = [e.sup.int] - [e.sup.out] - [delta][v.sub.II]{q([e.sup.int]) - q([e.sup.out])} < [e.sup.int] - [e.sup.out] - ([e.sup.int] - [e.sup.out]) = 0.

Since D(0) < 0 < D([v.sub.II]) and D'(x) > 0, the claim follows immediately. Q.E.D.

Proof of Proposition 2

If [v.sub.I] - [v.sub.II] [greater than or equal to] 0, the profit function [PI](e) is strictly decreasing in e. Since [e.sup.out] is decreasing in [lambda], [[PI].sup.out] is increasing in [lambda]. If [v.sub.I] - [v.sub.II] < 0, the profit function [PI](e) is strictly concave and attains its maximum at e = [e.sup.com] > 0. Notice that [e.sup.out] = [e.sup.com] if [lambda] = [v.sub.I]/[v.sub.II] [member of] (0, 1). This implies that, treated as a function of [lambda], [[PI].sup.out] must be increasing for [lambda] [member of] (0, [v.sub.I]/[v.sub.II])and then decreasing for [lambda] [member of] ([v.sub.I]/[v.sub.II], 1). Q.E.D.

References

Aghion, Philippe, Mathias Dewatripont, and Patrick Rey. "Renegotiation Design with Unverifiable Information." Econometrica 62 (1994): 257-282.

Aghion, Philippe and Jean Tirole. "The Management of Innovation." Quarterly Journal of Economics 109 (1994): 1185-1209.

BusinessWeek. "Outsourcing Innovation." March 21, 2005, 84-94.

Che, Yeon-Koo and Donald B. Hausch. "Cooperative Investments and the Value of Contracting." American Economic Review 89 (1999): 125-147.

Chen, Yongmin. "Vertical Disintegration." Journal of Economics and Management Strategy 14 (2005): 209-229.

Edlin, Aaron and Stefan Reichelstein. "Holdups, Standard Breach Remedies, and Optimal Investment." American Economic Review 86 (1996): 478-501.

Fishman, Arthur and Rafael Rob. "Product Innovation by a Durable-Good Monopoly." Rand Journal of Economics 31 (2000): 237-252.

Fudenberg, Drew and Jean Tirole. "Upgrades, Tradeins, and Buybacks." Rand Journal of Economics 29 (1998): 235-258.

Grossman, Gene and Elhanan Helpman. "Integration versus Outsourcing in Industry Equilibrium." Quarterly Journal of Economics 117 (2002): 85-120.

McLaren, John. "Globalization and Vertical Structure." American Economic Review 90 (2000): 1239-1254.

Milgrom, Paul and John Roberts. Economics, Organization & Management. Englewood Cliffs, NJ: Prentice-Hall, 1992.

Noldeke, Georg and Klaus M. Schmidt. "Option Contracts and Renegotiation: A Solution to the Hold-up Problem." Rand Journal of Economics 26 (1995): 163-179.

Waldman, Michael. "Planned Obsolescence and the R&D Decision." Rand Journal of Economics 27 (1996): 583-595.

Notes

(1.) See BusinessWeek (2005) for more details of this trend.

(2.) Leading manufacturers of mobile phones like Motorola, Nokia, and Sony-Ericsson out source the design of low-end models while developing high-end models in house. Also, top producers of digital cameras such as Nikon and Canon are known to buy cheaper models from outside vendors.

(3.) This is only one aspect of the idea regarding make-or-buy decision. In fact, the concept may be explored in several different dimensions. Identifying core activities, for instance, leads to the question of scope economies. Developing core competencies over time involves a particular form of scale economies, namely learning-by-doing (see, e.g., Milgrom and Roberts (1992)).

(4.) There will be no qualitative change in the analysis even if one assumes that vertical integration involves additional costs, say 'governance cost', compared to outsourcing. In previous models with non-durable goods (e.g., Grossman and Helpman (2002) and McLaren (2000)), such an assumption becomes essential in order to obtain a non-trivial tradeoff between the two forms of organization.

(5.) Although the amount of improvement may not be verifiable, the amount of sales may be. Then, writing a contract contingent on sales becomes a potential alternative. Such a contract, however, will be meaningless as long as the pioneer's input is also non-verifiable. This is because the pioneer can always refuse to provide its input and hence hold up the out sourcee. As both the pioneer and the out sourcee have the power to block the production and hence the sales of an improvement, any initial contract contingent on sales will be renegotiated away as long as it does not give both parties their ex-post bargaining shares.

(6.) If secondhand market is prohibited by law, as in computer software, physical collection of used products is not necessary to implement price discrimination. Upgrades (Fudenberg and Tirole (1998)) then may be a less costly way to resolve the commitment problem.

(7.) The following quotes from BusinessWeek (2005) exemplify the prevalence of such a thinking. "You have to draw a line," said Edward J. Zander, the CEO of Motorola, "core intellectual property is above it, and commodity technology is below." Also, Pertti Korhonen, Nokia's Chief Technology Officer is quoted saying, "You have to figure out what is core and what is context."

Sanghoon Lee, School of Business Administration, Holy Family University, 9801 Frankford Avenue, Philadelphia, PA 19114; Phone (267)341-3522; Email slee@holyfamily.edu.