Economising, Strategising and the Vertical Boundaries of the firm

1 Introduction

This paper aims to shed light on the organisational and internationalisation strategies of firms in oligopolistic industries.

There has been a rapid expansion in outsourcing in recent years, with firms subcontracting activities as diverse as final assembly, R&D and after-sales services – both domestically and internationally. The growing importance of outsourcing, particularly across national borders, has resulted in a huge increase in interest in the factors determining the vertical boundaries of the firm and the “fragmentation” of the production in both the applied ^[1] and theoretical academic literatures.

The vertical boundaries of the firm have been analysed by two fairly distinct traditions in economics. ^[2] The first, within Organisational Economics, dates back to Coase (1937) and Williamson (1975, 1985, 1991) and treats vertical integration as a response to contractual frictions. The second, emerged within Industrial Economics, focuses on market structure (with or without oligopoly). By endogenising a firm’s make-or-buy trade-offs and showing how they are affected by its strategic interactions with competitors, this paper brings together the oligopolistic strategic strands of the Industrial Economics and the Organisational Economics literatures on the make-or-buy decision of the firm. In so doing, the paper contributes more broadly to the development of an “Organisational Industrial Organisation” (OIO) approach, as advocated by Legros and Newman (2014), capable of incorporating insights from incomplete contracting into industrial economics. ^[3]

The organisational economics strand of the theory has focussed on the incentives issues surrounding the emergence of the boundaries of the firm within bilateral (e. g. buyer-supplier) settings and studied the sources of transaction costs involved in market relations that can be overcome by vertical integration. Central to the bulk of this line of research is the concept of “hold-up problem” that arises, in the presence of contract incompleteness, from the need by one party to undertake relationship-specific investments that are of little value outside the particular relationship. In the transaction cost theory of the firm, vertical integration thus emerges as a solution to the hold-up problem.

Until fairly recently, its firm-pair level focus had to a great extent set the transaction cost tradition apart from strands of the industrial economics literature concerned with the role of market structure, as well as from areas that have developed from advances in microeconomic and industrial economic theory, e. g. “modern” international trade and investment theories. The last decade has seen the emergence of a number of path-breaking contributions that have succeeded in contextualising the bilateral buyer-supplier relationships within broader market structures that also allow for the incorporation of international interactions. ^[4] One group of papers endogenises the mode-of-operation choice in the presence of a specialised input within the property-right approach: see Antràs (2003, 2005), Antràs and Helpman (2004), Grossman and Helpman (2004), and Feenstra and Hanson (2005). ^[5] Another set of papers is based on the transaction cost approach and highlights the importance of “market thickness effects” (McLaren 2000; Grossman and Helpman 2002, 2005) for the emergence of bilateral buyer-supplier relationships. In both of these strands of the literature, the decision to outsource is endogenous, contracts are incomplete and the intermediate input is specialised and requires relationship-specific investment. ^[6] Their fundamental contribution is to embed the mode of operation decision of the firm within general equilibrium frameworks that can account for the role of the standard drivers of international trade specialisation (i. e., differences in factor endowments and/or product differentiation and love of variety). Given their emphasis on general equilibrium effects, however, these models (that are developed mostly within monopolistically competitive market structures) rule out by assumption the existence of strategic interaction between firms.

We argue that additional insights into the determinants of firms’ boundaries can be obtained by contextualising the transaction cost approach ^[7] to the make-or-buy decision of the firm within a broader market structure that is characterised by oligopolistic behaviour.

We develop a model in which final good production requires the use of a customised intermediate, and oligopolistic final good firms decide whether to source this input from a non-affiliated outside supplier or to produce it in-house. Downstream firms that outsource ^[8] enter a bilateral relationship with an upstream firm that must carry out a relationship-specific investment in the quality and customisation of the input. A major innovative feature of our model is that it fully endogenises the investment decision in the quality and customisation of the intermediate good. The endogeneity of the quality of the intermediate, in turn, translates into an endogenous marginal cost of production for the final good. As a result, our approach implies that the key trade-off at the core of the outsourcing decision does not, as in the bulk of the extant oligopolistic literature on the make-or-buy decision of the firm, exist by assumption, but emerges endogenously. A vertically integrated firm incurs additional governance costs that can be avoided by outsourcing. If the outside supplier is not significantly more efficient at providing the intermediate to the required specifications, however, outsourcing will raise the final good producer’s marginal production costs since, due to the hold-up problem that results from contract incompleteness, the supplier will tend to under-invest in the quality of the intermediate. Outsourcing then involves accepting higher marginal costs in exchange for a saving on governance costs. ^[9] This result provides a theoretical rationale for the stylised facts emerging from case studies and econometric analyses that outsourcing may not lead to increases in quality and/or reductions in production costs. ^[10]

However, while the traditional transaction cost approach places emphasis on the economising dimension of the make-or-buy decision of the firm, by embedding the endogenous emergence of the hold-up problem within a strategic setting, in our model strategic considerations interact with economising considerations in determining the mode-of-operation choice of firms. This interaction underpins the possibility that both strategic vertical integration and strategic outsourcing arise in equilibrium. We show that outsourcing by one firm reduces the investment of its rival: hence, outsourcing can be characterised as a defensive business strategy – in contrast to vertical integration that can be viewed as an aggressive business strategy. This is the most important result of our paper which is the first to identify this particular strategic incentive to outsource. Typically, in the literature, optimal governance structures are those that minimise overall efficiency losses. We show that, even though contract incompleteness with ex-ante costly private investment can lead to efficiency losses, the optimal governance structure may not be the one that minimises these losses: by affecting a rival’s behaviour, defensive outsourcing implies that it may be optimal to adopt an internal structure that is not in itself the most cost efficient if doing so softens the behaviour of rivals. We also demonstrate that the incentive to outsource is relatively greater for smaller/higher cost firms: given its effects on a rival’s investment, the strategic incentive to outsource is most effective when used by a less efficient firm against a highly efficient low cost and high investing rival.

Another result of our paper is that “mixed outcomes” can arise endogenously in equilibrium: even when they are ex-ante symmetric, firms may choose different modes of operation – resulting in different levels of investment in the customisation of the intermediate, and different final production costs and profitability. ^[11] The endogenous emergence of differences in mode-of-operation among firms thus contributes to explain observed inter-firm cost and performance heterogeneity (see, e. g. Syverson 2011) as well as offer a rationale for the stylised facts that not all firms in the same industry adopt the same mode of operation strategy.

An important contribution of the paper is therefore to examine the “make-or-buy” decision in a context in which final good firms compete on the product market as oligopolists and in which issues related to relationship-specific investment and incomplete contracts are also taken into account: in earlier oligopoly papers, the role of these key features of the transaction costs approach in determining the nature of the trade-offs facing firms when making their mode-of-operation decisions is disregarded. ^[12] Within a Cournot setting, Nickerson and Vanden Bergh (1999) show that organisational choices are affected by strategic considerations in the firm-customer transactions, but disregard transaction costs and contract incompleteness. Shy and Stenbacka (2003) show that competition in the upstream industry affects production efficiency and the choice in the mode-of-operation of a downstream differentiated Bertrand duopoly when vertical integration involves higher fixed costs but lower marginal costs. In their paper, the trade-off between fixed and marginal cost is however exogenous. ^[13]

A reason for the revival of interest in the literature on the boundaries of the firm has been the perceived relationship between outsourcing and globalisation. We apply our model to examine the effect of trade liberalisation on the mode-of-operation decision of firms and show how increased competitive pressure can affect the vertical structure of firms – further highlighting how market interaction effects are entwined with organisation decisions.

In Section 2, we start with the analysis of a monopoly model that will offer a useful reference point for the analysis of the effects of strategic interaction between firms. In Section 3, we set up and discuss the oligopoly model. Section 4 explores strategic behaviour first considering the case of ex-ante firm symmetry and then going on to discuss how it relates to inter-firm asymmetries showing that outsourcing can often be a defensive business strategy. In Section 5, we examine the effects of trade liberalisation on equilibrium outcomes and on the welfare of consumers. ^[14]Section 6 draws some conclusions from the analysis.

2 The Monopoly Model

In this section we consider the make-or-buy decision of a monopolist firm. This useful benchmark allows us to abstract from the strategic interaction between rival downstream firms. In the section that follows we will show what difference oligopolistic interaction makes to the mode-of-operation decision of the firms.

Consider a monopoly that produces a homogenous product. The inverse demand for the final good is given by:

where p and y are the price and quantity of the good respectively, and a and b are positive constants.

We assume that the production of the final good requires a non-generic intermediate component or service. The firm can choose a vertical integration strategy in which it invests in the development of and produces this input itself, or an outsourcing strategy in which it sources it from an outside unaffiliated supplier. Due to the specialised nature of the input, if the firm chooses to outsource, it will not be able to purchase the intermediate from a spot market. Instead it must buy it from a supplier that has made a relationship-specific investment (RSI) in the development of the input. ^[15]

Thus, we allow the firm to decide whether to become vertically integrated or to follow an outsourcing strategy. Specifically, the firm can make the intermediate in-house at a marginal cost of r or buy it from an upstream supplier at a price q. We assume that the intermediate must be combined in fixed proportions with other factors of production; we model these factors as a composite input whose price is normalised at unity. Units are chosen so that one unit of the customised intermediate is required per unit of output. Let e=eˉ−z>0 be the per-unit input requirement for the composite input, where eˉ is a constant and z captures the “usefulness” of the intermediate: a better intermediate, from the point of view of the downstream firm, is one that requires to be combined with fewer other inputs in order to produce a unit of output. Using the superscripts V and O to denote vertical integration and outsourcing respectively, the monopolist’s marginal production cost will thus be:

if the intermediate is produced in-house, and:

if it is outsourced.

Let K be investment in quality and customisation of the intermediate, with K=γz2/γz222. Thus, the usefulness of the input (z=2K/γ) increases in K but at a diminishing rate. The parameter γ determines the cost of investment in quality.

In line with the literature on vertical integration, we assume that vertically integrated firms incur fixed governance costs – à laWilliamson (1975, 1985) – that are higher than those of a firm that outsources; without loss of generality, we shall then set the fixed governance cost for the latter to zero. ^[16] If the firm is vertically integrated, its profit function is therefore given by:

where G represents the fixed component of the governance costs of running a larger and more complex organisation. ^[17] If the firm chooses to outsource, its profit function will therefore be:

Note that, by outsourcing, the firm avoids both the governance cost associated with vertical integration and the investment cost associated with the intermediate. The latter, is now borne by the upstream supplier. The supplier earns operating profit: (q−ru)m, where ru is the marginal cost it incurs in producing the intermediate and m is its output. Note that we assume that the marginal production cost of the intermediate can differ depending on whether it is produced in-house or by the upstream firm: thus, ru is not necessarily equal to r. Differences between ru and r can be due to a host of reasons – e. g. higher marginal costs associated with the governance of a vertically integrated firm, factor cost advantages that a supplier might enjoy, technological differences or differences in expertise between the firms. Making use of the fact that one unit of the intermediate is needed in the production of each unit of final output, we can write m = y. In addition to investment cost, the firm must pay a fixed entry cost F. Its total profit is:

The model is a four stage game. In stage one, the monopolist decides whether to outsource its intermediate or to produce it in-house. If it decides to outsource, the firm approaches a specialised supplier firm which will produce the input. In stage two, the downstream firm (if it is vertically integrated) or the supplier (if the downstream firm chooses to outsource) invest in the development of the intermediate. If outsourcing, in stage three the monopolist bargains with the intermediate supplier over the price of the input. We assume that the final good producer only has enough time to negotiate with a single supplier. As in Grossman and Helpman (2003), should bargaining breakdown, the producer will not have sufficient time to produce the intermediate itself, and so will exit the market – while the supplier will have wasted its investment. ^[18] In stage four, the intermediate is supplied and the final output is produced. ^[19]

We are concerned with the subgame perfect equilibria, hence the game is solved by backward induction. In the final stage, the monopolist’s outputs is determined by the following first-order conditions:

where c^h will vary depending on the mode-of-operation (h = V, O) chosen by the firm. The resulting equilibrium output will then be:

where (h = V, O).

In stage three, recognising that all fixed and investment costs are now sunk, the final good firm (if outsourcing) bargains with an upstream supplier over the price of its intermediate. The price q of the intermediate good results from the maximisation of the following Nash bargain:

where β and (1−β) represent the bargaining power of the downstream firm and its upstream partner respectively, with 0≤β≤1. Note that we have used m = y to eliminate m. Taking the first–order condition for the maximisation of N with respect to q and rearranging, we obtain:

The equilibrium mark-up of the intermediate supplier, q−ru, falls in the downstream firm’s bargaining power, but increases in its output y. ^[20] The rent-extracting ability of the intermediate firm will be higher, ceteris paribus, the weaker is the bargaining position of the final good producer and the larger is the latter’s output. Although q must be larger than ru, it needs not be higher than r. ^[21] Furthermore, even if q is lower than r, it may still be the case that the marginal production cost of a vertically integrated firm is lower than that of a downstream firm that chooses to outsource. This is because the final good marginal production cost also depends on the quality of the intermediate and thus on the level of investment in its development. As we shall see, in fact, the level of investment may be lower under outsourcing.

In stage 2, the firms (either the downstream monopolist when it vertically integrates, or the intermediate supplier when the former outsources) choose their investment levels. We can model this decision as firms choosing the level of z, since this is directly related to that of investment. A firm that produces the intermediate in-house, will choose z to maximise eq. [3a]. The corporate governance costs, G, have already been sunk before the firm invests so they play no part in the optimal choice of investment levels. Thus, the vertically integrated firm first-order condition is:

which implies

and where η=1/bγ is a measure of the effectiveness of investment.

If the intermediate is outsourced, then the investment is carried out by the upstream firm which only receives a share (determined by its bargaining power) of the rent generated by the investment; as a result, it does not fully appropriate the marginal benefit of its investment and this reduces its incentive to invest. We can use eq. [8] in eq. [4] to obtain:

The first order condition for the profit maximising choice of z is then:

where b(dy/dz)=−12(dcO/dz) from eq. [6] and dcO/dz=(dq/dz)−1 from eq. [2b]. Notice that investment affects the marginal cost both directly and through a change in the negotiated price of the input. We can make use of eq. [8] in the above to obtain b(dy/dz)=(1+β)/4. We can then eliminate b(dy/dz)in eq. [12]. Rearranging, this implies

Thus, vertical integration results in a higher investment to output ratio than outsourcing.

In the first stage of the game, the monopolist chooses its mode-of-operation. To establish whether the firm will choose to outsource or to be vertically integrated, we must compare its profits under the two regimes. To facilitate this comparison, it proves helpful to derive an expression for the profits in terms of outputs and parameters only. By using the first-order conditions in eqs [5] and [10], we can rewrite the profit functions in the two regimes respectively as:

and

It is immediately obvious from eqs [14a] and [14b], that a sufficient condition for outsourcing to yield higher profits is yO≥yV. Another way to state this sufficient condition is to say that outsourcing must yield higher profits if cO≤cV. Hence, if outsourcing results in an increase in output (perhaps because the marginal cost of producing the intermediate is so much lower if it is carried out by a specialised upstream producer), then it dominates vertical integration.

3 The Oligopoly Model

We now extend the model of the previous section and allow for two oligopolistic final good firms (labelled 1 and 2) serving the same market and producing a homogenous product. ^[22] To begin with, we shall not need to specify the international trade context. Thus, the two firms can be thought of as competing on a home market, a foreign market, or an integrated market such as would exist in a customs union. We will be more specific in Section 5, where we shall consider a number of alternative trading setups in order to analyse the effects of trade liberalisation. ^[23]

Let y1 and y2 be the quantities produced by firm 1 and 2 respectively, with y=y1+y2. The inverse demand for the final good is given by expression [1] above.

We allow both firms to decide whether to become vertically integrated or to follow an outsourcing strategy. Each firm i = 1, 2 can make the intermediate in-house at a marginal cost of ri or buy it from an upstream supplier at the price qi. We assume that if both outsourcing, the firms use different specialised producers. We allow for the possibility that firms have different efficiencies hence the marginal costs of downstream firms are firm specific. Thus, modifying eqs [2a] and [2b], the marginal production cost for firm i = 1, 2 will be: ciV=ri+eˉi−zi if the intermediate is produced in-house and: ciO=qi+eˉi−zi if it is outsourced. The profit functions for firms under the different modes of operation are appropriately modified versions of those in the monopoly case (expressions [3] and [4]).Thus, profits of the downstream firms are: πiV=(p−ciV)yi−Ki−G and πiO=(p−ciO)yi (i = 1, 2) under vertical integration and outsourcing, respectively. The upstream firms’ profits are: μi=(qi−riu)yi−Ki−F (i = 1, 2).

As in the monopoly case, the model is a four stage game. In stage one, the downstream firms simultaneously decide whether to outsource their intermediate or to produce it in-house. In stage two, the firms simultaneously invest in the development of intermediates. In stage three, the firms that outsource bargain with their intermediate suppliers over the price of the input. When both firms outsource, the two upstream and downstream pairs bargain simultaneously. In stage four, the intermediate is supplied and final outputs are chosen simultaneously.

In the final stage, the two firms engage in Cournot competition. The resulting equilibrium output of firm i will then be:

where (h, k = V, O) and (i, j = 1, 2) with (i≠j).

In stage three, if outsourcing, the final good firms bargain with an upstream supplier over the price of their intermediate. Again, let β and (1−β) represent the bargaining power of the typical downstream firm and its upstream partner respectively, with 0≤β≤1. Then, maximisation of the Nash bargain Ni=(p−ciO)yiβ(qi−riu)yi1−β of bargaining pair i yields the following intermediate good price:

In stage 2, the firms choose their investment levels. We first examine the investment decision of a downstream firm that produces the intermediate in-house. In making its investment decision, the firm takes account of both the direct cost-reducing effect of its investment on its own profit and the strategic effect on its rival’s output in the final stage. Thus, firm i’s first-order condition is:

where the first term on the right-hand side, ∂πi/∂zi=−∂ciV/∂ziyi−γzi=yi−γzi, is the direct effect of z_i on own profits. The second term captures the strategic effect on the investment decision of the firm. Specifically, in the second term, ∂πi/∂yj=yip′=−byi. The expression for the term dyj/dzi differs depending on the mode-of-operation of firm j. If the rival firm j is vertically integrated, then dyj/dzi=(1/3b)(∂ciV/∂zi)=−1/3b. Thus, in this case, the strategic effect ∂πi/∂yjdyj/dzi is positive and hence encourages the firm to invest more in the development of the intermediate good. The first-order condition for a firm that is vertically integrated and faces a vertically integrated rival can then be rewritten as:

We adopt the convention that, when there are two superscripts, the first refers to firm i and the second to firm j. ^[24] If, instead, the rival firm j outsources, then even though firm i’s first-order condition takes the same form as in eq. [17], the derivative dyj/dzi is different, as z_i now also affects yj through changes in qj. Hence, the strategic incentive for firm i’s investment is lessened as a result of the endogenous change in the price of the intermediate because now dyj/dzi = (1/3b)(∂ciV/∂zi)−(2/3b)(∂cjO/∂zi), with the derivative dcjO/dzi=dqj/dzi=(3/2)[(1−β)/(1+β)]bdyj/dzi. Rearranging, we get: dyj/dzi=−(1/6b)(1+β)<0, the absolute value of which is less than that in the vertical integration case (where dyj/dzi = –1/3b) except when β=1, that is when downstream firms have has maximum bargaining power in its negotiations with the supplier firm. Thus, the first-order condition for a vertically integrated firm facing a rival that outsources can be rewritten as:

Therefore, since θVO≤ θVV, outsourcing by one firm “softens” the behaviour of its rival, i. e. it reduces its aggressiveness in investment. We will return to this issue later when we discuss the strategic motive for outsourcing.

If the intermediate is outsourced, then the investment is carried out by the upstream partner. We can use eq. [16] in the expression for upstream profits to obtain:

The first order condition for the profit maximising choice of z_i is then:

The expression for dyi/dzi differs depending on whether the rival is vertically integrated or outsourcing. When the rival is vertically integrated, it is straightforward to combine ciO=qi+eˉi−zi and eq. [15] to show that dyi/dzi=−(2/3b)(∂ci/∂zi)+(∂ci/∂qi)(dqi/dzi) which simplifies to: dyi/dzi=(1+βi)/3b>0. We can use this in eq. [20] to obtain:

However, when the rival firm is outsourcing, then straightforward (if lengthy) calculations show that the effect of z_i on y_i becomes dyi/dzi=(2/3b)(7+β)(1+β)/(15+2β−β2)>0. The use of this in eq. [20] yields:

Again, since θOO≤θOV, outsourcing by one firm “softens” the investment behaviour of its rival in the sense that zi/yi is lower when its rival outsources its intermediate than when it chooses to vertically integrate.

Furthermore, as in Lemma 1 for the monopoly case, vertical integration implies a more aggressive investment strategy than outsourcing.

In the first stage of the game, the firms simultaneously choose their mode-of-operation. To establish whether a firm will choose to outsource or to be vertically integrated, we must compare its profits under the two regimes for a given mode-of-operation choice of its rival. To facilitate this comparison, it proves helpful to derive an expression for the profits in terms of outputs and parameters only. By using the first-order conditions for output and investment, we can rewrite the profit functions in the two regimes respectively as:

and

where k = (V, O), ΩVV=(1−89η) and ΩVO=1−(7+β)272η.

4 The Mode-of-Operation Equilibria: Aggressive and Defensive Business Strategies

We turn now to the discussion of the mode-of-operation equilibria. There are four possible candidate equilibrium regimes: (VV), (VO), (OV), and (OO), where the first letter refers to the mode-of-operation selected by firm 1 and the second letter refers to that chosen by firm 2.

Our model is quite rich and there are many possible asymmetries between firms. Later in this section we explore firm behaviour in the presence of asymmetric underlying costs. However, to introduce the importance of adding strategy to the transaction cost approach, we shall begin with the case of ex-ante symmetry. Specifically, we assume that the downstream firms are ex ante identical, in that neither firm has an underlying cost advantage, and that the upstream firms are also ex ante identical to each other. We also assume that there is no underlying marginal cost advantage or disadvantage from outsourcing – i. e., the marginal production cost of the input is the same regardless of whether it is made by the downstream or by the upstream supplier (i. e. ri=riu). With this setup, we obtain the following proposition:

Proof. See Appendix.

Hence, for a range of G, asymmetric outcomes emerge despite the fact that the firms are fully symmetric ex ante.The underlying reason for this derives from a negative interdependence between the firms’ mode-of-operation decisions. Vertical integration, which entails exchanging higher fixed costs for lower marginal costs, is a higher output strategy. Outsourcing involves trading off lower fixed costs for higher marginal costs and is a lower output strategy. ^[25]

Both strategising and economising considerations are at work in determining the equilibrium outcomes; in particular, oligopolistic strategic interaction means that – even when firms are ex-ante symmetric – asymmetric equilibria (in which firms choose different mode-of-operation strategies) can emerge.

It is important to clarify that although the asymmetric result in Proposition 1 depends on there being a trade-off between fixed and variable production costs, and on the fact that firms are engaged in quantity competition, it does not require the presence of investment in customisation and endogenous input quality. Indeed, a similar result is obtained by Buehler and Schmutzler (2005), in the context of vertical mergers without investment, endogenous input quality or incomplete contracts. However, our setting implies that even with full ex-ante symmetry, strategic behaviour can generate asymmetric ex-post outcomes not only in terms of mode-of-operation, but also in terms of marginal costs and investment levels.

A better appreciation of how strategic behaviour can be used to soften a rival’s investment and output decisions can be gained by considering underlying asymmetries between firms, to which we now turn. As highlighted in Lemma 2, outsourcing by one firm softens the investment behaviour of its rival. This gives rise to a “strategic motive” to outsource. This strategic feature arises from oligopolistic interaction and is of course absent in the monopoly model discussed in Section 2. We now show how the choice of the mode-of-operation can be used strategically by firms to affect the oligopoly game between them. To this end, we ask how the make-or-buy decision affects the equilibrium market shares and profit levels. A natural approach to answering this question is to consider the effect of the mode-of-operation on the firms’ output reaction functions and thus on outputs. The reaction function of firm i, that is obtained from the first-order condition ∂πi∂yi=p−cih−byi=0, can be written as yi=ψi(yj; ci). Note that the effect of outsourcing on ci occurs via changes in zi and qi. It therefore proves useful, by making appropriate substitutions given the solutions of previous stages of the game, to eliminate zi and qi. The resulting functions, which we call output response functions, ^[26] take account of the indirect effect of outsourcing on outputs through changes in the level of investment and the price of the intermediate good. We will use these functions to illustrate what happens when one of the firms chooses to outsource rather than to vertically integrate. In the absence of outsourcing, these output response functions for firm 1 and firm 2 are, respectively:

and

where A=(a−eˉ1−r1) and MVV=(2−θVVη). The parameter Φ=eˉ2+r2−eˉ1−r1 can be thought of as the underlying (“pre-investment”) marginal cost disadvantage of firm 2 which can reflect relative productivity differences (of course Φ could be negative, giving firm 2 an ex ante cost advantage). When firm 2 chooses to outsource but firm 1 remains vertically integrated, the corresponding output response functions are:

and

where M1VO=(2−θVOη) and M2VO=7+β−2η(1−β2)/2(1+β). Note that here we are using the first superscript to refer to firm 1 and the second to firm 2. Thus, y2VO is the output of firm 2 when firm 1 is vertically integrated and firm 2 is outsourcing. The parameter ρ2=r2−r2u captures the difference between the marginal costs of producing the intermediate incurred by the downstream firm 2 (when it is vertically integrated) and by its upstream intermediate supplier. Thus, when ρ2>0, the upstream firm has a cost advantage over the downstream firm in producing the intermediate.

These functions are illustrated in Figure 1. In the figure, we assume ex ante symmetry between the firms, so that Φ=0, and allow for both ρ2=0 and ρ2>0. We begin by discussing the case in which ρ2=0 and shall return to consider the case in which ρ2>0 later in the section. The curves labelled R1 and R2 are the output response functions for firm 1 and 2 respectively when both firms are vertically integrated. The equilibrium is at point E. The curve labelled R1′ is the output response function of firm 1 when firm 2 outsources the intermediate; the curve labelled R2′ is the output response function of firm 2 when it outsources. In this case, the corresponding equilibrium is at point E′. Inspection of eqs [23] and [24] reveals that, at ρ2=0, a switch to outsourcing by firm 2 does not affect the zero-output intercept of these curves (which depend only on the terms in the numerators). It does, however, lead to a pivoting inwards of firm 2’s output response function about the zero-output point – provided that MVV<M2VO, which is the case illustrated in the figure. ^[27] The reason why firm 2’s output response function pivots inwards is twofold. First, the firm now faces a higher marginal cost of the intermediate, as the upstream firm captures some of the available rents. Second, the investment behaviour is now less aggressive as explained earlier. Firm 1’s output response function always pivots inwards when its rival outsources, as MVV<M1VO given that θVV>θVO. At the new equilibrium E′, total production is lower.

Figure 1:

Output response functions (Φ = 0).

The effect of outsourcing on firms’ market shares will depend on Φ, the extent of the relative cost difference between the two firms. When Φ is small (as in Figure 1), so that the firms have ex-ante very similar efficiencies, outsourcing by firm 2 lowers its market share and raises the market share of firm 1. This does not imply, however, that outsourcing necessarily reduces firm 2’s profits, since it must be remembered that it also saves on governance costs. When Φ is large enough, i. e. when firm 2 is sufficiently less efficient than its competitor, then the market share shifting effect of outsourcing is reversed. We show this in Figure 2 in which ρ₂ = 0 and Φ is large. Compared to Figure 1, firm 2’s output response functions have moved inward. Inspection of eqs [23] and [24] reveals that firm 1’s output response curves are independent of Φ, whilst an increase in Φ shifts firm 2’s output response functions inwards in a parallel manner. In Figure 2, outsourcing by firm 2 increases its own market share at the expense of firm 1. As we have seen, the change in regime between outsourcing and vertical integration causes the output response curves to pivot around the firms’ zero output points. Thus, the effect of outsourcing on an output response curve is greater the further away we are from the firm’s zero output point. When Φ is high, firm 2’s relative market share is small and the negative impact of outsourcing on firm 2’s output response curve is locally very small, while the negative effect on the corresponding curve for firm 1 is locally much larger. The net result is that firm 1’s output falls and firm 2’s output rises.

Figure 2:

Output response functions (Φ is large and ρ2 = 0).

The results obtained so far in this section can be summarised by the following proposition:

Note that the seemingly paradoxical result that y2VO>y2VV when Φ is very large, despite an inward shift of the output response curve, is due to the strategic interaction between firms under oligopoly and does not occur under monopoly. The firm’s decision to outsource can raise its own market share when the effect on the strategic aggressiveness of its rival is very strong. This is more likely to be the case the larger is the rival’s market share in the equilibrium with vertical integration; the reason for this is that the bigger and more powerful is one’s competitor, the larger is the gain from reducing its aggressiveness. ^[28] In this sense, outsourcing can be thought of as a defensive business strategy helping a firm to hold on to its market share and, in some cases, to remain in business when it otherwise would not. Because of this strategic effect, under oligopoly, outsourcing can sometimes be optimal even when it is unambiguously cost increasing. ^[29]

As we saw in the previous section, y2VO≥y2VV is a sufficient condition for π2VO > π2VV. Thus, even when ρ₂ = 0 (or even when ρ2 is not too negative), outsourcing is preferred if, due to an underlying cost disadvantage, firm 2’s market share is small enough. Thus we have the following corollary to Proposition 2(ii):

These results are in stark contrast to the monopoly case, where firms have an incentive to outsource only if it involves some cost saving.

When vertical integration reduces the rival’s output it can be seen as an aggressive business strategy. This is the case for firm 2 when Φ is not too large, as in Figure 1, when the firm has a strategic incentive to vertically integrate.

Sometimes outsourcing can lead to much lower production costs than in-house production. This is the case when the upstream firm is much more efficient than its downstream partner in producing the intermediate. Thus, we can see in Figure 1 that if ρ2>0, then firm 2’s output response function, in addition to pivoting inward, also shifts outwards in a parallel manner. A comparison of eqs [23] and [24] reveals that whilst firm 2 switching to outsourcing does not affect the numerator in the output response function for firm 1, it will affect that of firm 2 if ρ2>0 – i. e. when the underlying marginal cost of producing the intermediate is lower under outsourcing than under vertical integration. Note that outsourcing can be an aggressive business strategy that raises foreign output at the expense of firm 1 (as illustrated in Figure 1) even when Φ is zero. For this to happen, however, ρ2 needs to be positive and very large. In Figure 1, the dotted curve labelled R2′′ is the output response function of firm 2 when it outsources and ρ2 is large enough to cause its equilibrium output to rise.

5 Outsourcing and International Trade

A major reason for the upsurge of interest in the literature on the mode-of-operation decision of firms has been the perception that there is a positive relationship between outsourcing and trade liberalisation. However, it is noteworthy that much outsourcing is actually domestic in character, being carried out within national boundaries. Also, firms can offshore production of intermediates while keeping them in house through foreign direct investment. Thus, how globalisation and trade policy affect the internalisation decision of a firm depends on whether the outsourcing or the vertical integration is domestic or international. In this section, we will apply our model to a number of different trading setups in order to examine how the internationalisation and internalisation strategies of firms interact. Specifically, we will examine the effect of trade liberalisation, modelled as a fall in trade costs, on the incentives of firms to outsource – and thus on the mode-of-operation equilibria. We will show that changes in trade costs can have an impact on these incentives by affecting the underlying cost differences between firms. Thus, for instance, if firms are located in different countries, then trade liberalisation can affect their costs of supplying a market asymmetrically. We discuss this case in Section 5.1. Trade liberalisation can also affect firms’ costs by making it relatively cheaper to procure inputs from abroad; we discuss this in Section 5.2.

5.1 Trade Liberalisation as an Intensification of Competitive Pressure

In this subsection we consider how outsourcing can be a response to an increase in foreign competition resulting from trade liberalisation. To examine this, we consider the following setup: downstream firm 1 is located in the home country while firm 2 produces its final good in a foreign location. The firms compete on the home market. To focus on the effect of trade liberalisation on the relative incentive to outsource via the intensification of competitive pressure route, we will assume that firms outsource from domestic suppliers, i. e. we rule out international outsourcing. The effect of trade liberalisation on the relative cost of foreign outsourcing will be discussed in the next subsection. Clearly, one could consider a setup with foreign outsourcing that combines the two effects, but this would yield less transparent results.

The trade costs faced by firm 2 will be parameterized by a per-unit tariff τ. This can be neatly incorporated into the firm’s marginal cost by including it in eˉ2. As a result, the cost difference parameter Φ is now increasing in the tariff. Trade liberalisation will reduce Φ and this will have implications for output, prices and investment under a given regime and, under certain circumstances, it will also lead to a regime shift. We shall begin by examining the effects of trade liberalization within a given regime and then consider its effects on regime outcomes.

Under a given regime, a fall in τ improves the relative competitive position of firm 2 at the expense of firm 1 and this will yield a market share reallocation in favour of the former. Under outsourcing, this market share reallocation results in a fall in the negotiated price of the intermediate good in the home country. This is because trade liberalisation decreases the available rents to be bargained over by the home downstream and upstream firms.

A fall in trade costs can also lead to regime shifts as it can affect firms’ decisions about their mode-of-operation. A fall in τ (and hence in Φ) will increase the incentive of firm 2 and decrease the incentive of firm 1 to choose vertical integration. ^[30]

In Figure 3, at free-trade, firm 2 has an underlying cost advantage. In notational terms: Φ < 0 at τ = 0. Giving firm 2 a cost advantage at free-trade allows us to present cases in which Φ is positive and cases in which it is negative on the same diagram. At high values of τ (Φ > 0), firm 1 has a cost advantage, while at low values of τ (Φ < 0), firm 2 has a cost advantage. ^[31]

Figure 3:

The effects of trade liberalisation when the foreign firm has an underlying cost advantage in the absence of a tariff.

As can be seen from the figure, ^[32] at sufficiently low levels of governance costs, and with Φ > 0, a fall in τ will eventually lead to a switch from the (V, O) to the (V, V) regime (as firm 1 stays vertically integrated and firm 2 is induced to change regime). At negative values of Φ, further trade liberalisation can result in a switch from (V, V) to (O, V). At sufficiently high levels of governance costs, and with Φ > 0, trade liberalisation leads to a move from (V, O) to (O, O), as firm 1 is induced to outsource whilst firm 2 remains outsourced. When Φ < 0, further reductions in trade costs can result in a shift to the (O, V) equilibrium region.

In Figure 3, we see that (V, O) is the typical outcome when τ is high and hence firm 2 has a strong competitive disadvantage; however, for low trade costs, (O, V) can emerge as the competitive advantage swings towards firm 2. Also note that the range of G over which multiple equilibria occurs is at its largest when Φ is zero.

Finally, it is interesting to briefly explore the implications of the analysis for the effects of trade liberalisation on the consumer in the home country. With this particular trading set up, trade liberalisation at a given regime raises output and thus works to increase consumer surplus. This increase in consumer surplus is further enhanced when the fall in trade cost reaches a threshold level of τ that causes firm 2 to switch to vertical integration. This is because when firm 2 switches to vertical integration, both its own output and that of the industry experience a discrete upward jump. However, a tariff reduction will lead to a discrete downward jump in consumer surplus when it results in the crossing of a threshold τ that brings about a switch to outsourcing by firm 1. This implies that, somewhat counter-intuitively, consumer surplus is not always maximised at free-trade.

5.2. Trade liberalisation and the costs of international outsourcing

Trade liberalisation may also change the relative cost of outsourcing. This is particularly plausible if the firms have the possibility to outsource abroad. To disentangle the effect of trade costs on the costs of outsourcing from the effect of trade costs on the competitive pressure faced by firms, we shall assume that the two downstream firms are located in the same country or in a customs union so that further trade liberalisation does not affect the ex-ante relative cost differences between them. To begin with, we shall focus on the case in which the firm chooses between domestic vertical integration and foreign outsourcing – i. e. we shall rule out the possibility of vertical foreign direct investment. We again parameterize trade cost by a per-unit tariff τ. To deliver the input to the home country when a firm outsources from abroad, the firm must pay τ per unit of output. ^[33] This can be neatly incorporated into the firm’s profits by adding it to its marginal costs when the firm outsources abroad, but not when it produces the intermediate in-house domestically. When we adopt this specification, the parameter ρi – which captures the difference between the marginal costs of producing the intermediate incurred by the downstream firm and its upstream outsourcing partner – is decreasing in the tariff.

Figure 4 illustrates the effect of trade liberalisation on the mode-of-operation when the two firms are ex-ante symmetric but the upstream firms have lower marginal production costs than the downstream firms. Unsurprisingly, a fall in tariff leads to an increase in the range of parameter values at which firms outsource. Interestingly, once again, trade liberalisation does not necessarily have a monotonic effect on consumer surplus if it leads to more outsourcing – since a switch to outsourcing will lead to an upward jump in the price of the good.

Figure 4:

Domestic vertical integration versus international outsourcing: trade liberalisation favours outsourcing.

We have now seen two routes by which trade liberalisation may encourage outsourcing. However, we will now consider a setup in which, by contrast, trade liberalisation leads to more vertical integration. Suppose that the costs of setting up a fully owned subsidiary in which the intermediate can be developed and produced are not prohibitively high, as we had implicitly assumed above by ruling out this mode-of-operation option. Instead, assume now that foreign vertical integration dominates domestic vertical integration – perhaps because production or investment costs are lower abroad than in the home country. Hence, the relevant trade-off is now between international outsourcing and international vertical integration. We will refer to the latter as FDI. Assume that under both outsourcing and vertical integration the downstream firm must pay a trade cost of τ per unit of output to deliver this input to the home country where it is combined with the composite input. In the interests of clarity, we continue to assume that the firms are ex-ante symmetric. In order to focus on the trade-off between the different modes of operation, we restrict attention to parameter values that imply a lower ex-post marginal production cost for the final producer under FDI than under outsourcing. Outsourcing however involves a lower fixed cost. This is due to lower investment and governance costs.

We find that in this case trade liberalisation reduces the amount of outsourcing relative to FDI. There are two main reasons for this. First, in exchange for facing higher fixed costs, the firms that choose FDI have a higher output scale than those that outsource. This is because they have lower marginal costs under vertical integration. This means that any fall in per unit trade costs applies to a larger output level under FDI and hence is more beneficial to firms choosing the FDI option. Second, trade liberalisation raises the available rents – but this increases the opportunity for rent extraction by the upstream firm under outsourcing. A fall in trade costs thus leads to an increase in the bargained intermediate price and this reduces some of the benefit of trade liberalisation to the downstream firm.

The effect of trade liberalisation on the mode-of-operation outcomes when the trade-off is between FDI and international outsourcing is illustrated in Figure 5.

Figure 5:

International vertical integration (FDI) versus international outsourcing: trade liberalisation favours FDI.

6 Concluding Remarks

In this paper we have developed a model of endogenous outsourcing in an oligopoly setting. In showing that the choices of firms’ organisational boundaries affect and are affected by a firm’s strategic interaction with its competitors, the paper takes a major step towards a more realistic analysis of the make-or-buy decision and obtains a number of new results that contribute to our understanding of the vertical boundaries of the firm.

In line with some other recent theoretical contributions, the outsourcing arrangement is modelled as one where a final good producer enters a bilateral relationship with an upstream supplier which undertakes a relationship-specific investment. Previous authors who have adopted this approach have done so within non-strategic environments (either a single buyer-supplier pair, or a monopolistically competitive market structure). In addition, we are the first within the oligopoly literature on outsourcing to fully endogenise the investment decision in the quality and customisation of the intermediate good. This enables us to endogenise the trade-off between lower governance costs and higher marginal production costs that lies at the core of the make-or-buy decision, and that exists by assumption in the extant oligopoly strand of the literature. Thus, in our model, the choice of the mode-of-operation by firms is shown to be more complex than that implied by standard transaction cost theory and to depend on the combined influence of cost considerations (the incentive to economise) and strategic considerations.

We have demonstrated that the interaction between the oligopolistic setup and contract incompleteness implies that additional strategic considerations play a role in explaining the choice of mode-of-operation of firms, and that these considerations underpin the possible emergence of both strategic vertical integration and strategic outsourcing. In particular, we have shown how the interaction between strategic behaviour and the endogeneity of marginal costs can produce our novel result that outsourcing – even when it leads to lower overall cost efficiency – can be used as a defensive business strategy. This is because when a firm chooses outsourcing, the rival firm’s incentive to invest strategically is reduced. This implies that, when it has a sufficiently small market share under vertical integration, a firm has an incentive to strategically switch to outsourcing so as to increase its own and reduce its rival’s investment and output (which also implies that smaller, less productive, firms have a greater incentive to outsource). In a Cournot oligopoly setting, we also show that there exists an additional strategic incentive to vertically integrate – as the lower marginal costs reduce the rival’s output and thus indirectly raise the integrated firm’s profits.

Thus, our framework enables us to provide a theoretical rationale for the important stylised fact (emerging from case studies and econometric analyses) that outsourcing may not lead to the hoped-for increases in quality or reductions in production costs: even if a supplier has an underlying cost advantage, vertical integration may be preferable if contractual incompleteness results in underinvestment and a lower quality of the intermediate.

Furthermore, unlike most contributions in the outsourcing literature (e. g. Grossman and Helpman, 2002), this model gives rise to the possibility of “mixed outcomes” in which, even when firms are ex-ante symmetric, they may choose different modes of operation in equilibrium; this is consistent with existing stylised facts whereby not all firms in the same industry adopt the same mode-of-operation.

In the paper, we have assumed Cournot competition. It is fairly straightforward to extend our framework to Bertrand competition with heterogeneous goods. In that case, to the extent that outsourcing increases the marginal cost of production, the novel strategic incentive to outsource that we find as a result of the endogeneity of investment would be reinforced by a standard Bertrand strategic incentive to raise the rival’s price.

Finally, we examined the effects of trade liberalisation on the relative incentive to outsource. Trade liberalisation can mean that domestic firms face tougher competition and a firm under greater competitive pressure is shown to have a greater incentive to outsource. Furthermore, trade liberalisation can also reduce the cost of international outsourcing. If the relevant trade-off is between domestic vertical integration and international outsourcing, then trade liberalisation increases the incentive to outsource. However, if international vertical integration in the form of FDI is the viable alternative to outsourcing, then our model suggests that trade liberalisation actually reduces the incentive to outsource.

A number possible avenues for future research suggest themselves. As pointed out by a referee, an interesting one would be to consider the case in which more than one stage of the production process can be outsourced, resulting in a richer characterisation of strategies and behaviours.