5.2 Innovation Incentives
We now study how partial backward ownership affects the innovation incentives. For a profit share
\(\delta _{i}>0\) that firm
i obtains in
U, the equilibrium downstream profit is a weighted sum of the outside option flow profit—
\(\pi (c^{I},c^{U})\)—and the equilibrium flow profits:
\(\pi (c^{U},c^{U})\)—see Eq. (
4). Recall that when
\(c^{U}\) decreases, the deviation profit
\(\pi (c^{I},c^{U})\) decreases, but the actual flow profit
\(\pi (c^{U},c^{U})\) increases. As
\(\delta _{i}\) increases, the weight on
\(\pi (c^{I},c^{U})\) decreases, and the weight on
\(\pi (c^{U},c^{U})\) increases.
To understand better the knowledge-sharing incentives, we take the derivative of the downstream firms
i’s profit, Eq. (
4), with respect to
\(c^{U}\) and solve for the critical level of partial ownership that ensures that
\(\partial (\pi _{i}-f_{i}+\delta _{i}\cdot \pi ^{U})/\partial c^{U}>0\). This yields that for any partial ownership level
$$\begin{aligned} \delta _{i}>{\widetilde{\delta }}:=\dfrac{\partial \pi (c^{I},c^{U})/\partial c^{U}}{\sum _{j\ne i}\frac{1}{1-\delta _{j}}\cdot [\partial \pi (c^{I},c^{U})/\partial c^{U}-\partial \pi (c^{U},c^{U})/\partial c^{U}]}\in (0,1), \end{aligned}$$
technology sharing with
U is profitable. The critical level
\({\widetilde{\delta }}\) lies in the feasible range of (0, 1) as
\(\partial \pi (c^{I},c^{U})/\partial c^{U}>0\) and
\(\partial \pi (c^{U},c^{U})/\partial c^{U}<0\). We summarize the results in the following proposition.
Proposition
2 shows that a large enough backward ownership share—a share close to 100% is always sufficient—makes the sharing of cost-reducing technology with
U incentive-compatible for the downstream firm. This is because partial ownership allows participation in the upstream flow profits and thus the gains from a reduction in
\(c^{U}\). Participation in upstream profits can also be achieved through bargaining over tariffs. In Sect.
6.1, we show that large enough downstream bargaining power can also align knowledge sharing incentives.
It is important to note that this critical threshold of partial ownership falls in the ownership shares of its rivals. This implies that as
i’s rivals increase their ownership stake in
U, the ownership requirement is less stringent for
i to share knowledge of cost-reducing technology. To provide intuition, we rewrite the profit of downstream firm i expressed in Eq. (
4), as
$$\begin{aligned} \pi _{i}-f_{i}+\delta _{i}\cdot \pi ^{U}=\pi (c^{I},c^{U})+\delta _{i}\sum _{j\ne i}\underbrace{\frac{(\pi (c^{U},c^{U})-\pi (c^{I},c^{U}))}{1-\delta _{j}}}_{f_{j}}. \end{aligned}$$
(5)
An increase in the ownership stake of a rival downstream firm increases the fixed fee of the rival firm (see Lemma
3). This increases the supplier’s profits which also benefits firm
i through its ownership stake
\(\delta _{i}\). In particular, the relative weight of
\(\pi (c^{U},c^{U})\) in the profit of firm i increases (see Eq.
5). As a result, a smaller ownership stake
\(\delta _{i}\) is needed to ensure that knowledge sharing by firm
i occurs.
Technology sharing with
U does not imply that there is no incentive for technology sharing with
I. Instead, it is clear from Eq. (
4) that sharing cost-reducing technology with
I increases the profit of a downstream firm and it therefore always shares technology with
I. Moreover, we show that for
\(\delta _{i}>{\widetilde{\delta }},\) downstream firm
i shares cost-reducing knowledge with
U as well under the threat that in the event of a contractual breakdown, it sources its input from
I. This way the downstream firm maximizes the profit that it obtains through its supply relationship with
U. This is summarized below.
Even if a downstream firm’s incentives are to share cost-reducing knowledge with
U, it still wants to maximize the surplus extraction for a given ownership level. Increasing the outside option profit
\(\pi (c^{I},c^{U})\) increases the downstream firm’s equilibrium profit, as can be observed in Eq. (
4). This profit increases if the cost-reducing technology is shared with
I. Therefore, even with partial ownership, downstream firm
i induces innovation in the alternative supplier to maximize its profits.
We do not consider the case of a vertical merger (which involves
\(\delta _{i}=100\%\)) as it allows full control of firm
U. In this article, we are interested in aligning the incentives of a downstream firm
i with the industry incentives without endowing full control to the downstream firms.
30 Moreover, a vertical merger might not be feasible, either due to financial constraints or anti-trust concerns. Anti-trust concerns can arise as the merged entity can prevent any cost-reducing knowledge spillover to rivals. This implies that the knowledge is now used to improve the production process for the benefit of the downstream entity and to the detriment of its rivals. With a large enough ownership share, knowledge sharing occurs and is used to improve the total production process. This leads to an industry efficiency enhancement while a vertical merger improves the production process only for the merged entity. This result is valid due to the assumption in our paper that technology transfer is costless.
Instead, if the technology transfer is costly, then transferring technology to the inefficient supplier implies a waste of resources. This is an example of burning resources to improve the terms of trade.
31 Depending on the technology and the process of technology transfer, it might not be feasible to share knowledge with a second firm. Formally, the costs of knowledge transfer could be convex so that it is prohibitively costly to share knowledge with a second supplier.
32 In this case, partial backward ownership can induce the downstream firm(s) to redirect the technology transfer from the inefficient to the efficient supply source. To further fix ideas, we discuss how partial ownership affects the amount of knowledge sharing.
Relationship between backward ownership and the amount of knowledge sharing
Suppose that downstream firm
i can share information that decreases the cost
\(c^{U}\) of the efficient supplier. Sharing more information decreases the cost more but sharing information is increasingly costly. Suppose that the cost for downstream firm
i of reducing the cost
\(c^{U}\) is given by
\(\phi (k)\) with
\(\phi (0)=0\),
\(\phi '(k)>0\) and
\(\phi ''(k)>0\). The profit of the downstream firm thus becomes
\(\pi _{i}-f_{i}+\delta _{i}\cdot \pi ^{U}-\phi (\Delta )\), which equals
$$\begin{aligned} \pi (c^{I},c^{U}-k)\left[ 1-\delta _{i}\sum _{j\ne i}\frac{1}{1-\delta _{j}}\right] +\pi (c^{U}-k,c^{U}-k)\left[ \delta _{i}\sum _{j\ne i}\frac{1}{1-\delta _{j}}\right] -\phi (k). \end{aligned}$$
Recall that the profit of
i increases when
\(\Delta\) increases through the term
\(\pi (c^{U}-\Delta ,c^{U}-\Delta )\) but decreases through
\(\pi (c^{I},c^{U}-\Delta )\) and
\(\phi (\Delta )\). As the relative weight of
\(\pi (c^{U}-\Delta ,c^{U}-\Delta )\) increases in
\(\delta _{i}\), the optimal choice of
\(\Delta\) increases in
\(\delta _{i}\) as well. In other words, more cost reductions at
U through knowledge sharing occurs when the ownership share is higher.
Consequently, other things equal, a downstream firm tends to share more (or, more costly) information if the backward ownership share is higher.
Knowledge sharing by several downstream firms
It might be that all downstream firms could potentially induce cost-reducing innovations at the common supplier. For instance, each downstream firm could, with certainty or some probability, induce a different innovation, such that the cost reductions add up. One could also imagine that there is complementarity across downstream firms such that each firm needs to have incentives to cooperate in order to achieve an upstream innovation.
33 In this case, it is desirable to align the incentives of all downstream firms. Suppose that all downstream firms have the same ownership share
\(\delta\). The profit of a downstream firm stated in Eq. (
4) decreases to
$$\begin{aligned} \pi _{i}-f_{i}&+\delta \pi ^{U}=\pi (c^{I},c^{U})\left[ 1-(n-1)\frac{\delta }{1-\delta }\right] +\pi (c^{U},c^{U})\left[ (n-1)\frac{\delta }{1-\delta }\right] . \end{aligned}$$
(6)
We observe that, at
\(\delta =0\), the downstream firm’s profit on the right-hand side of Eq. (
6) equals
\(\pi (c^{I},c^{U})\), whereas for
\(\delta =1/n\), it equals
\(\pi (c^{U},c^{U})\).
34 Recall that the derivative of
\(\pi (c^{I},c^{U})\) with respect to
\(c^{U}\) is positive, whereas the derivative of
\(\pi (c^{U},c^{U})\) with respect to
\(c^{U}\) is negative. While a share of 1/
n perfectly aligns the incentives with respect to industry profits, a smaller share is sufficient for downstream profits to increase when supplier
U becomes more efficient—when
\(c^{U}\) decreases—and thus for efficient innovations to occur. Therefore, we can conclude that there exists a threshold
\(\underline{{\delta }}\) with
\(0<\underline{{\delta }}<1/n\), such that for any
\(\delta \in ({{\underline{{\delta }}},1/n})\) each downstream firm’s profit increases when the efficient supplier’s cost
\(c^{U}\) decreases.
To further fix ideas, suppose that each downstream firm has a symmetric non-controlling backward ownership share of 1/n. A downstream firm’s equilibrium profit is \(\pi (c^{U},c^{U})\) and each downstream firm is willing to induce innovations that reduce the costs \(c^{U}\) of supplier U, while no downstream firm has an incentive to reduce the production costs \(c^{I}\) of the alternative supply source.
We abstract here from the question of corporate control of
U—which is not central to our main arguments, but is a natural question when the
n downstream firms together have all the profit rights of
U. In principle, it may still be the case that an outside investor with no or hardly any profit rights holds a “golden share” or has other rights of control.
35