Spoiling synergy

Abstract

Assets may be complementary–producing more return together–but substitute at the margin–generating lower marginal return when assets are together, leading agents to underinvest. When the effort effect dominates the synergy effect, merging complementary assets may not be efficient.

Full text

Spoiling synergy:
When complementarity fosters indolence
By Roland Bel*, Vladimir Smirnovb, Andrew Waitb
Abstract
Assets (or agents, activities) may be complementary – they produce more
return when performed together – but substitute at the margin – the return
of an extra effort is lower than when the activities are independent, leading
agents to underinvest. When the effort effect dominates the synergy effect,
merging complementary assets may not be efficient. This result has
implications for mergers and acquisitions. In particular, agents may
engage in inefficient mergers, while principals may forego efficient
mergers.
Key words: complementarity; synergy; mergers
JEL Classification: D21; L23
I. Introduction
Complements go together, and this intuition has been applied to the allocation of tasks
within an organization and to the choice of team members (see Brickley et al., 2009 for
example). This reasoning also underlies the prediction in the property-rights model that
complementary assets should be owned together (Hart and Moore, 1990). In contrast, this
paper presents a model in which complementary assets should not always be used
together.
Complementary assets (or agents, activities) generate a higher level of surplus together
than when they are separate, for a given level of effort. However, complementary assets
can be substitutes at the margin – merging them decreases the marginal return of effort.
Consequently, as their marginal return from effort is lower, agents have a decreased
incentive to put in effort when assets are merged: With substitution at the margin, the
* Kedge Business School, Marseille, France. email: roland.bel@kedgebs.com. Roland Bel would like to
thank University of Sydney for their support and hospitality. b School of Economics, The university of
Sydney, NSW 2006, Australia
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presence of complementary assets crowds out incentives to invest (Bel, 2013). In fact
marginal substitution involves substitution between investment and assets. When the
complementarity of assets ‘automatically’ brings additional return, why make extra
effort? There is a spoiling effect of synergy, which can have crucial consequences. The
loss in surplus from lower levels of effort when assets are merged might outweigh the
synergy coming from complementarity, meaning that complementary assets should
indeed not be merged.
Our study is closely related to the literature on the paradoxes of synergy. Synergies, for
example in the form of economies of scope (Panzar and Willig, 1981) are a key
motivation for mergers and acquisitions. But most mergers destroy value and synergies
fail to materialize, especially in mergers of related businesses (Chatterjee, 2007), or are
offset by post-merger transaction costs, leading to ‘dissynergy’ (Jones and Hill, 1988).
The integration of previously independent activities adversely affects the merger outcome
through agency costs (Jensen, 1986), influence costs (Rajan et al., 2000), contagion or
capacity effect (Shaver, 2006), or coordination costs arising from managing task
interdependencies (Jones and Hill, 1988), implementing and maintaining coordinated
production (Hill and Hoskisson, 1987), or monitoring the interdependencies between
different business lines (Penrose, 1959). The present study investigates the consequences
of a different phenomenon: synergy may endogenously crowd out effort through a
substitution effect. In a way, there is a parallel with the literature on incentives in teams.
In this literature, the work environment, being the flow of information (Winter, 2010) or
the composition of the team (Bel et al., 2015), may affect investment incentives,
sometimes leading to incentive reversal, a situation where higher rewards induce some
agents to reduce their effort (Winter, 2009). We show here that asset complementarity
may have a similar effect1.
Two assets (or resources or activities) are generally viewed as complementary when
the marginal return with one asset increases in the presence of the other, i.e. if the
production function is supermodular in assets (Milgrom and Roberts, 1990). Using the
theory of supermodularity, several authors (e.g., Siggelkow, 2002, Cassiman and
1 Nevertheless, the mechanism underlying reduced investment is different here. It is a substitution effect,
not the relative difference in marginal returns between complementary and independent agents (Bel et al.,
2015) or the systematic investment of another agent (Winter, 2009, 2010), that drives the results.
2

Veugelers, 2006; Stieglitz and Heine, 2007; Hess and Rothaermel, 2011) have studied the
effect of asset complementarity or substitution, but it is not always clear whether those
scholars consider the effect among assets – i.e. whether the cross-partial derivative
between assets is positive or negative – or between assets and investment – considering
the cross-partial derivative with respect to investment and assets. Our purpose here is to
make this mechanism explicit. Complementarity among assets does not prevent
substitution between investment and assets; and this is precisely this substitution effect
that may overcome the advantage of synergy.
II. The model and results
Consider a model with a principal and two agents2. A principal owns two physical
assets and that are necessary for ‘production’. The agents and can
independently make some human capital investment3 on their respective asset,
at a cost to produce an output . The principal is
considering merging the two assets to benefit from some complementarities. With the
merged assets, the agents would produce . are
standard concave twice differentiable production functions. The assets are said to be
complementary if the marginal benefit of an asset increases with the presence of the
second asset4, i.e. if . Or, assuming
:
In other words, the assets are complementary if the combined output is greater than the
sum of the individual outputs, keeping investment levels constant. The value
represents the synergy between the two assets, which
are complementary if .
2 This model can be extended both in terms of the number of agents and the exact nature of the synergies
between them.
3 Throughout the paper, we will use the terms investment or effort indifferently.
4 See Milgrom and Roberts (1990) for a definition of complementarity.
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Assets can be complementary but this is not necessarily the case at the margin and it is
possible that , i.e.:
11\*
MERGEFORMAT ()
With substitution at the margin, when investment increases, the return increases less
when the second asset is present. Hence, with higher investment the advantage of the
complementary asset decreases and the benefit of synergy decreases with investment.
Inequation 1 above is equivalent to:
Result 1. When assets are complementary but substitutes at the margin, the benefit of
synergy is decreasing in effort.
When assets are substitutes at the margin, the presence of an additional asset interacts
with the level of investment. Assets are not directly substitutes among themselves (in fact
they are complementary), but they are substitutes to investment5. The presence of the
additional asset decreases the incentive to invest of the first agent and the benefit of
synergy is lower when investment is higher. For example, a repair shop and a car dealer
may be complementary in a sense that additional customers who bought their car from
the dealer may come to the repair shop and additional customers come to the car dealer
secured by the presence of a repair shop for their maintenance. For the owner of the
repair shop, increasing his marketing efforts results in attracting new customers, reducing
the additional benefits brought by the presence of the car dealer, as a large part of the
additional synergetic customers have been brought to the shop by the extra marketing
5 Consider the following production function: , where is the investment by
and . The assets are complementary if and substitutes at the margin if
. The cross-partial derivative between assets and investments is negative, which is
precisely the definition of substitution between investments and assets (see Milgrom and Roberts, 1990).
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efforts. In a way, the marketing efforts are substitute to the synergy, and increased
marketing efforts crowd out the benefits of synergy.
At date 0, the principal can choose to merge or not to merge the two assets to
maximize ex ante surplus. At date 1, the agents choose their level of relationship-specific
non-contractible effort. Finally, and at date 2, the agents bargain over the share of surplus
with the principal. Following the literature, we assume that ex post surplus is distributed
according to a linear bargaining solution (for example the Shapley value). Furthermore,
no date 1 variable is contractible at date 0.
Equilibrium Investments
The principal (and its assets) and the agents are indispensable. The bargaining power of
the principal is such that her share of ex-post surplus is6:
,
The ex ante payoff for each agent is then:
In the merger, anticipating bargaining, the agents set their effort to maximise their ex ante
payoff, and the equilibrium level of effort is given by:
On the other hand, when the assets are independent, the equilibrium level of investment
by the agents is given by:
Given the concavity of the production functions:
6 The bargaining power on (which is assumed to be identical with each agent) may be different from the
bargaining power on , since the principal has to bargain independently with each agent on , but with
the two agents on .
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Proposition 1. When the assets are complementary but substitutes at the margin, agents
invest a lower level of effort after merger.
In the example above, the existence of the synergy between the car dealer and the repair
shop materializes with additional synergetic customers that reduce the repair shop
owner’s incentives to invest in marketing.
Social welfare
Welfare will be higher with [without] a merger if and only if:
22\*
MERGEFORMAT ()
In a first-best world the agents would choose their level of effort, respectively with
merged and independent assets, so that:
33\*
MERGEFORMAT ()
44\*
MERGEFORMAT ()
Comparing 3 and 2, it turns out that welfare is always higher with a merger.
However, in an incomplete contract setting, the agents choose their level of investment
to maximize their individual ex ante net surplus. In a merger it means that:
55\*
MERGEFORMAT ()
Whereas, when the assets are independent:
Summing for both agents, these two conditions become respectively (where
, , , ):
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66\*
MERGEFORMAT ()
77\*
MERGEFORMAT ()
From inequation 2, welfare will increase [decrease] with a merger if:
88\*
MERGEFORMAT ()
Comparing 6 and 8, it turns out that a sufficient condition for welfare to increase with a
merger is:
99\*
MERGEFORMAT ()
Comparing 7 and 8, a sufficient condition for welfare to be higher when assets are
separate is7:
Proposition 2. (i) When the assets are complementary but substitutes at the margin, a
merger is socially efficient if (ii) Conversely, a merger is
inefficient if .
The intuition for the result is best shown with Figure 1. The synergy is monotonically
decreasing in effort . The marginal return of is lower in a merger, and the agents’
7 Note that since .
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equilibrium investment level . The two effects – the synergy from the merger and
the higher effort with separate assets – work in different directions. It is possible, as
shown in Figure 1, that the effort effect dominates the synergy effect, and welfare is
higher with separate assets. The above Proposition highlights the maximum and
minimum values of that assure respectively an efficient or inefficient merger. In-
between those values the efficiency of the merger is uncertain.
Figure 1: Effort levels and surplus with merged and independent assets
Decision to merge
Substitution at the margin (or decreasing synergy) has several consequences. If the agents
(and not the principal) decide on the merger, they will choose to merge if:
1010\*
MERGEFORMAT ()
Comparing 10 to 5, the agents will always choose to merge, even if it is not socially
efficient, leading to inefficient merger when .
8

When the principal takes the decision, she will decide to merge if
, i.e. if:
1111\*
MERGEFORMAT ()
It turns out from Proposition 2 that when the principal chooses to merge, the merger is
always socially efficient. On the other hand, the principal may renounce a merger when it
could have been socially efficient, resulting in a lost opportunity.
Finally, human capital investment (let alone its cost) being not observable, the criteria for
the efficiency of a merger is often taken by comparing the ex-post surplus of the merger
with the ex-post surplus when the two activities are separate8. The ex-post surplus
increases [decreases] with a merger if , i.e. if . It
turns out from inequation 11 that, when , the principal may choose to merge even if
ex-post surplus will decrease, but also from 9 that an efficient merger might exhibit
decreasing ex-post value (the merger will be said to be pseudo-inefficient). The different
cases when the principal or the agents take the decision are summarized in the following
Proposition.
Proposition 3. The following merger decisions will be taken.
- An efficient merger when (it is pseudo-inefficient if )
- A lost opportunity if the principal decides or an efficient merger (pseudo-inefficient if
) if the agents decide, when
- An uncertain decision not to merge (sometimes a lost opportunity) by the principal or
an uncertain merger (sometimes inefficient) by the agents, when
8 In empirical studies, value creation or value destruction is generally assessed without accounting for the
human capital efforts invested by the agents.
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- An efficient decision not to merge by the principal or an inefficient merger by the
agents when
III. Conclusion
When contracts are incomplete, a merger of complementary activities may be inefficient
if they are substitute at the margin. Substitution at the margin generates a trade-off
between intrinsic synergy and lower effort that may result in inefficient mergers or lost
opportunities.
Consider a market in which consumers potentially purchase a computer and a printer.
Given their complementary nature, if consumers buy a computer of a particular brand
they are more likely to purchase a printer from the same company, other things equal.
However, this complementarity could lessen the incentive of a salesperson to put in effort
given the fact that a customer is more likely to buy the complementary printer from her.
If the loss in firm value from lower sales effort is sufficiently large, a firm selling
computers should not sell the related product. While a merger between the computer and
printing firms would increase profitability for a given level of sales effort, the merger
could be inefficient if it reduces incentives.
This phenomenon contradicts the standard prediction in the property-rights literature
that complementary assets should be owned together (Hart and Moore, 1990, for
example). In Hart and Moore (1990), this prediction depends critically on the assumption
that marginal and total values are correlated (their assumptions 5 and 6). This conjecture
is not innocuous, and allowing for a more general relationship between total and marginal
surplus suggests that there are times when complementary assets should not be owned
together.
Those inefficiencies in mergers are compounded by the identity of the agent who takes
the decision to merge, whose interests may diverge from maximizing social welfare. In
particular, principals may forego efficient mergers while agents may engage in inefficient
mergers. Overall, mergers can be efficient, pseudo-inefficient or inefficient all together.
On the other hand, the decision not to merge can be efficient or inefficient, leading to lost
opportunities.
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