Multinational corporations control structure choices
under uncertainty environment
Ma Jianhua1, Ai Xingzheng2
1. Management and Economics, University of Electronic Science and Technology of China, Chengdu, China
2. Management and Economics, University of Electronic Science and Technology of China, Chengdu, China
1. majianhuamail@126.com, 2. aixz@uestc.edu.cn
Abstract: For a multinational corporation manufacturing and selling two kinds of substitute products under
the price as well as exchange rate uncertainty, what control structure would be chosen is tied closely to the
corporation performance. By calculating the equilibria and performance of both horizontal integration and
disintegration structures, we indentify the dominant control structure of the two-product multinational corporation. We furthermore analyze the impact of the degree of risk-aversion, substitute coefficient and risks on
control structure choice.
Keywords: uncertainty environment; risk aversion; control structure
1 Introduction
Multinational corporations often locate facilities all
over the world, and products flow across national boundaries, managers face the uncertainties and complexities
of the global environment. Exchange rate and price uncertainties are two of the complicating factors faced by
the multinational corporations. In particular, the fluctuations of price as well exchange rate can be significant
with drastic impact on multinational corporations control
structure choices. Multinational corporations often produce multi kinds of substitutable or complementary
products instead of only one kind. The horizontal centralized control structure means only one manager is employed to manage the production and sale of all kinds of
products, and the horizontal decentralized control structure means each kind of product is dominated by one
special manager. Then which one control structure
should be chosen by the headquarters? It is a matter of
importance, because the correct control structure is tied
closely to the firm performance. Usually, centralized
structure features the system with redundancy and inefficiency，but can copes with risks effectively, while decentralized structure just features contrarily. Hence, under the uncertainty environment, to reveal which control
structure can trade off the risks and the efficiency is very
important and practical for the multinational corporations.
There is a vast literature on the choice of the firm’s
internal control structure. One could start from the classical paper of Severinor[1], in which three organizational
forms- centralization, decentralization and delegation
-are compared, and it is found that the optimal organizational form depends on the degree of complementarity/substitutability between the inputs in the final use.
Hart and Moore[2], focusing on specialized assets, anaGrant from:Major Program of National Natural Science Foundation of
China (70932005); National Natural Science Foundation of China
(70772070)
lyzed the conditions under which the decentralized organization has the advantage over the centralized organization. Alonso etal [3] compared the centralized and the
decentralized coordination when managers are informed
privately and communicate strategically, and concluded
that decentralization dominated centralization if the divisions are not too biased towards their own divisions and
the divisions are not too different from each other.
Rankakari[4] investigated the impact of environment volatility and the cost of information on organization structure, with stable environments generally populated by
tightly integrated and centralized organizations and volatile environments generally populated by loosely integrated and decentralized organizations. Organization economics analyzed how the firms design
cross-functional coordination strategies, which needs to
pool the decentralized and incomplete information(Aoki[5]; Hart &Moore[2]; Alonso etal[3];Dessein et
al[6]). These literatures set focus on vertical control
structure of different echelons in the internal supply
chain, and considered the impact of internal organization
management costs caused by uncertainty environment,
delay costs, private information, degree of diversification
of resources on choice of control structure. It is considered that the performance of centralized coordination
under stable environment is dominant, while decentralized coordination is dominant under volatile environment
and different opportunities of employing business units.
The interaction of influence factors on the horizontal
control structures of the same echelon is scarcely studied.
Whether centralized or decentralized structure can result
in effective communication and coordination is always a
focus in Organization Economics, and there are some
literatures
(Shapiro[7];Montgomery&Hausman[8];Karmarkar&Lele[9]
) analyzed the necessity of the coordination to the potential conflict between different departments. Another kind
of literatures aimed at designing compensation mechanism in order to achieve more precise demand forecast(Gonik[10]; Rao[11]; Celikbas et al[12]; Chen [13]),
which can help to design operational projects more
effectively.
These studies simply put Principal-agent
theory into the vertical incentive mechanism design in
different echelons between headquarters and department
units, ignoring the super-additives effect on firm performance set by the interaction relation of the different department units. This paper will study the horizontal control structures of internal supply chain, in order to make
up for the sparseness of the study on internal supply
chain control structure.
This paper constructs the model of a multinational
corporation which product and sell two kinds of substitutable products, that is, two-product corporation. Depending on the controlling and management model of
two types of products, two horizontal control structures
of centralization and decentralization are classified. Under the price and exchange rate risks environment, by
comparing and calculating the equilibria and performance of centralized and decentralized structures, we
reveal the dominant control structure which can improve
the system performance. Meanwhile, we also analyze the
integrated impact of degree of risk aversion, risks and
substitutability on the choice of internal horizontal control structure, by which we provide the theory basis for
the multinational corporation to choice the internal control structure. The random variables in this paper are independent to each other, all information is common
knowledge, and the risk is represented by the variance of
the corresponding random variable.
pi  a  qi  bq3i , i  1,2;
a  a0  e, e ~ N (0, va ),
a , following the normal distribution with the
mean value of a 0 and the variance of va , can be
where
explained as the value of customer acceptance of the
product, va represents the degree of volatility of the
market price , and can be called the price risk for short.
b  (0,1) is the degree of product substitution, and the
bigger is the value of b which equivalently means the
higher is degree of substitution, the severer is the competition between two types of the product. pi and
qi are the retail price and the quantity for the product i ,
respectively. For convenience and without loss of generality, the marginal cost of each kind of product is the
same and with the sign of c , which is measured in the
domestic currency. r is the foreign market currency exchange rate in stage 2, that is, the value of one unit of the
foreign currency measure in the domestic currency, and
r is a random variable with the mean value of r0 and
the variance of
vr . We assumed that a0  r0c , which
is reasonable and can assure the marginal profit of the
product is positive.  presents the firm’s profit. The
utility functions of the manger(s) and the headquarters
are denoted by U M ( ) and U H ( ) , respectively.
2 The model
E () and V () present the expectation and variance
Consider a firm that produces two types of substitutable goods domestically, while sets production facility
in a foreign country because of the lower manufacturing
cost. We use a two-stage stochastic program to model the
firm’s decisions. In the first stage, a “product-production” plan for the production facility is developed by the manager(s). Under centralized control structure, there is a single manager who manage the production and the sale of two kinds of products; while under
the decentralized control structure, each type has one
special manger who exclusively manage the production
and the sale of the special type consequently, hence,
there are two managers employed by the shareholders.
The payment to the manager(s) depend on the revenue(s)
of the type(s) managed by him, and the manager(s)
is(are) under the administration of the headquarters
which is controlled by the shareholders of the corporations. The headquarters has the right to decide which
control structure to conduct. The manager(s) and the
shareholders(headquarters) are all risk aversion, and they
are all the Mean-Variance optimizers, while have the
different risk aversion attitudes.
The market price is given by the inverse demand
function
operator respectively. The superscript c and d indicate the centralized and decentralized control structure,
respectively.
3 The performance of the internal control
structure
3.1 The performance of the horizontal centralized control structure
Under the centralized structure, the production and
sale of two types of product are both managed by only
one manager. At the stage 1, the manager decides the
quantity of all products to produce in the foreign facility
to maximize his utility, which is the expectation-variance
utility function
1
U M ( )  E ( )  k MV ( ) ,
2
where k M ( 0) denotes the degree of the manager’s
risk aversion.
  (a  q1  bq2  cr )q1  (a  q2  bq1  cr)q2 ,
and
E ( )  (a0  q1  bq2  cr0 )q1  (a0  q2  bq1  cr0 )q2 ,
U M ( ) 
d
V ( )  (va  vr c 2 )( q1  q2 ) 2 .
The quantity decision hence is
q1  q2 
a0  cr0
.
2(b  k M vr c 2  k M va  1)
The expectation-variance utility function of the
headquarters is
1
U H ( )  E ( )  kV ( ) ,
2
where k ( 0) denotes the degree of the headquarters’
risk aversion. At stage 1, the expectation profit of the
system is
(a  cr0 ) 2 (2k M v r c 2  b  1  2k M v a ) ,
E ( c )  0
2(b  k M v r c 2  k M v a  1) 2
and the expectation utilities of the manager and the
headquarters are
(a 0  cr0 ) 2
c
,
U M ( ) 
2(b  k M v r c 2  k M v a  1)
(a  cr ) 2 (2k M vr c 2  kvr c 2  b  kva  2k M va  1) .
U H ( )  0 0
2(b  k M vr c 2  k M va  1) 2
c
U H ( ) 
d
(a0  cr0 ) 2 (2  k M vr c 2  k M va ) ,
( 2  b  k M vr c 2  k M va ) 2
2(a0  cr0 ) 2 (k M vr c 2  kvr c 2  1  kva  k M va ) .
(b  k M vr c 2  k M va  2) 2
3.3 The choice of the internal control structure
Let
 b  3  9b 2  14b  9
,
4k M c 2
vr 0 
1 b2 1
v r1 
( v r 0 ) ,
kM c 2
va 0 
 b  3  9b 2  14b  9
 vr c 2 ,
4k M
va1 
1  b2 1
 v r c 2  (v a 0 ) ,
4k M
A  3vr c2b  3vab  6vr c2kM va  3va kM
2
 4vr c 2  4va  3vr c 4 kM ,
2
B  b 2  b  bvr c 2 kM  bkM va  2vr kM c 2 M
3.2 The performance of the horizontal decentralized control structure
 3vr c4kM  2kM va  4k M vavr c2  3kM va 。
Proposition 1
For va  va 0 or vr  vr 0 ,
if
Under the decentralized structure, the production
and sale of each type of product has one special manager.
The subscripts 1 and 2 denote the first type and the
second type of product, respectively. At the stage 1, the
manager i (i  1,2) decides the quantity of product
0  k  B / A , there is U H ( )  U H ( ) , else if
i to maximize his expectation-variance utility function
U M i ( i )  (a  qi  bq3i )qi  crqi
1
2
 k M (va  vr c 2 )qi ,
2
where  i denotes the profit of the type i , and
  1 2 . k M
represents the degree of the manager
i ’s risk aversion, which for convenience is the same to
each other as well as the same to that of the manager’s
under centralized structure. The quantity decision hence
is
a0  cr0
q1  q2 
.
2  b  k M vr c 2  k M va
At stage 1, the expectation profit of the system is
E ( d ) 
2(a0  cr0 ) 2 (1  k M v r c 2  k M v a )
,
(2  b  k M v M c 2  k M v a ) 2
and the total expectations utilities of the two managers
and the headquarters are
2
2
2
2
2
c
d
k  B / A there is U H ( )  U H ( ) ; for
0  va  va 0 and 0  vr  vr 0 , there is
c
d
U H ( )  U H ( ) .
c
d
Proof
U H ( )  U H ( ) 
c
d
(a0  cr0 ) 2 (b  k M vr c 2  k M va )( Ak  B)
,
2(b  k M va  k M vr c 2  1) 2 (b  2  k M va  k M vr c 2 ) 2
the signal of the equation above is equivalent to
Ak  B . Obviously, A  0 , and B is a concave quadratic polynomial of va . It is easy to prove that v a 0 is
the positive solution of the equation B  0 . If va  0 ,
there is
B  b 2  b  bv r c 2 k M  3v r k M c 2  2v r c 4 k M ,
which is negative when 0  vr  vr 0 , and is positive
2
when
2
vr  vr 0 . The proposition 1 hence can be con-
cluded by the property of the quadratic polynomial. The
proof is completed.
Proposition 1 shows that when the price risk and
exchange risk are both less than the corresponding
thresholds, the utility of the headquarters under the centralized structure is dominant than that under the decen-
tralized structure. If the price risk or the exchange risk is
higher than the corresponding threshold, then if the degree of risk aversion of the headquarters is smaller
enough, the utility of the headquarters under the decentralized structure is dominant than that under the centralized structure, otherwise the utility of the headquarters
under the centralized structure is dominant. Hence, the
headquarters will choose the best internal control structure in term of the circumstances.
Proposition 2
For va  va 0 or vr  vr 0 ,
there is
E ( c )  E ( d ) ;
0  va  va 0 and
for
0  vr  vr 0 , there is E ( c )  E ( d ) .
The proof is similar to that of proposition 1, hence is
omitted here.
v a 0 , v r 0 are the thresholds of the price risk and the
exchange risk, respectively, and are both increasing
with the substitute degree b , decreasing with k M and
c . v a 0 is also decreasing with vr .
Proposition 2 indicates that when the price risk and
exchange risk are both less than the corresponding
thresholds, the expectation profit of the system under
centralized structure is better than that under the decentralized structure, and when If the price risk or the exchange risk is higher than the corresponding threshold,
the expectation profit of the system under decentralized
structure is better than that under the centralized structure.
Proposition 1 and proposition 2 imply that If condition va  va 0 , 0  k  B / A , or vr  vr 0 ,
0  k  B / A , or 0  va  va 0 , 0  vr  vr 0 is
satisfied, then the control structure chosen by the headquarters can bring firm dominant expectation profit, else
the control structure chosen by the headquarters can’t
bring the firm dominant expectation profit.
Proposition 3 For va  va1 or vr  vr1 , there is
U M ( )  U M ( )
c
d
;
for
0  va  va1
(v a , v r ) is in the set (0, va1 )  (0, vr1 ) , then the control structure chosen by the headquarters is just the dominant control structure of the manger(s) , else, the control
structure chosen by the headquarters is just not the dominant control structure of the manager(s).
4 Conclusion
For a two-product multinational corporation under
the price as well as exchange rate uncertainty, the headquarters will choose the internal control structure to
maximize their utility. If the price risk and exchange rate
risk are lower than the corresponding thresholds, the
centralized control structure will be chosen. If the price
risk or exchange rate risk is higher than the corresponding thresholds, the decentralized control structure will be
chosen for the case of the lower headquarters risk aversion degree, while the centralized control structure will
be chosen for the case of higher headquarters risk aversion degree. Consequently, we get to the conclusion that
the decentralized control structure will be dominant under the higher risk or the lower headquarters’ risk aversion; whereas, the centralized control structure will be
dominant under the lower risk or the higher headquarters’ risk aversion.
References
[1]
[2]
[3]
[4]
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[6]
[7]
and
[8]
The proof is similar to that of proposition 1, hence is
omitted here.
By proposition 1 and proposition 3, we know that for
if (v a , v r ) is in the set
0  k  B / A ,
[9]
(0, va1 )  (0, vr1 )
set
[11]
(va 0 ,)  (vr 0 ,) , then the control structure cho-
[12]
0  vr  vr1 , there is U M ( )  U M ( ) .
c
or
d
in
the
sen by the headquarters is just the dominant control
structure of the manger(s) , else, the control structure
chosen by the headquarters is just not the dominant control structure of the manager(s). For k  B / A , if
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