Multiple product positioning : a note on incorporating effects of synergy

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FACULTY WORKING
PAPER NO. 1048

Multiple Product Positioning: A Note
on Incorporating Effects of Synergy

D. Sudharshan
K. Ravi Kumar

THE LIBRARY OR DOffi

JUL 6 1984

UNIVERSITY OF ILLINOIS
URBANA CHAMPAIGN

College of Commerce and Business Administration
Bureau of Economic and Business Research
University of Illinois, Urbana-Champaign

BEBR

FACULTY WORKING PAPER NO. 1048
College of Commerce and Business Administration
University of Illinois at Urbana-Champaign
June 1984

Multiple Product Positioning: A Note
on Incorporating Effects of Synergy

D. Sudharshan, Assistant Professor
Department of Business Administration

K. Ravi Kumar, Assistant Professor
Department of Business Administration

Abstract
This paper proposes formal models of synergy for incorporation
into analytical methods for product-market planning. It is also
demonstrated that some conventional inferences about multiple product
performance might be substantially revised if synergies among such
products are considered.

1.0 Introduction

There are several factors that affect the determination of the
exact positions of entry of multiple-products into a market. Some of
these are 1) consumer preferences, which has received the greatest
attention in the marketing research literature, 2) competitive reac-
tions, which has been modeled in the economics research literature
using gaming behavior, and 3) product interaction, in the form of can-
nibalization and synergy. While potential cannibalization has been
explicitly incorporated, the effects of synergy have not. Consider-
able synergies between products positioned in the same product market
can be obtained through production, distribution and administration.
Syngergy from promotion is also possible, depending largely on the
strategic decision as to whether such an effect should be developed.
Thus, when a firm having multiple products in a product market is con-
sidering introducing a new product into this market or when a firm is
thinking of introducing multiple new products into a market, it should
incorporate not only the deleterious effects of cannibalization, but
also evaluate and incorporate the positive effects (called synergy)
between multiple products in its analysis. For example, consider the
perceptual map used by Chrysler (Exhibit 1). General Motors
Corporation (in this map) has five positions under the names Cadillac,
Buick, Oldsmobile, Pontiac, and Chevrolet. In areas of highest
expected profitable demand, it has multiple brands, e.g., Buick and
Oldsmobile. We expect that taking advantage of the synergy from
production technology from Toyota and GM, design from Toyota, plant
facilities from GM, and marketing/distribution from both GM and

_?_

PERCEPTUAL MAP- BRAND IMAGES

~._^. • Lacoia
CadHlic*

Merre>*fs»

0

#3uick

HAS » TOt CT1 OF CLASS
U«rD BE PWXT) TOO%X
DISTlNfr.VE LOOSING

• Parses*

ro\<ER\ \riAF

LOOKING
\PPF XU- TO
OLDER PFOPtF

' Plyrr.wi!: <

• Dr.

S<*rc-e C*<-r-

H\>i SPIRITED

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vn no pf on*

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\T\>RTY LOOklM.

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PRt>\ !l>»> . ,OOD liAS MILEAGE

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Exhibit 1
(Source: Wall Street Journal, , March, 1984.)

-3-

Toyota, the new GM-Toyota product will be in the southeast quadrant,
competing more with the Datsuns and the Hondas. Obviously one would
expect some cannibalization of their existing brand shares, but in the
aggregate, considering synergy and capturing share from competitors
(and a larger share of new consumers entering this market), the new
portfolio of products in this market is expected to be more profit-
able.

In this paper, we discuss how these three factors, namely consumer
preferences, competitive reactions and product interactions, can be
jointly analytically modelled. Explicit forms for synergistic
interactions are developed and a computational methodology specified
for the calculation of the optimal positions of the products.

2.0 Brief Review of Literature

In the marketing strategy literature, several models have emerged
for generating an optimal new product concept for a specified product
market. Consumer preferences are modeled as being measurable using
conjoint analysis — a special case of which is the ideal point model.
See Shocker and Srinivasan (1979), Green and Srinivasan (1978), and
Sudharshan (1982) for recent overviews of this literature.

Typically, the research in this area has conceived of the problem
as one of optimizing, say, preference shares with resource allocation
and technical feasibility modelled as constraints — a non-linear
programming problem with non-linear constraints (Shocker and
Srinivasan, 1974). Alternative solution procedures have been
suggested [Albers and Brockoff (1979), Zufryden (1979), May, Shocker
and Sudarshan (1983)] and their relative merits evaluated in simulated

-4-

market environments by May, Shocker and Sudharshan (1983). These
methods, while being important contributions to this area of strategic
market planning, need to consider some additional effects, namely the
effects of possible competitive reactions and synergy, in their frame-
work. (The deleterious effects of cannibalization have been explicitly
modelled and accounted for in the objective function specified by
Shocker and Srinivasan (1974)).

The fundamental work on product positioning in the economics
literature came in the form of spatial location of firms. Hotelling
(1929) modelled the markets based on homogeneous products, competitive
reaction from firms based on gaming behavior and used the concept of
equilibrium to generate optimum positioning strategies. Extensions of
this basic work has been conducted by Leland (1974), Lancaster (1975)
and Spence (1976). Lane (1980), building on Lancaster's work, models
the consumer preferences based on two attributes of the product, per-
fect information availability and non-cooperative gaming behavior by
the firms in deciding individual product characteristics and prices.
However, he introduces a major assumption that all firms operate with
perfect foresight which makes it unnecessary for any changes in stra-
tegy by any firm. Hauser and Shugan (1984) have built on Lane's work
by introducing marketing variables, such as responsiveness of consumer
demand to both advertising and distribution expenditures. They
attempt to understand product market structures with emphasis and
thrust on establishing the optimal strategy a firm should follow given
that its product is being attacked by a specified new product. They
do not, however, attempt to find the optimal new product strategy

-5-

(position, advertising effort, distribution effort and price). Also,
their modelling of competition involves the reactions of only imme-
diately local (adjacent) product firms ignoring the reactions of other
firms in the market. This is a restrictive assumption and does not
permit a complete understanding of the realignment of all firms' stra-
tegies after new product entry.

In the models considered so far (to the best of our knowledge),
evaluation of products for new product entry is considered only for
a single new product at a time. The market place (for consumer non-
durable products and automobiles) is replete with firms having
multiple products in the same product market (e.g. , Procter and
Gamble, Colgate Palmolive, General Foods, etc.). These firms also
appear to have a policy for such positioning of multiple products in a
given market. It appears obvious, therefore, that a priori knowledge
is available that multiple products are to be positioned. Thus it is
equally obvious that an attempt should be made to consider such
multiple positions (if possible) simultaneously. Even in the case of
single new product entering into a market where the firm has one or
more existing products already, analysis has so far been restricted to
incorporating the possible effects of cannibalization. The effects of
synergy have not been explicitly incorporated in such models. In the
strategic management area, Hofer and Schendel (1978) specify synergy
as one of the four components of strategy, the others being scope,
resource deployments and competitive advantages. They specify that
synergy becomes very important at the business level and the func-
tional level strategic planning with focus on product line, market

-6-

development and distribution, R&D and manufacturing system design.
Abell and Hammond (1979, pp. 125-127) refer to this synergistic effect
as "shared experience," as does Henderson (1979, p. 107), and state:
"Opportunities for shared experience must be carefully sought,
analyzed, and exploited to gain cost advantage over competition,
especially in diversified companies. By focussing new product efforts
where shared experience plays a major role, a firm can build diversity
and strength."

In the next section, we will put together the factors that affect
multiple-product entry strategies in an analytical model that draws on
the existing marketing and economics research and adds to it explicit
accounting for product-interactions and the computational solution
method for obtaining equilibrium product positioning strategies.

3.0 The Basic Model

The situation that we would like to describe as the outcome of our
model is that of a firm that introduces multiple products in the same
product market. The basic model incorporates both the consumer choice
problem and also the supply side strategy decision problem. Non-
cooperative competition interaction between the actor firms is
assumed. We also incorporate the effects of synergy between a firm's
own products and permit firms to have objectives other than that of
maximizing profit (for the latter, see Anderson (1983)).

We expect a natural limit on the number of products that a firm
desires in a given market. The intuition behind this expectation is
premised on the following logic:

-7-

1) The modelling of synergy as first decreasing costs with
increasing number of products. However, beyond a critical point,
managing several products becomes cumbersome and costs actually
increase. This is consistent with the concept of the "focused factory'
in production management (Skinner (1974), Schmenner (1983)). These
would naturally limit the number of products that a firm might desire
to position in any given market.

2) Use of return on investment (ROI) as the objective of the firm
rather than profit. Consider a firm with just one product in a prod-
uct market. Let its revenue be AS, and let AF, be its fixed costs.
With the addition of a second product in the same market, let its
incremental sales be AS~ and the incremental fixed cost be AF„ with
AF2 < AF, (due to synergy). It is possible that

AS + AS? AS,
■ <

AF, + AF2 AFj^

i.e., the ROI after introduction of the second product is lower than

the ROI with just the first product.

In general, two possible stopping rules could exist:

a) If a firm has a hurdle rate (R) to be crossed for new product

entry, then the firm will choose the number of products n such that

AS, + AS„ + .. . + AS

2 n > R

and

AF, + AF„ + ... + AF
12 n

AS, + AS~ + ... + AS ,.

1 2 Dli < D

AF, + AF0 + ... + AF J,
1 2 n+1

b) Under ROI maximization, the number of products n will be such
that

n

I
i=l

AS.

1

n

I
i=l

AF.

1

is maximum.

To capture this intuition in a sample model, let us assume a three

product market, the size of the number of products being exogeneously

set and each product differentiated by two attributes. Following Lane

(1980), we specify a consumer choice model for product i as

a.
a. = J X vf(a)do, i-1,2,3

Vl

where a. is the quantity demanded of product i, v is the number of

units consumed by each customer (assumed to equal one in this model),

each consumer is associated with a unique value of the parameter a,

which is distributed on the interval [0,1] with density function f(a).

Note that a = 0 and a = 1. Let M be the total market demand for

this product and let it be exogeneously specified. Further, let f(a)

be uniform and under these conditions, f(a) = M and

a. = M(o -a. , )

l i i-l

= M0 , 1*1,2,3

where Q. is the market share of product i. We can conceptualize the
market distributed over [0,1] as being partitioned into three mutually

exclusive connected sets M. where

l

-9-

Mj - [0,o1], M2 = [alta2]t M3 = [a2,l]

as shown below:

Product

1

Product
2

Product
3

where a is the customer indifferent between products 1 and 2 and a
is the customer indifferent between products 2 and 3. (See Hauser and
Shugan (1984) for a similar consumer preference distribution.)

To specify the indifferent customers, one needs to specify the
consumer choice function and following Lane (1980), let it be of the
Cobb-Douglas form given by:

TT a (1-a). . .too

U = w.z. (Y-P.), i=l,2,3

a li l ' ' '

where w. and z . are the amounts of the two characteristics contained
l l

in product i, P. is the price of product i, a identifying (as before)
the individual consumer (whose behavior is being described), and Y is
the consumer's income. This allows us to obtain a closed-form solu-
tion for a., i=l,2, given by:

in (-2- * -i)

S v

-10-

22 * (Y-IV

S V

(See Lane (1980), p. 244 for this derivation.) This clearly gives a

closed-form solution for the market shares 0. of the three products as

l r

a function of the amounts of two characteristics in each product as
well as their prices. It should be noted that the market -share of
each product depends only on its own as well as its adjacent com-
petitor's characteristics and prices.

Turning to the producer side, there are three industry structures
that are possible, given the exogeneous restriction of the three prod-
ucts, namely:

A) Three firms each producing one product — this has been con-
sidered by Lane (1980) and has no synergistic effects present.

B) Two firms with one holding two products and the other one
product.

C) One firm holding all three products (assuming no legal barriers
to monopoly).

Both cases B) and C) contain product interactions within a firm,
i.e., possibilities of synergy and cannibalism. To model these
effects, we will assume that the management of the individual products
in a multi-product firm do not act in cooperation with each other.
This situation is fairly typical in a (packaged consumer durable
goods) firm with product-management type of organizational structure.
Product managers of different "'brands*' compete for organizational

-11-

resources and for consumer demand. Then, the cannibalistic effect of
product interaction is captured by allowing each product to compete
for demand independently.

The effects of synergy in distribution, manufacturing, adver-
tising, etc. will be modelled to affect the fixed costs of producing

n k
and selling the products. Let us denote by ^ the profit from

product k for a firm which also has products j, I, ... in the same

product market, there being a total of n products in the product market,

3 2
For example, II- is the profit from product 2 to a firm which has both

products 1 and 2 in a product market consisting of 3 products. To

specify the synergy effect, we will assume a sequential ordering of

the products that a firm enters into the market, i.e., a firm having

products j, k, i in the market introduces them in that order over

time. This assumption allows us to allocate synergy effects in the

following way: product j derives no synergy benefits since it is the

first product for that particular firm and its fixed costs are F.

Product k derives synergy benefits from product j and we will allocate

this cost reduction in the form of F[l-d.. (w., z., w, , z, ) ] . To make

Jk j J k k

the model simpler, we will assume, as Lane (1980) does, that the pro-
duction technology is predetermined by the constraint w + z = 1 — this
just reduces the problem to a one-characteristic one and leads to the

fixed cost of product k being F[l-d., (z., z. )]. Finallv, product I

jk j k j * r

derives synergy benefits from both products j and k and its fixed
costs are given by F[l-d ff(z., z , z )].

J K* J K. *

How should this function d be defined? Some criteria for d that
are desirable (to some extent driven by our previously discussed

-12-

intuitions on natural limits to the number of products entered by a
single firm), are:

1) d should be bounded from above, i.e., given a fixed cost of
F[l-d19 v^zi» •••» z\r )1 » ^ snould be bounded away from one, as
otherwise the fixed cost would be negative.

2) For a given value of k, the number of products belonging to the
same firm, d „ , should increase as the products are positioned

J.*- • • • K.

closer together and should decrease as the products are positioned
farther apart. The strategy of closer positioning will decrease fixed
costs while that of farther positioning will increase it. Of course,
there is the opposite effect of cannibalism acting in reverse, i.e.,
the closer the positioning, the more severe the intra-firra product com-
petition and vice versa.

3) With the number of products k, that a firm enters into the product
market, & n will first increase (due to synergy) and after a crit-

- — • • • K

ical point decrease (implying dysfunctional effects).

Some possible forms for d10 , , which meet the above criteria and
are also parsimonious (see Naert and Leflang (1978) for parsimony as a
modelling criterion) are as follows:

d12.,.k^Zl' ***' zv) = 6 [l-^(z1, ..., zk)]

with 5 < 1 and

1 k 2

a) ft - -r- Z min (z.-z.)
k . z. l j
1=1 j

or

-13-

k k

b) ^liFU^yvV2

j*i

or

1 k — 2
k 1-1 X

For example, c) is just a variance measure of the product charac-
teristics, with lower variance implying larger d,~ . and larger
variance implying lower synergy benefits.

Other approaches to measuring synergy has been from a purely sta-
tistical viewpoint. For example, in the finance literature [Firth
(1978), Franks et al. (1977), Haugen and Langetieg (1975), Mueller
(1977)], the effect of synergism is measured in mergers/acquisitions
by estimating the values of the firms before and after the merger/
acquisition. The standard technique is to use regression including a
"synergy" variable. Mahajan and Wind (1983) use information from the
PIMS data base to statistically test relationships between various
synergy proxies and profitability of a business unit. It should be
noted the efforts are to measure the effects of synergy a posteriori
rather than to model synergy and use it as a priori information for
strategic decisions.

Given this structure for fixed costs, the sales from a particular
product k is given by:

-14-

where p, is the price for product k and 8 is its market share

K. K.

(derived previously). Then, the profit function for a product k is
given by:

and the return on investment for product k given by:
ROI

jkZ... F[l-d., (z.,z. )]
jk j k

We now need to develop the competitive reaction between firms and
the behavioural implications leading to a computational algorithm to
calculate optimal multiple product positioning strategies for a three
product market. Similar to Lane (1980), we will assume a sequential
entry of products and firms with perfect foresight. This implies a
Stackelberg leader-type behavior with respect to characteristic posi-
tioning for the early entrants relative to the later entrants. Any
product in the sequence takes the positions of the preceding products
as given while perfectly forecasting the optimal positions of the suc-
ceeding products as a function of its own and the preceding products'
positions. For example, in a three product market, product 2, in
making its positioning decision, takes the first firm's position as a
given while perfectly forecasting the optimal behavior of product 3 as
a function of product 2 and l's positions.

For price setting, however, we assume that a Nash equilibrium may
emerge. This implies that the behaviour of any firm regarding pricing

-15-

will take Che prices of all its competitors as given, and will opti-
mize its own decision. The equilibrium (Nash) prices are such that,
even knowing its competitors are using their equilibrium prices, there
is no incentive for any firm to change from its equilibrium price. In
a sense, it is a stable price system, which once reached, nobody wants
to break out of.

Equilibrium analysis provides insights into behavior and structure
of markets, enabling management to understand where their product
market may be headed and developing strategies that would either
foster or hinder such movement. Equilibrium analysis could also indi-
cate if a firm is capitalizing on all its strengths, whether it is
actually receiving its equilibrium profits/market share, and if not,
how to strategically achieve it [Karnani (1982), Kumar and Thomas
(1983)].

We are now ready to specify the computational algorithm for eval-
uating optimal equilibrium positioning with respect to characteristics
and prices. We will do this, using the three product market assump-
tion, for cases B) and C), which assumed two firms and only one firm
respectively in the market.

B) Let us assume that Firm 1 has products 1 and 2 and Firm 2 has
product 3, and let Firm 1 be the leader.

Firm 2 takes the positions for products 1 and 2, z, and z9, as

fixed variables. For every position z~, it computes the Nash

* * *
equilibrium prices (p,, p~ > Po ) that will obtain, given (z- , z?, z~).

Lane (1980) shows that such an equilibrium exists and also that there

is a closed form solution, assuming that firms maximize profits. The

-16-

same is true if one used the behavioral assumption that firms maximize

return on investiment ROI. Then Firm 2 picks that combination of

* * 3 3

p and z_ as a function of z and z , which maximizes ROI~.

Firm 1 has its two products managed by different product managers.

The position of product 2 is chosen the following way: for fixed z1 ,

*

and for every position z„, it computes z~, the optimal position for

product 3, and then computes the price equilibrium. Then the manager

* *

for product 2 picks that combination of z„ and p? , as a function of

3 2
z. , which maximizes ROI.~. It must be noted that the benefits of

2
synergy are allocated solely to product 2.

The position of product 1 is then easily computed since for each

* * *

z., one can compute z~(z..) and also z_(z. , z„ (z..)). Given all three

positions, the Nash price equilibrium can be computed. The manager

* * 3 1

for Firm 1 picks that combination of p1 and z that maximizes ROI..,,,

which in turn defines the equilibrium positions z«(z.), z-Cz.. , z~(z..))

and the Nash equilibrium prices.

In a similar way, one would compute the equilibrium positions and
prices for all other combinations of the firms, products and product
entry position, such as for example, Firm 1 with products 1 and 3 and
Firm 2 with product 2.

C) Here we have one firm introducing all three products. The com-
putation of the optimal positions and prices proceeds similar to the
algorithm described above.

Manager for product 3, given z1 and z_, computes that combinations

* * 3 3

of z^ and p~, as functions of z. and z„, that optimizes ROI^- with

synergy from products 1 and 2 included. Then, the manager for product

-17-

* * 3 2

2 computes z„ and p„ , as a function of z.. , that maximizes ROI..„_

including synergy benefits from product 1. Finally, the optimal posi-

* *

tion and price of product 1, z.. and p , is computed, which in turn

gives z9(z ), z_(z , z (z )) and the Nash price equilibrium.

The logical question as to which of these market structures will
obtain depends on the total profits that the firm with multiple prod-
ucts obtains. Consider the firm that enters the first product; it

will enter a second product if and only if

3 *1 , 3 *2 3 *1 3 *3

3™T1 , r 12 12 i f &13 b13 n

ROI < [ j — j — J or [ j — j — J

F + F(l-d12(z1,z2)) F + F(l-d13(z1,z3))

3 12
i.e., the combined return on investment ROI.^ with both products,

whether the product 2 is entered second or third, is greater than that

of having a single product, in a three product market.

Similarly, it will enter a third product if and only if

t * i 1*9 3*3

Js + s + s

3DnT12 . r 5123 5123 5123 i

ROI < I - - ^ j - J

F + F(l-dl2(z ,z2)) + F(l-d123(z1,z2,z3))

3 123
i.e., the combined return on investment ROI __ with all three prod-

3 12
ucts is greater than ROI ~. Why does it not enter a fourth product?

A i o 'j / O TOT

Possibly because ROI 9_, is lesser than ROI 9_.

Why does it choose to enter only two products? Possibly because

3 12 3 13 3 123

ROI ? or RoI-,3 is larger than ROI ~ . Why does a second firm enter

3 3
when Firm 1 has products 1 and 2? Possibly because its ROI- is

greater than 1. In a similar fashion, why does a second firm not

enter when Firm 1 has products 1, 2 and 3 in the market? Possibly

-18-

4 U
because ROI , is less than 1, i.e., the firm is losing monev or it

does not meet its ROI objective.

One can envision many such multiproduct situations and the

questions as to product entry strategy can be analyzed in a fashion

similar to that above. One can answer strategic questions as to:

a) How many new entries?

b) When to enter them?

c) When to allow competition in (and possibly flank' them)?
Clearly, we could easily substitute profit maximization as the firm's
objective, rather than ROI optimization, and the preceding analyses
carries over to this case also.

Discussion and Conclusion

We have shown, in this paper, how multi-product market structures
could be modelled and also the methodology to compute equilibrium
positioning and pricing strategies. We have also shown how the incor-
poration of synergy could easily sway the decision of how many prod-
ucts (and their corresponding positions, prices and entry point) that
a firm could have in a given market. For a given market, we can com-
pute the maximum number of products, positions and prices, that would
be optimal for the first, second, etc. firms. We can thus normatively
understand product market structure evolution. The calculation of
equilibria is a hard problem and currently partial enumeration simula-
tion methodology or grid-search non-linear optimization methods are
suggested for its solution.

There are numerous avenues open to extend this basic model. The
assumptions of Cobb-Douglas consumer preference function could be

-19-

relaxed to allow uncertainty and information asymmetries, thus
requiring search strategies by consumers and the important effects of
information advertising. The allocation of synergy benefits to the
succeeding products and the modelling of intra-firm competition can be
made more sophisticated by evolving synergy benefit allocation schemes
that will allow independent product manager locally optimizing leading
to firm optimization over all its products. Another extension could
be to relax the assumption of perfect foresight with some sort of
myopic behavior, or even conjectural variations, on the part of firms
to estimate competitive reaction. The development of efficient
algorithms that aid in computing the equilibrium strategies will cer-
tainly aid in building more complex, and realistic, models of consumer
preferences and producer objectives.

-20-

Footnotes

The reason for not assuming Nash behavior in both price and loca-
tion is due to the possibility of nonexistence of the equilibrium
(Eaton and Lipsey, 1976). Also, given technological constraints on
product design, foresight is easier to understand for product posi-
tions. This allows a natural assumption of Stackelberg type leader-
ship for positions.

2
While this assumption is debatable, our reasoning is as follows:

If these products are going to be introduced sequentially, then the

second product is entered after the first one has been in for some

time. The product manager of the second product is faced with

managing a riskier product, than the first one, and could be given

additional motivation in the form of a lower cost structure. This

would be a truer evaluation of his performance since he is to be

judged on incremental contribution and thus also incremental cost. It

would also provide him with a wider range of pricing policies to

choose from.

D/217

-21-
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