UNIVERSITY OF
ILLINOIS LIBRARY
AT URBANA-CHAMPAIGN
BOOKSTACKS
Digitized by the Internet Archive
in 2011 with funding from
University of Illinois Urbana-Champaign
http://www.archive.org/details/multipleproductp1048sudh
330 STX
B385
1048 COPY 2
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
. PFRFORVWT
\PPE VLs T\>
vn no pf on*
FIN TO PRJIV \T\>RTY LOOklM.
• Vtt
\FR> PS.UTICU
PRt>\ !l>»> . ,OOD liAS MILEAGE
Vi-~VU.xO»BL£
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- List of References
Abell, D. F., and Hammond, J. S. (1979), Strategic Market Planning. Englewood Cliffs, N.J.: Prentice-Hall, Inc.
Anderson, P. F. (1983), "Marketing, Strategic Planning and the Theory of the Firm," Journal of Marketing, 46 (Spring), 15-26.
Albers, S., and Brockoff, K. (1979), "A Comparison of Two Approaches to the Optimal Positioning of a New Product in an Attribute Space," Zeitschrift fur Operations Research, 23 (June), 127-142.
Eaton, B. C. , and Lipsey, R. G. (1976), "The Non-Uniqueness of Equili- brium in the Loschian Location Model," American Economic Review, Vol. 66, pp. 77-93.
Firth, M. (1978), "Synergism in Mergers: Some British Results," Journal of Finance, 33 (May), pp. 670-672.
Franks, J. R. , Broyles, J. E., and Hecht, M. J. (1977), "An Industry Study of the Profitability of Mergers in the United Kingdom," Journal of Finance, 32 (December), pp. 1513-1525.
Green, P. E. , and V. Srinivasan (1978), "Conjoint Analysis in Consumer Research: Issues and Outlook," Journal of Consumer Research, 5 (September), 103-123.
Haugen, R. A., and Langetieg, T. C. (1975), "An Empirical Test for
Synergism in Merger," Journal of Finance, 30 (June), pp. 1003-1114.
Hauser, J. R. , and Shugan, S. M. (1984), "Defensive Marketing Strategies, Marketing Science, Vol. 2, No. 4 (Fall), 319-360.
Henderson, B. (1979), Henderson on Corporate Strategy, Abt. Books, Cambridge, Mass.
Hofer, C. W. , and Schendel, D. (1978), Strategy Formulation: Analytical Concepts , West Publishing Co., St. Paul, Minn.
Hotelling, H. (1929), "Stability in Competition," Economic Journal, 39 (March), 41-57.
Karnani, A. (1982), "Equilibrium Market Share — A Measure of Competitive Strength," Strategic Management Journal, Vol. 3, pp. 43-51.
Kotler, P. (1984), Marketing Management, Englewood Cliffs, N J : Prentice Hall.
Kumar, K. R. , and Thomas, H. (1983), "A Game Theoretic Rationale for
Henderson's Rule of Three and Four," Working Paper No. 1004, College of Commerce and Business Administration, University of Illinois (May).
-7">-
Lancaster, K. J. (1975), "Socially Optimal Product Differentiation," American Economic Review, 65 (September), 567-585.
Lane, W. J. (1980), "Product Differentiation in a Market with Endogenous Sequential Entry," Bell Journal of Economics, 11 (1), (Spring), 237-260.
Leland, H. E. (1974), "Quality Choice and Competition," Working Paper No. 29 (Finance), Graduate School of Business Administration, University of California, Berkeley (December).
Mahajan, V., and Wind, Y. (1984), "Business Synergy and Profitability," Working Paper No. 83-803, Edwin L. Cox School of Business, Southern Methodist University.
May, J. H. , Shocker, A. D. and Sudharshan, D. (1983), "A Simulation Comparison of Methods for New Product Locations," Working Paper No. 932, Bureau of Economic and Business Research, University of Illinois, Champaign (February).
Mueller, D. C. (1977),, "The Effects of Conglomerate Mergers: A Survey
of the Empirical Evidence," Journal of Banking and Finance (December), pp. 315-347.
Naert, P., and Lefland, P. (1978), Building Implementable Marketing Models, Boston: Martinus Nijhoff Social Sciences Division.
Schmenner, R. W. (1983), "Every Factory has a Life Cycle," Harvard Business Review, March-April, pp. 121-129.
Shocker, A. D. , and Srinivasan, V. (1974), "A Consumer-Based Methodology for the Identification of New Product Ideas," Management Science, 20 (February), 921-937.
Shocker, A. D. , and Srinivasan, V. (1979), "Multi-Attribute Approaches to Product-Concept Evaluation and Generation: A Critical Review," Journal of Marketing Research, 16 (May), 159-180.
Skinner, W. (1974), "The Focused Factory," Harvard Business Review, May-June, p. 113.
Spence, A. M. (1976), "Product Selection, Fixed Costs and Monopolistic Competition," Review of Economic Studies, 43 (June), 217-253.
Sudharshan, D. (1982), On Optimal New Product Concept Generation: A
Comparison of Methods. Unpublished Doctoral Dissertation, Graduate School of Business, University of Pittsburgh.
Urban, G. L. , and Hauser, J. R. (1980), Design and Marketing of New Products , Englewood Cliffs, NJ: Prentice Hall.
Zufryden, F. (1979), "A Conjoint Measurement-Based Approach for Optimal New Product Design and Market Segmentation," in A. D. Shocker, ed. , Analytic Approaches to Product and Marketing Planning, Cambridge, MA: Marketing Science Institute, 100-114.
HECKMAN
BINDERY INC.
JUN95