In the literature on firm strategy and product differentiation, consumer price-quality trade-offs are sometimes represented using consumer “value maps”. These involve the geometric representation of indifferent price and quality combinations as points along curves that are concave to the “quality” axis. In this paper, it is shown that the value map for price-quality tradeoffs may be derived from a Hicksian compensated demand curve for product quality. The paper provides the theoretical link between analytical methods employed in the existing literature on firm strategy and competitive advantage with the broader body of economic analysis.Value map; competitive advantage; quality; price; strategy

Connelly, Luke B.

English

Research Papers in Economics

 
 
 
 
 
 
 
 
THE PATERNITY OF THE PRICE-QUALITY  
“VALUE MAP”
† 
 
 
 
 
 
by  
 
L.B. Connelly 
Associate Professor of Health Economics 
Centre of National Research on Disability and Rehabilitation Medicine 
The University of Queensland 
 
 
ABSTRACT 
 
In the literature on firm strategy and product differentiation, consumer price-quality 
trade-offs are sometimes represented using consumer “value maps”. These involve the 
geometric representation of indifferent price and quality combinations as points along 
curves that are concave to the “quality” axis. In this paper, it is shown that the value 
map for price-quality tradeoffs may be derived from a Hicksian compensated demand 
curve for product quality. The paper provides the theoretical link between analytical 
methods  employed  in  the  existing  literature  on  firm  strategy  and  competitive 
advantage with the broader body of economic analysis. 
 
 
JEL: D00, D21, D40. 
Keywords: value map, competitive advantage, strategy. 
                                                
† Corresponding author: Luke Connelly, Centre of National Research on Disability and Rehabilitation 
Medicine (CONROD), The University of Queensland, Mayne Medical School, Herston Road, Herston 
Q 4006, AUSTRALIA. Tel.: +61 7 3346 4838; Fax: +61 7 3346 4603; Email: l.connelly@uq.edu.au.  
  1
1  Introduction 
Of central concern in the literature on firm strategy is the notion of “competitive 
advantage” (Porter, 1980): a firm is said to enjoy a “competitive advantage” when its 
profits are consistently greater than those of its rivals (Besanko, Dranove and Shanley, 
2000). A large part of the strategy literature is concerned with the sources, creation 
and  sustainability  of  such  an  advantage.  These  issues  are  central  to  a  large,  and 
growing literature, on entrepreneurship and strategic management. The purpose of this 
paper is to expose the theoretical basis for a conceptual device that is often central to 
analyses of these issues, viz. the consumer “value map”. 
A “value map” consists of indifference curves, drawn in price-quality space, 
that represent indifferent combinations of price and quality for a consumer (or a group 
of  consumers  whose  preferences  over  quality  and  price  are  identical).  Figure  1 
presents an example of  a “value map” for a consumer who, in this  example, has 
quasilinear  preferences  over  price  and  quality.  Along  each  of  these  indifference 
curves: 
0
/
/
=
¶ ¶
¶ ¶
P U
L U
i
i   (1), 
where L is quality, P is price, and U is utility. Thus consumer surplus and utility are 
invariant along each indifference curve. The marginal rate of substitution (MRS) of 
price for  quality along an indifference curve may be derived, as for conventional 
indifference curves (drawn in quantity-quantity space), from its slope, i.e. as 
L
P
MRSLP D
D
- =   (2). 
The MRS is negative in such cases because  
0 ³
¶
¶
L
U
  (3); 
and,  
  2
0 <
¶
¶
P
U
  (4). 
That is, “quality” is a good, while price is a bad: increases (decreases) in price must 
be compensated by increases (decreases) in quality in order to maintain condition (1). 
It also follows that: 
2 1 0 U U U > >   (5). 
In the literature on strategy, the value map is used to describe the development 
of a competitive advantage. This involves, inter alia, the production of a price-quality 
combination that provides greater consumer surplus than the imperfect substitutes of 
rivals. 
Suppose  that  the  indifference  curves  in  Figure  2  now  represent  the 
(homogeneous)  preferences  of  every  individual  for  whom  the  product  is  a  utility 
function argument. The loci LX, PX; LY, PY; and LZ, PZ, represent the price-quality 
combinations offered by profit-maximising firms X, Y and Z. Note that, although Z’s 
output is a higher-quality substitute for X’s, the combinations LX, PX and LZ, PZ are 
located on the same indifference curve, U0. Thus, consumers are indifferent between 
the output produced by X and Z, given their prices.
1 However, consumers are not 
indifferent between Y’s price-quality combination and those of rivals (X and Z): LY, PY 
provides greater consumer surplus than either of the substitutes, as indicated by its 
position on a lower indifference curve, U1. 
In a monopolistically competitive market, competition on price and quality will 
continue until a price-quality equilibrium is reached. Briefly, assume that the cost 
function is 
) (L C C =   (6), 
                                                
1 In the strategy literature, Firms X and Z are said to have achieved “surplus parity”.  
  3
where C is cost and  0 >
¶
¶
L
C
. The curve C0=min[C(L)], in Figure 2, is the efficiency 
frontier for quality production: it depicts the least-cost production of each level of 
quality. The quality equilibrium in Figure 2 occurs at the tangency of U2 and C0 with 
the production LY at the price PY. At this point, there is zero opportunity to increase 
profit  by  modifying  the  price-quality  combination  offered,  since 
E
E
E
E
L
P
L
C
¶
¶
=
¶
¶
  and 
CE=min[C(LE)]. Note that, by assumption, firm Y currently enjoys some monopoly 
power, since PY>CY.
2 
 
2  The Derivation of the Value Map 
It can be shown that the consumer’s price-quality indifference curves can be derived 
from a Hicksian compensated demand (HCD) curve for product quality. Conversely, 
the HCD can be derived from the price-quality value map. 
Consider  consumer  trade-offs  between  product  quality  (L)  and  quantity  (T), 
where  0 ³
¶
¶
L
U
 and  0 ³
¶
¶
T
U
. More generally, one might invoke Lancaster’s (1966a, 
1966b)  approach  to  consider  product  characteristics,  or  bundles  of  these,  that  are 
utility-producing. In this way, one could, for example, focus on consumer indifference 
between quantities of a particular product characteristic, and the quantities of the 
product, per se. For example, one could consider trade-offs between the quantity of 
meat consumed, and the quality of meat, as measured by reductions in its fat content, 
ceteris paribus. 
Insofar as it is recognised that variations in “quality” per se can arise due to 
variations  in  more  than  one  characteristic  of  a  good,  the  analysis  becomes  more 
                                                
2 A further implication is that of constant-returns to scale: firm Y is on the efficiency frontier C0 despite  
  4
complicated. For example, using the example of meat, reductions in the quantities per 
kilogram (kg) both of fat and/or of gristle, ceteris paribus, may be responsible for 
“quality-improvements” in the product. Furthermore, if both gristle and fat are bads, 
consumers might be indifferent between various combinations of these.  
Figure 3 presents indifference curves in quantity-quantity space for these two 
characteristics of meat that, for the consumer preferences represented, are “bads”.
3 
That is,  0 <
¶
¶
F
U
, and  0 <
¶
¶
G
U
, where F is the quantity of fat per kg, and G is the 
quantity  of  gristle  per  kg.  In  Figure  3,  indifference  curves  closer  to  the  origin 
represent higher levels of utility: at the origin, there is a zero quantity of each bad, 
while  north-east  movements  represent  increasing  quantities  of  one  or  both  bads.
4 
Supposing gristle and fat are the only two characteristics of meat that affect quality, it 
may  thus  be  said  that  each  bad-bad  combination  on  a  single  indifference  curve 
indicates meats that are considered of identical quality by the consumer. Thus, the 
indifference curves in Figure 3 provide, at least conceptually, the basis for deriving a 
quality index. 
Thus,  one  need  not  be  constrained,  conceptually,  by  the  multi-characteristic 
nature  of  quality  for  meat,  or  any  other  product.  The  analyses  developed  in  the 
following  diagrams  do  not  demand  cardinal  measures  of  “quality”:  all  that  is 
necessary is that consumers be able to rank, completely, bundles of different quality, 
ceteris paribus. 
                                                                                                                                       
its monopoly profiit. 
3 Here it is acknoweldged that quality, like beauty, is “in the eye of the beholder”. For this consumer, in 
the range depicted, reductions in fat and gristle are utility-increasing. In reality, reductions in fat may 
also reduce the tenderness of meat so, for some consumers, reductions in fat (over some range) will 
likely be utility-reducing. 
4 Note that the axes of Figure 3 will be constrained by the fact that the maximum quantity of fat or 
gristle per kg of meat is 1kg.  
  5
It  is  convenient  to  return  now,  to  the  notion  of  “quality”  as  a  single 
characteristic. Consider Figure 4, in which the consumer’s budget line is indicated, in 
quality-quantity space, by the line 1-2. This budget line represents all quality-quantity 
combinations of good X available to the consumer. The consumer’s preferences over 
quality  and  quantity  are  assumed  to  be  well-behaved  (i.e.,  reflexive,  complete, 
transitive, continuous, convex and non-satiable) and preferences over the quality and 
quantity  of  X  are  given  by  the  indifference  curves  I0,  and  I1.  The  initial  utility-
maximising  bundle,  given  the  budget  1-2,  involves  the  consumption  of  TA  of  the 
commodity at quality LA. 
Now, suppose that the price of “quality” falls ceteris paribus, and the budget 
line pivots to 1-3. The price effect is LB-LA. Taking the equivalent variation (4-5), the 
substitution effect is LC-LB and the income effect is LB-LC. Figure 4(b) presents a 
Hicksian (income-) compensated demand curve (HD) for quality, derived from Figure 
4(a). This compensated demand curve may now be used to derive a price-quality 
indifference curve for the consumer. 
Figure  5(a)  presents  the  Hicksian  demand  curve  derived  in  Figure  4  and, 
together with Figure 5(b), the derivation of the price-quality indifference curve, U0, is 
indicated.  The  derivation  of  U0  may  be  understood  by  commencing  with  the 
observation that the Hicksian demand curve, HD, is the consumer’s marginal benefit 
curve  for  quality  when  real  income  is  held  constant.  Expressed  differently,  HD 
describes  the  consumer’s  willingness  to  pay  for  marginal  increments  in  product 
quality. At this point, it is perhaps useful to think of the case of perfect first-degree 
price discrimination and its consequences in terms of consumer surplus: if first-degree 
price discrimination were practised along HD, consumer’s surplus (CS) is zero for all 
L.  
  6
An  element  of  the  consumer’s  value  map  may  has  now  been  derived: 
indifference curve U0 is the consumer’s price-quality indifference curve for CS=0. 
Thus, U0 is, in fact, the consumer’s total benefit curve for quality, derived from HD. 
A  noteworthy  reference  point  in  this  diagram  occurs  at  quality  LMAX,  where  the 
marginal benefit of quality improvements is zero. Since  0 =
¶
¶
L
U
 for all L>LMAX, it 
follows that  0 =
¶
¶
L
P
 for U0 all L>LMAX. 
Indifference curve U0 has an important meaning that may be understood by 
recalling the elements of Figure 4(a) from which U0 was derived. Specifically, U0 was 
derived  by  varying  the  relative  prices  of  quality  and  quantity  along  I0  from  the 
equilibrium point A, where 1-2 was exhausted. If the budget constraint and relative 
prices implicit in 1-2 apply, it follows that LA, PA in Figure 4 is the utility-maximising 
quality-price combination for this consumer. All price-quality combinations for L<LA 
on U0 are affordable to the consumer, however, the relative prices implicit in 1-2 
indicate that qualities L<LA are available only at P>P(U0). Price-quality combinations 
L>LA on U0 are, on the other hand, not affordable to this consumer. In terms of the 
consumer’s  current  real  income  then,  U0  represents  the  maximum  total  benefit 
available to the consumer from the consumption of various qualities of good X. Points 
on  indifference  curves  above  U0  represent  combinations  of  price  and  quality  that 
would only be available to the consumer if real income were increased. 
It is then a straightforward matter to derive the remainder of the consumer’s 
“value  map”. The derivation of  indifference curves  (geometrically) lower  than  U0 
merely  involves  starting  with  a  real  income  less  than  I0  in  Figure  3,  while  the 
derivation of (geometrically) higher indifference curves involves commencing with 
real incomes greater than I0. For the analysis of consumer welfare in this framework,  
  7
consumers  located  on  successively  lower  indifference  curves  than  U0  enjoy 
successively higher levels of consumer surplus 
 
3  Conclusion 
This paper links a conceptual approach referred to in the strategy literature as “value 
map analysis”, to other tools of consumer theory, including the Hicksian compensated 
demand curve. The paper shows that the price-quality indifference curves employed 
in the literature are, in fact, total benefit curves for quality, and may be derived from 
the Hicksian-compensated demand curve for product quality. The analysis may also 
be applied to consider consumer preferences over price and a single quality-affecting 
characteristic of a commodity, or via a quality index derived from a bundle of product 
characteristics.  This paper provides the  foundation for analytical methods that are 
presently being used, without a substructure, in the economic literature. 
 
ACKNOWLEDGEMENTS 
A conversation with Darrel Doessel gave rise to this paper. I am also grateful to him 
for his comments on an earlier draft. Deficits that remain are solely my responsibility. 
 
REFERENCES 
Besanko, D,  Dranove, D. and  Shanley, M., 2000, Economics  of strategy,  2
nd edn 
Wiley, New York. 
 
Lancaster,  K.J.  (1966a)  A  new  approach  to  consumer  theory,  Journal  of  Political 
Economy, 74, pp. 132-57. 
 
Lancaster, K.J. (1966b) Change and innovation in the technology of consumption, 
The American Economic Review, 56, pp.14-23.  
 
Porter,  M.  (1980)  Competitive  strategy:  techniques  for  analyzing  industries  and 
competitors, Free Press, New York.  
  8
FIGURE 1 
PRODUCT DIFFERENTIATION AND EQUILIBRIUM 
 
Price ($) 
 
PZ   C0 
 
  PX 
 
 
  PY  U0 
 
 
 
  CY  U1 
 
 
  U2 
 
 
 
  0  LX  LY  LZ  Quality 
 
 
 
 
 
 
FIGURE 2 
THE CASE OF TWO “BADS” IN CONSUMPTION 
 
Gristle 
per kg of 
Meat 
 
 
 
 
 
 
 
 
 
  I2  I1  I0 
 
  0  Fat per kg of Meat 
 
  
  9
FIGURE 3 
DERIVATION OF A HICKSIAN COMPENSATED DEMAND CURVE FOR THE 
QUALITY OF GOOD X 
 
Quantity 
of X 
 
  1 
 
 
  A 
  TA 
  4  B 
  TB 
 
  C  I1 
  TC 
 
  I0 
 
 
  2  5  3 
  0  LA  LC  LB  Quality of X 
 
 
(a) 
 
 
Price of  
Quality 
($) 
 
 
 
  PA  A 
 
 
 
 
  C 
 
 
 
 
 
 
 
  0 
  LA  LC  LMAX  Quality of Good X 
(b)  
  10
FIGURE 4 
DERIVATION OF CONSUMER A’s INDIFFERENCE CURVE FOR PRICE AND 
QUALITY OF GOOD X 
 
 
Price of  
Quality 
($) 
 
 
 
  PA  A 
 
 
 
 
  C 
 
 
 
 
 
  HD 
 
  0 
  LA  LC  LMAX  Quality of Good X 
(a) 
 
Price of  
Quality  U0 (CS=0) 
($) 
 
  C 
 
 
 
 
 
  A 
 
 
 
 
 
 
 
 
   
  0  LA  LC  LMAX  Quality of Good X 
(b) 

The Paternity of the Price-Quality "Value Map"

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