Doshissha Universsity Center for the Study of the Crreative Economy
Discussio
on Paper Seeries No. 2013-01

KNOW
WLEDGE CRREATION BY
B CONSU
UMERS ANND
OPTIMALL STRATEG
GIES OF FIRMS

Tadashi Yagi
Y
Faaculty of Economics
D
Doshisha Un
niversity

DiscussiD
ion Pape
er Series

KNOWLEDGE CREATION BY CONSUMERS AND OPTIMAL STRATEGIES OF FIRMS
Tadashi Yagi*
Faculty of Economics, Doshisha University, Kamigyo, Kyoto 602-8580, Japan.
Telephone:+081-75-251-3629 E-mail: tyagi@mail.doshisha.ac.jp.

Abstract
In this paper, we analyzed the patterns of knowledge creation from the collaboration of producers
and consumers. The essential differences from traditional knowledge creation mechanisms arise
from consumers’ contribution to knowledge creation in three areas. The value of a product to theconsumer depends on the amount of knowledge creation by consumers, which is affected by theamount of public infrastructure, which in turn affects the price of the product. It should be notedthat the pattern of knowledge creation varies drastically depending on the shape of the response
function of effort time for knowledge creation between consumers.

(JEL categories: L15, M15)

1

I.

INTRODUCTION

Increasing awareness of the major influence of creativity and innovation on the competitivenessof business organizations has prompted research into the mechanisms of knowledge creation byresearchers from various disciplines. Previous studies have focused on knowledge creation
within the firm, with analysis pioneered by Nonaka (1994) and Nonaka and Takeuchi (1995) of
the organizational characteristics of knowledge creation mechanisms. Their model of theknowledge creation mechanism in organizations is a spiral of socialization, externalization,
combination, and internalization, which they called the “SECI” process. At the core of the spiralprocess is a continual dialogue between explicit and tacit knowledge which drives the creation of
new ideas and concepts. They clarify the conditions which enable knowledge creation, andexplain the process of creating tacit knowledge.
Nonaka's model gained much attention and was well regarded as a practical theory oforganizational knowledge creation, but some recent critics of the theory, for example, Bereiter(2002, 175–9) and Gourlay (2006), argue that the model does not fit the reality of thecontemporary business world, in which research and development and innovation occur due tointeractions of actors both inside and outside the firm. A typical example is the open innovation
model, in which research and development outputs of venture companies are purchased andbecome new research and development inputs of major companies.
Complementing the organizational mechanism of knowledge creation is the economic analysis ofknowledge creation, as pioneered by Berliant and Fujita (2008; 2009; 2011; 2012), who studied
the knowledge creation process by identifying diversity as a key factor. Melnikas (2010)
observes that the creation and development processes in a knowledge-based society and theknowledge economy are determined by the economic system, which transforms the global2

movements of the economy into sustainable development processes. Gunn and Johri (2011)
model the endogenous production of knowledge capital through a learning-by-doing process, anddescribe the situation where the value of knowledge capital rises when firms are induced toinvest more staff time in the development of knowledge capital.
The questions we pose here are twofold. First, how is new knowledge created through thecollaboration of producers and consumers? Second, how is the market value of new knowledge
determined? The importance of knowledge creation through collaboration with consumers indesigning products has been recognized in the modern economy as discussed by Esper et al.
(2010). A typical example is the Genius Bar located in Apple stores. Formally, the Genius Bar isdesigned to provide support to customers. Apple, however, utilizes this support system as aknowledge creation system by collaborating with “innovative” or “cyber” consumers who are
sophisticated and informed consumers, influencers and potential advocates for the brand.
Rogers (1995) classified consumer attitudes toward purchasing products into five categories in
his book Diffusion of Innovations. These categories include innovators (2.5% of consumers),
opinion leaders or early adopters (13.5%), early majority adopters (34%), late majority adopters(34%), and laggards or very late adopters (16%). For more information on the concept of the“cyber”

consumer,

see

the

RealBusinesswebsite(accessed

September2012):

http://realbusiness.co.uk/advice_and_guides/3-ways-to-satisfy-the-cyber-customer.
By employing these types of consumers as support staff in the Genius Bar, Apple createsknowledge on the real-time needs of consumers and provides proactive opinions on the products
from interacting with “mass customers.”
Consumer-focused knowledge creation systems are gaining in importance as social
networking services have gained a larger role in society and the economy. Cross et al. (2001)
3

examine the effectiveness of social networking in problem solving. By analyzing how consumers
use social media, it becomes possible to track the competitive landscape and monitor consumer
feedback. Questions and complaints can be analyzed to identify trends and build brand affinity.
Kotler et al. (2010) argues that the concept of knowledge creation in the consumer market has
moved from mere customer satisfaction to attaining higher affirmation of the human spirit. In
their book, they argue that today’s customers choose products and companies which satisfy
deeper needs for creativity, community, and idealism. That is, the knowledge creation system
incorporates the essence of humanity in creating value in the market. Meeting these needs ofconsumers is one reason why collaboration between producers and consumers is deemed to beimportant.
The purpose of the paper is to describe the behaviors of consumers and producers in theknowledge creation process, and derive the optimal strategy for increasing the value of creativity
in the market.

II.

CONSUMER BEHAVIOR AND KNOWLEDGE CREATION

We consider an economy consisting of two consumers, A and B, and one producer. Eachconsumer devotes time ( ei ) for contributing to knowledge creation, which is used to improve theutility from consumption activities. For example, consider a consumer who devotes time todevelop new ways of utilizing the Apple iPad and contributes to feedback through the Genius
Bar and social networking services.
Knowledge created by a consumer (i) is given by the knowledge creation function, which isformulated as follows:ni  ni (ei ; ei ),ni
 2 ni 0, i  A, B .
0,
ei
ei 2

(1)
4

The knowledge creation of consumer A depends on the time spent on related activities such as
using social networking services, given the time spent by consumer B.
The utility function (U) is assumed to be a concave function given by the following equation:

U i   (n A (e A , e B )  n B (e A , e B ); sg s )U (ci , s i , l i ), i  A, B .

(2)Here, g s is the public infrastructure investment by an information technology (IT) producer forknowledge creation. Examples of public infrastructure investment ( g s ) include services provided
by companies such as Apple, Google, and Microsoft.  is the knowledge function by which theutility of each consumer is improved and serves as a public good in the economy, and is assumed
to be concave function. c is a general consumption good whose price is set to 1 as numéraire, s is
the IT product and l is leisure time.
The budget constraint on consumers is given byw(T  l i  ei )  ci  psi ,(3)

where w is a wage rate, T is the total time endowment, and p is the price of the IT product. The
utility maximization problem of individual A is formulated as follows:
Maxc ,l ,e , s  ( n A (e A , e B )  n B (e A , e B ); sg s )U (c i , s i , l i ),s.t. w(T  l i  ei )  c i  ps i .

The Lagrangian function of individual A is defined as follows:L(c, l , e A ,  )   (n A (e A , e B )  n B (e A , e B ); sg )U (c, s, l )   ( w(T  l  e A )  c  ps) .
The optimality conditions are given by the following five equations:

1 

L
U

  0,
c
c

2 

L

U

 p  0 ,gU  s  ( sg )
s

(5)

(6)

5

(4)

3 

L
U

 w  0 ,
l
l

(7)

4 

L 

U  w  0 , and
e e

(8)

5 

L
 w(T  l  e)  c  ps  0 .


(9)

By combining optimality conditions (5) and (6), we derive
(


U
U
.
gU  
)/ p  ( sg )
s
c

(10)

This new equation states that the optimal combination of the general consumption good (c) andIT product (s) is given at the point where the marginal utility from the IT product (s) per $1
equals the marginal utility from the general consumption good (c). The marginal utility from IT
product (s) is generated through the marginal contribution to the knowledge creation of the IT
product and the direct utility increase from consumption of the IT product.
Combining optimality conditions (7) and (8), we derive

U
.
U 
e
l

(11)

This states that the optimal allocation of time to knowledge creation is determined at the point
where the marginal increase in utility from knowledge increase equals the marginal utility ofleisure.
The demand function of the IT product (s) is given bys D  s D ( p, w, g ) .

(12)

By assuming that the wage rate (w) is given exogenously in a general labor market, we rewrite
the equation ass D  s D ( p, g ) .

(13)
6

III.

RESPONSE FUNCTION

To examine the slope of the response function, we conduct a comparative static analysis using
the following equation:

 11  12  13  1e  1
B 21 22  23  2eB  p
1
de A 31 32  33  3eB  w ,
de B | H | 41 42  43  4eB  w
1  p  w 0

(14)

0

where

 11  

 2U
 0,
c 2

 U
 2U

 0,
s c
cs

 12 

 2U
 13  
 0,
cl
 U
 0,
e c

 14 

 15  1 ,
2 

L

U

 p  0 ,gU  s  ( sg )s 21 


U
 2U

 0,
g
 ( sg ) csc

 22 

 2

U

U
 2U
2
,




g
U
g
g
 ( sg ) 2
 ( sg ) s  ( sg ) ss 2

 23 


U
 2U

0,
g
 ( sg ) lsl7 24 

 2
 U
 0,
gU 
 ( sg )e ( sg ) s

 25   p  0 , 2U
 31  0,l c 32 


U
 2U

0,
g
 ( sg ) ll s

 33  

 34 

 2U
0,
l 2

 U
0,
e l

 35  w  0 , 41 

 U
 0,
e c

 42 

 2
 U
 0,
gU 
e ( sg )e s 43 

 U
0,
e l

 44 

 2
U  0,
e 2

 45  w  0 , 51  1  0 , 52   p  0 , 53  w  0 , 54  w  0 ,8

 55  0 , 1e 
B

 U
 0,
e B c 2e 

 2
 U
gU  B0,B
 ( sg )ee s 3e 

 U
 0,e B l 4e 

 2
U  0 , andee B

B

B

B

 5e  0 .
B

The second-order condition for the maximization requires that the determinant of the bordered
Hessian must be positive (i.e., | H | 0 ). Thus, if the determinant of the numerator is positive,
we can derive that de A / de B  0 . In general, it is nontrivial to examine the sign of thedeterminant because of the complex combination of mixed effects. Thus, in this paper, wehighlight the interesting case where the response function has a positive slope, which possibly
occurs in certain situations. For example, in the specific case where the second-order effects ofthe consumer good (c) and leisure time (l) are negligibly small, and the market wage (w) rate isgiven exogenously at 1, we can derive

de A
1

U
 2U
 2U
 U
 2U  U

(
g


)((


2


)
)0
de B | H |  ( sg ) l
sl
l s
s c
cs e B l

(15)

by using the first-order condition



U
U
.

c
l

This implies that the slope of response function may be positive at some local point. Depending
9

on whether de A / de B exceeds 1, the stability of the equilibrium is determined. As shown in
Figure 1, the equilibrium is stable when de A / de B  1 . That is, when neither consumer changes
his or her time for knowledge creation more than the other consumer does, the equilibrium
becomes stable. On the other hand, the equilibrium is unstable when 1  de A / de B (Figure 2). In
this case it is possible that one consumer increases his or her time for knowledge creation morethan the other does, and the investment time for knowledge creation increases sharply in a local
range. This situation seems to be realistic if the consumers are sensitive to interactions withothers on social networking services and debate increases as consumers voice their opinion
though social networking services. In addition, we should pay attention to any increase in thevalue of IT products over the course of debate on social networking services. That is, as theknowledge creation among consumers increases, the value of IT products increases and demandfor IT products increases.
In the case where two consumers want to decrease the time spent for knowledge creation, it isreasonable to consider the case where the response function has a negative slope. When one
consumer increases time for knowledge creation and the other decreases his or her time, and theamount of the increase is less than the amount of the decrease, the equilibrium is stable as isshown in Figure 3. On the other hand, when the consumer is strongly sensitive to the behavior of
the other consumer and the amount of increase is less than the amount of decrease, theequilibrium is unstable as is shown in Figure 4. In contrast to the case with a positive slope, there
is no possibility of a case where both consumers increase their time for knowledge creation. In
this case, the equilibrium becomes unstable, and no equilibrium point is attained.

FIGURE 1
10

eB

eA(eB)eB(eA)

4

eB1
eB0

2
1

3

eA0

eA1

eA

Stable Equilibrium Case ( 0 

de A
 1)
de B

FIGURE 2eB

eB(eA)eA(eB)

eB0

3

2
4
eA1

1
eA0

eA

Unstable Equilibrium Case ( 1 

11

de A
)
de B

FIGURE 3

eB
eA(eB)eB0

2
eB(eA)
3
1
eA0

eA1

eA

Stable Equilibrium Case ( 1 

de A
 0)
de B

FIGURE 4eB

eB(eA)eB0

2

3

eA(eB)

1eA1 eA0eA
1

12

Unstable Equilibrium Case (

IV.

de A
 1 )de B

PRODUCER BEHAVIOR AND MARKET EQUILIBRIUM

The profit function of the producer is given by ( s, g ; p )  p ( s, g ) s  C ( s )  g ,(16)

where C ( s ) is the cost function.
The optimality conditions for profit maximization are given by the following two equations:

1 

 p
dC ( s )1 dC ( s )ds / s,s  p ( s, g )  p (1  )  0, where   dsds
dp / p

s s

(17)

and

2 

 p
s 1  0 .

g g

(18)

From equation (12), the optimal production level of the IT product (s) is given bys S  s S ( p, g ) .

(19)

The optimal public infrastructure investment (g) is determined such that equation (18) holds.
That is,g  g (s) .

(20)

From the market equilibrium condition and optimality condition (20), we derives D  s S  s  s 1 ( g )   ( g ) .

(21)

The market equilibrium levels of the IT product price (p) and the public infrastructure investment(g) are found by solving this system of equations.
Totally differentiating (18), we derive
13

(

2 p
p
2 p
s  )ds  2 sdg  0.
g s
g
g

(22)

In other words, we derivedg
2 p
p  2 p (s  ) / 2 s  0.
ds
g s
g g

(23)

g

p

D0(s)

D1(s)

S0(s)
S1(s)

Shift from anincrease in e

p0

g0

s0

s1

s

s0

s1

s

Figure 5 g-s curve and market equilibrium

The equilibrium is attained at the intersection of the demand and supply curve, where the
combination of public infrastructure investment (g) and the IT product (s) is on the optimality
condition (20). When consumers increase the amount of time for knowledge creation (e), thevalue of s increases through a shift of the utility function, as shown in Figure 5. It should be
noted that profit-maximizing firms will adjust their optimal production by responding to the shift
in the marginal revenue function caused by the change in the amount of time for knowledge
creation (e). This implies that both the demand and supply curves possibly shift rightward, and14

their intersection shifts rightward, as is shown in Figure 5. The equilibrium supply of the IT
product increases with increased knowledge creation by consumers.
The pattern of the shift of equilibrium therefore depends on the relative slope of the response
functions. The analysis in Section 2 shows that there are three patterns of equilibrium effort
levels. In the case of stable equilibrium, the equilibrium effort level is determined at a certain
level, given the level of public infrastructure investment (g). In this case, the producer observes
the equilibrium effort levels of consumers, and the equilibrium price and quantity of an IT
product are determined in the market. If the optimality condition for public infrastructure
investment (g), which is given by (18), is not satisfied, the level of this investment is adjusted.
This affects the optimal effort level of consumers, and a new market equilibrium is attained. The
adjustment process continues until all the control variables satisfy the optimality conditions.
Contrary to the stable equilibrium case, the unstable cases lead to the sharp increase of effort
levels or zero effort levels. When the effort levels increases to the upper bound, the equilibrium
quantity and public infrastructure investment (g) increase until the effort level reaches the upperbound. Whether the equilibrium price increases or not depends on the shape of function (20). If
an increase in the quantity of IT production decreases the marginal cost of the product throughthe decrease in per unit cost of providing public infrastructure g, the market equilibrium level ofproduct price might not increase.
On the other hand, as the equilibrium effort level converges to zero, the demand for the IT
product decreases and the equilibrium quantity decreases. In this case, the IT product could
possibly disappear from the market.

15

V.

CONCLUDING REMARKSIn this paper, we analyzed the patterns of knowledge creation from the collaboration of
producers and consumers. The essential differences from traditional knowledge creation
mechanisms arise from consumers’ contribution to knowledge creation in three areas. The first is
the possibility of free ride in knowledge creation. The knowledge created by consumers is a
public good, and they do not charge for its creation and this knowledge is available for free. The
second is the complicated strategy that producers use to price and provide public infrastructure.
The value of a product to the consumer depends on the amount of knowledge creation by
consumers, which is affected by the amount of public infrastructure, which in turn affects theprice of the product. Finally, the pattern of knowledge creation varies drastically depending on
the shape of the response function between consumers. A sharp increase in knowledge creation
may occur when the value of knowledge generated by consumers is large.
These characteristics of knowledge creation should be analyzed in various settings. Suchanalysis is expected to bring about important results for understanding the mechanism ofknowledge creation.

VI.

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18