This paper examines the situation in which a monopolist offers freeware as an advertisement to increase the demand in order to maximize profit even though the existence of such freeware will reduce the power of the monopolist in the market. We prove that the successful application of freeware is dependent on the number of potential consumers and there exists an optimal quality design for freeware in this situation.Freeware; Software; Advertisement

Niem Le Duc

English

Research Papers in Economics

 
D DE EP PO OC CE EN N   
Working Paper Series  No. 2011/05
 
 
 
 
 
 
 
 
 
 
Freeware as an Advertisement 
 
 
 
Le Duc Niem* 
 
 
 
 
   
     *       PSEDepartment of Economics, Tay Nguyen University, Vietnam. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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FREEWARE AS AN ADVERTISEMENT 
 
LE DUC NIEM 
*   
 
Department of Economics, Tay Nguyen University, Vietnam. 
 
Abstract: This paper examines the situation in which a monopolist offers freeware as an 
advertisement to increase the demand in order to maximize profit even though the existence of 
such freeware will reduce the power of the monopolist in the market.  We prove that the 
successful application of freeware is dependent on the number of potential consumers and there 
exists an optimal quality design for freeware in this situation.  
JEL classification: L86; D83; D42 
Keywords: Freeware; Software; Advertisement 
 
1.  Introduction 
“Freeware” is very frequently observed in software markets. For example, “Logmein”
1, a 
web-based computer-remote-control service, provides some services for free but offers other 
services for paying customers. Avast
2 provides free antivirus and commercial antivirus versions 
at the same time. Why would any company offer a component of its software at no charge? 
While it is copyrighted, freeware is distributed and re-distributed freely without any 
payment from end users.
3 Haruvy and Prasad (2005) proposed that a firm offering freeware may 
do so as an advertisement to catch the attention of consumers. Also, they suggested that the 
existence of freeware may help achieve a competitive advantage. That is, one company can offer 
for free what another competitor may offer as a commercial product, thereby achieving a 
monopolist position. However, another convincing reason for the use of freeware is that firms 
may want to inform potential customers of the quality of their products (Shapiro and Varian, 
1998).  Gaudeul (2004) examined whether a firm may offer a lower quality version (“shareware”) 
of the software it wants to sell at a later stage, in order to demonstrate to potential customers 
aspects of product quality.  However, shareware is typically offered as a time-limited product. 
                                                 
* Corresponding author: E-mail: Leniem@gmail.com ( Le Duc Niem), tel: (+84) 905200804 
1 https://secure.logmein.com/US/home.aspx 
2 http://www.avast.com/ 
3 http://en.wikipedia.org/wiki/Freeware#cite_note-0   2
She found that firms providing information about their software via shareware make higher 
profits than competing firms that do not offer shareware. 
In this paper, we consider a monopolist setting in which time-limited shareware is not 
applicable. Such a situation may apply, for example, when users are willing to repeatedly re-
install their free sample (thus avoiding the time limitation), or when the costs associated with the 
‘trial’ sample are considerably high
4.  We prove that freeware of unlimited duration can be used 
as a persuasive and informative advertisement to attract potential consumers, and show that the 
optimal quality level of the freeware is uniquely determined, and it increases as the number of 
potential consumers in the market increases.   
In section 2 of this paper we provide the basic model, and in section 3 we derive the optimal 
freeware quality level over two periods. Section 4 presents our conclusions. 
2.  The model 
We assume that there is a monopolist who produces one type of commercial software that is 
non-time limited. This product is an ‘experience good’. The quality level of the software is 
normalized to 1. We assume that quality and production costs of these goods are so small as to 
be negligible. The goods are sold to a population of consumers with a range of preference for 
quality, and we assume each consumer can buy, at most, one unit of the product.  However, we 
imagine there are two types of consumers: ‘interested consumers’ and ‘potential consumers’. 
Interested consumers are those who are eager to buy the product and have full prior information 
regarding quality of the goods. Potential consumers are those who are not yet ready to buy the 
goods. These potential consumers need to experience the product for a period before some of 
them will become interested consumers. When a potential consumer becomes an interested 
consumer, he has become fully informed of the quality being offered. The number of interested 
consumers is normalized to 1 while the number of potential consumers is M. Each type of 
consumer is uniformly distributed in [0, 1] according to their taste for quality as in Wauthy 
(1996).  
We construct a game as follows (see figure 1):  In the first period, the monopolist decides 
upon a quality level q for the freeware. Then, it sets a price  1 p  to its goods (pay-version). In the 
second period, the monopolist will set another price 2 p  to its goods. It is worth noting that the 
freeware is freely distributed and copy-able over two periods. Additionally, the monopolist who 
                                                 
4 See Ilan (2001)   3
provides freeware with zero quality level carries the implication that it is not providing any 
freeware.  
It is reasonable to suppose that the rate of potential consumers becoming interested 
consumers after the first period is positively related to the quality level of the freeware provided. 
For simplification, we suppose that the number of potential-to-interested  consumers is qM  
( 1 0 ≤ ≤ q ). This implies that as quality is added to the freeware, more potential consumers will 
enter the market as interested consumers after the first period. When the quality of the freeware 
is 1, all potential consumers will turn into interested consumers.  
 
 
Figure 1: A monopolist’s decisions with freeware 
 
The consumer’s utility function is described as follows: 
p Q nJ J U i i − = ) (                                                           (1) 
Q is quality level built into the good and p is its price. If the good is expected to be used in 
one period, n =1, and if it is expected to be used in two periods, n =2. This function is an indirect 
utility function of consumer i, identified by the parameter i J  which measures the heterogeneity in 
consumer taste for quality
5. Consumers decide to buy the commercial version of the good only 
when they get higher utility compared with the utility obtained by the freeware. To solve this 
game, backward induction is applied. 
                                                 
5 See utility function in the paper of Wauthy (1996). 
1
1 M
0
1
0
Mq
1 Period
2 Period
q
p
J
−
=
1
2
2
) 1 ( 2
1
1 q
p
J
−
=  4
 
3.  Freeware quality design  
We regard the freeware as a low-quality product with zero-price as in Wauthy (1996). In the 
first period, the marginal consumer who is indifferent between buying the good or using the 
freeware is derived from 11 1 22 Jp J q −= .
6 That is   
) 1 ( 2
1
1 q
p
J
−
=                          (2) 
The marginal consumer who is indifferent between having the commercial version or the 
freeware in the second period is defined by  222 JpJ q − =  or: 
7 
q
p
J
−
=
1
2
2                              (3) 
Lemma 1:  In the second period, the monopolist will not set a price for its goods higher than a 
half the price it sets to the goods in the first period. 
Proof:   
Suppose the monopolist sets a pair of prices  ) , ( 2 1 p p  such that 1 2 2 p p > .  This implies that 
1 2 J J >  . As illustrated in figure 1, the profits in the first and second periods are independent, 
because only newly converting potential-to-interested consumers buy the good in the second 
period. In other words, the monopolist sells the good to the interested consumers in the first 
period and sells the good only to the converting potential-to-interested consumers in the second 
period. In this case, it is easy to find that the best response of the firm to price in the first period 
is ) 1 ( q − , and in the second period is 2 / ) 1 ( q −   . Thus, we can prove that
)
2
) 1 (
( ) 1 ( ) ( ) ( 2 1 2 2 1 1
q
q p p
−
Π + − Π < Π + Π . For this reason, such a pair of  ) , ( 2 1 p p is not the 
optimal choice because it is dominated by another pair of prices { 2 / ) 1 ( ), 1 ( q q − − }.  Lemma 1 is 
proved. 
                                                 
6 The commercial  and freeware versions are both not time-limited, and they are expected to be used for two periods. 
7 The commercial and freeware versions are expected to be used in only the second period.   5
We let 
) 1 ( 2
1
q
p
x
−
=  and 
q
p
y
−
=
1
1  (or 1 ) 1 ( 2 p q x = − , 2 ) 1 ( p q y = − ). For the sake of 
mathematical derivation, we can simply find the optimal value of  y x,  for profit maximization 
problems. 
•  Second period 
Referring to figure 1, the profit function of the monopolist in the second period is:
8 
y y q qM y y x q p a ] 1 )[ 1 ( ] )[ 1 ( ) , ( 2 2 − − + − − = Π             (4) 
The best response to y is defined by 0 / 2 = ∂ Π ∂ y  
) 1 ( 2
) ( *
qM
qM x
y
+
+
=                           (5) 
Substituting (5) into (4), the profit in the second period is 
) 1 ( 4
) )( 1 (
) (
2
2 qM
qM x q
x
+
+ −
= Π                       (6) 
•  First period 
Total profit function
9 of the monopolist is  ) , ( ) ( ) ( 2 1 y x x x Π + Π = Π or 
) 1 ( 4
) )( 1 (
) 1 )( 1 ( 2 ) (
2
qM
qM x q
x x q x
+
+ −
+ − − = Π          (7) 
The best response to x is defined by 0 / = ∂ Π ∂ x  
qM
qM
x
8 7
5 4 *
+
+
=                        (8) 
From (7) and (8), we can derive the profit function as follows: 
                                                 
8 It is worth noting that ) ( y x − is number of goods sold to “first period” interested consumers in the second period 
and  ) 1 ( y − is numbers of goods sold to potential-to-interested consumers in the second period. 
9 It is noteworthy that ) 1 ( x − is number of goods sold to interested consumers in the first period.  
Π
The b
5 (
For s
optimal q
 
 
Lemma 2
In fig
increases
−
Thus
5 . 0 = q ).
 
               
10 We calcu
changing f
1 ( 2
) (q
−
= Π
best response
1 ) 14 5 + − M
implicity, w
quality of fre
2: The optim
gure 2, we ca
s.
10 Now, we
42 5 ( 14 − + −
, if 5 . 0 ≥ q , a
. Thus, we c
                   
ulated the optim
from 0 to 40 wi
0
0.1
0.2
0.3
0.4
0.5
0
F
) 8 7 (
)( 1 )(
qM
qM q
+
+
e to quality o
) 3 ( 14 − Mq M
we solve for q
eeware is as 
Fig
mal quality of
an see that th
e prove that t
14 ( ) 2 + q M q
all terms in (
annot find an
               
mal quality lev
ith = Δ i M M
5
Freeware 
quality 
(q)
)
) 2 qM +
    (
of freeware 
45 8 ( − + M q
q in the cubi
in figure 2.
gure 2: Optim
f the freewar
he optimal q
this quality l
) 45 4
2 + − M q
(11) are nega
ny M that sa
vel of freeware
. 0 1 = − − i i M
10 15
6
(9) 
is derived by
16 ) 5
2 2 − q M
c expression
mal quality 
re increases 
uality level o
level cannot 
2 1 ( 8
2 − + q q
ative (actual
atisfies (11). 
e by the spreads
2 . The result i
20
Nu
y  0 / = ∂ Π ∂ q
0 6
3 3 = q M  
n (10) using 
of freeware
in M but les
of the freew
exceed 0.5. 
0 )
3 = M     
lly, the last t
Lemma 2 is
sheet program 
is presented in 
25 30
mber of pote
(M
0 
 (10) 
computer so
ss than 0.5 
ware increase
We rewrite 
       (11) 
erm can be z
s proven. 
‘Solver’ in Ex
figure 2. 
35
ential consum
M)
oftware. The 
 
s as M 
(10) as follo
zero when
xcel for all  i M
40
mers 
ows: 
   7
Proposition 1: The monopolist will only offer freeware as an advertisement when the number of 
potential consumers is large enough ) 8 . 2 ( > M . In addition, the optimal quality level of the 
freeware is defined, unique, and increases with the number of potential consumers in the first 
period. 
Proof: 
Let 
3 3 2 2 16 ) 45 8 ( ) 3 ( 14 ) 14 5 ( ) ( q M q M M Mq M M q f − − + − + − =   (12) 
i)  For 8 . 2 0 ≤ ≤ M : 
We have  0 ) ( < q f  because all terms in ) (q f are negative. The monopolist will maximize the 
profit by limiting the quality level of freeware as much as possible. Thus, it chooses 0 = q .  
Recall that zero quality means that the monopolist does not offer the freeware. 
ii)  For 2.8 3 M <<  
The function ) (q f  is cubic with the cubic coefficient
3 16 0 aM = −< . Differentiating ) (q f
with respect toq, we obtain: 
23 2 '( ) 14( 3) 2(8 45) 48 f qM M M M q M q =− +− −     (13) 
The function in (13) has two negative roots when2.8 3 M < < . Thus, the local maximum and 
minimum abscissa co-ordinates of  ) (q f  are less than zero. In addition, we have 0 ) 0 ( > f and 
0 ) 1 ( < f  . Thus,  ) (q f has only one root in [0, 1] . In other words, the optimal quality is defined 
and unique. 
iii)  For 3 = M , it is easy to prove that  ) (q f has only one root in [0, 1]: The optimal 
quality is defined and unique. 
iv)  For 3 > M  
The function ) (q f   is also cubic with the cubic coefficient 0 16
3 < − = M a .  The first 
derivative '( ) f q has one negative root and one positive root.  We also have 0 ) 0 ( > f and 0 ) 1 ( < f . 
Thus,  ) (q f has only one root in [0, 1], and the optimal quality is defined and unique. 
From (i), (ii), (iii), and (iv), proposition 1 is proven.  
 
 
   8
4.  Concluding Remarks 
This paper investigates a simple model where a monopolist uses freeware as an advertising 
strategy to attract potential consumers. First, we find that the monopolist will offer freeware as 
an advertisement only when the number of potential consumers is large enough. The reason is 
that when the number of potential consumers is small, the existence of freeware may reduce the 
willingness-to-buy of current interested consumers. As a consequence, the firm will make lower 
profit if it offers freeware. However, when the number of potential consumers is large, the firm 
will offer freeware because it expects more consumers will buy the goods in the future as they 
arrive in the market as interested consumers.  Second, we prove that the optimal quality level of 
the freeware is defined, unique, and increases as the number of potential consumers in the first 
period increases. This implies that it is possible for a monopolist to design freeware that best 
responses to a specific market setting. 
 
References 
Gaudeul, A. (2004). ‘Shareware competition: selling an experience’, Mimeo, University of 
Toulouse, CREMAQ. 
Haruvy, E. and Prasad, A. (2005). ‘Freeware as a competitive deterrent’, Information Economics 
and Policy, Vol. 17, pp. 513–543. 
Ilan Y. (2001). ‘The economics of software distribution over the internet revisited’, First 
Monday 6. 
Shapiro, C. and Varian, H. R. (1998). ‘Versioning: the smart way to sell information’, Harward 
Business Review, Vol. 76,  pp. 106–114. 
Wauthy, X. (1996). ‘Quality choice in models of vertical differentiation’, The Journal of 
Industrial Economics, Vol. 3, pp. 345-353. 
 

Freeware as a competitive deterrent’,

Quality choice in models of vertical differentiation’,

Shareware competition: selling an experience’,

The economics of software distribution over the internet revisited’,

Versioning: the smart way to sell information’,

Freeware As An Advertisement

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Freeware As An Advertisement

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