that do not distinguish between the general impact of communication technologies and the extent of the network effect.
One of the most popular explanations of the Solow productivity paradox is that output and inputs of information-using industries are not being properly measured
by conventional approaches. In our view, this measurement error also depends on having neglected some important determinants of the ITtelecommunications usage:
degree of network effects, market structure, consumer preferences and number of users. We thus suggest that some further empirical work is desirable, especially
ranking industries according to the expected extent of spillovers. Following our simulation results, we could expect that firms selling low differentiated products,
requiring a large and technologically efficient communication network and an intensive extent of communication externalities, would experience a positive impact
of ITtelecommunications on total factor productivity and then have the highest private incentive in communication technologies investment.
The remainder of the paper is organised as follows. After discussing the hypothe- ses of our model Section 2, we analyse firms’ decision making on telecommunica-
tion investment and technological level in a dynamic context Section 3. The second part of the paper focuses on the analysis of the steady state levels, together
with the welfare analysis Sections 4 and 5. The empirical implications of our model Section 6 are proposed before the conclusions Section 7.
2. Hypotheses of the model
The major feature of using a telecommunication network is captured by the externality effects. Here, we assume that the number of users and the externality
parameter, i.e. the usability of the knowledge obtained by communicating with other users — are the determinants of the spillover effect. The total amount of
knowledge obtained by communications can be thus interpreted as pure knowledge spillover.
The externality effects are specific for each network configuration. For the purpose of the present model, we choose a star shaped network Fig. 1, where each
firm has bi-directional links with the other n − 1 users. The amount of spillovers depends positively on the number of firms belonging to the network and on the
externality parameter.
We assume that each of the n firms is like firm 1 in Fig. 1, i.e. each firm knows that she is called by n − 1 users, and that she calls them. This hypothesis is more
realistic than that of considering a full connected network, where each firm talks with all of the others and benefits from symmetric network effects. Firms are less
interested than residential customers in network externality as simply the possibility of contacting everybody, but they are more reactive to the effective contacts they do
or they receive.
Let us consider a representative firm i. In a first step, firm i decides her telecommunications usage N
i
and the direct contacts with other j firms, in order to obtain the amount of information or spillover effect N
i
. Each time a firm i contacts
other firms, she adds a ‘piece’ of the total amount of their information to her own total amount of information N
SPi
, gathering
j
eN
SPj
. The total amount of informa- tion obtained from contacting other firms is weighted by the parameter e B 1, which
we interpret as the externality effect or the qualitybenefit of exchange firm i-firm j. The parameter e is taken as exogenous by each firm.
For simplicity, we assume that N
SPi
is a linear function of N
i
and of
j
eN
SPj
. Moreover, because of indirect links, N
SPj
will depend on N
j
and on the contacts between j and the other firms linked to j, because:
N
SPj
= N
j
+
k
eN
SPk
1 Taking into account the direct as well as indirect links, the networking function
for firm i becomes: N
SPi
= N
i
+
j
e N
j
+
k
eN
SPk
2 And so on, if firm k has other indirect links, they will be integrated in the firm i
’
s networking function. This process will stop when every indirect link of the network
has been considered
2
. In the case of the star-shaped network, the total amount of information spillovers
gathered by the communication network is: N
SPi
= 1
1 − n − 1e
2
N
i
+ e
n j = 1
i j
N
j
3
Fig. 1. Network interaction: the star-shaped network.
2
In a topological approach, this process would corresponds to the evaluation of the oriented graph obtained in the star-shaped network, where N
i
is the value associated with the node i and eN
SPj
is the value of the arc originating from the node i toward the node j.
Externality effects are positive if e
2
n − 1 B 1: we call this assumption the network stability condition.
Note that our formulation significantly differs from that of the RD spillovers model as for example Spence, 1984; Levin and Reiss, 1988; De Bondt et al., 1992,
which simply model the intra-industry pool of knowledge as follows:
N
SPi RD
= N
i
+ e
n j = 1
i j
N
j
The relevant intra-industry pool of knowledge for firm i only consists of the total amount of knowledge created with own RD efforts and a part of the knowledge
created by the other firms in the industry. Our claim is that, as ITtelecommunications are likely to create a web of links, the above formulation is not adequate to model
the multidirectional interactions of a network of users. In fact, Eq. 3 indicates that the intra-industry pool of knowledge is a non-linear positive function of the extent
of the spillover effect and the number of users; moreover, the sensitivity of the intra-industry pool of knowledge to both the parameter e and the number of users
n is stronger than that considered by the standard RD spillovers models. However, as in Levin and Reiss 1988, Romer 1990 and Grossman and Helpmann 1991,
we include a double counting effect: each time that firm i uses the telecommunication network, she contributes to the stock of general knowledge capital.
We discuss the case in which a representative firm engages in telecommunications investment in order to increase the efficiency of her production process. We consider
a simple Cobb-Douglas production function with constant returns to scale, as in Rebelo 1991:
Y = AK 4
where A
t
is the technical change or total factor productivity. The minimum total cost for producing Y
t
Sato and Suzawa, 1984, once the optimum allocation of capital has been performed, is as follows:
TC = Yc
K
A 5
Producers engage in telecommunications investment N
i
, to increase the productivity of their input and to obtain competitive weapons in market rivalry, because a higher
A yields lower prices and market expansion. Firms incur c
n
N
i
as variable costs of usage, which represents what managers frequently call the telecommunication budget.
We thus consider that the evolution of A, i.e. the dynamic change of the total factor productivity, is a non-linear function of telecommunications investment and
spillovers
3
.
3
For a static model where the total factor productivity level is influenced by the communication technologies’ usage, see Creti 1998. In that model, it is shown that, under perfect competition, the
substitution effect between traditional inputs, like capital or labour, and the input information is related to the network effect, or the advantage that a firm obtains by using an input whose costs are shared by
other users. Moreover, conditions under which the usage effects, or the factors that increase firms’ individual communications needs, overcome the network effect are investigated.
This cost reducing aspect is often used in the literature on technological change and RD. However, RD investment and the RD capital services and
spillovers are embodied in the production function. The main difference with respect to these models is thus the hypothesis on technological change: we choose
Hicks neutral technical change to better analyse the impact of communication technologies on TFP, without considering factor demand bias. For instance,
Jones 1995 suggests that perhaps computers and other forms of capital play a complementary role in the discovery of knowledge. We think that, in some way,
ITtelecommunication are more similar to RD than to other forms of input: as RD, they allow obtaining, processing and storing information useful to the
production process. However, RD is an internal source of information, while communication technologies are concerned with information channels external to
the firms, and for this reason we believe that the impact of the IT usage on TFP is better modelled by a disembodied technological change. We thus assume that
the telecommunication equipment is included in the variable capital, so it is not explicitly analysed. In our view what is new and interesting to model is ITtele-
com usage and network externality effects on the technological decision of firms.
The TFP dynamic is given by: dA
t
dt =
A
t g
N
t d
N
SPt d
d + d 0 BgB1
6 The term on the right-hand side is analogous to a conventional production
function, and, in that respect, it exhibits the standard neo-classical properties of positive marginal product and diminishing returns to communication technologies
investment and spillovers. Over time, the marginal productivity advantages are decreasing with respect to ITtelecommunications expenditures and spillovers.
This means that later contacts are less significant than earlier communications: there is a crowding of information.
Here d and d 0 can be interpreted as elasticities of respectively the firm’s own
communication investment and the spillovers to the TFP dynamics, and they have a different meaning than the parameter e or the extent of the externality
effect. The parameters d and d 0 have to be considered as the productivity or the
effectiveness of the communication technologies and of their spillovers. We thus assume that a technical improvement of the communication is reflected in an
increase of d and d 0 . For this reason, in the rest of the paper, we will refer to
these parameters, as proxies of the technological opportunities linked to network usage.
Several special cases of the productivity generating function 6 are used in other studies. If g = 1, d
0 =0, we obtain Romer’s 1990 technological progress function; in our specification g B 1 avoids the so-called scale effects, as pointed out by Jones
1995, because it is no longer intuitive to assume that more resources are needed if one possesses a higher productivity level. With g, d
0 =0, we recognise the Dasgupta and Stiglitz 1980 specification. When d, g = 0 and d
0 =1, we derive the
Spence 1984 specification, which is also used by De Bondt et al. 1992. The Levin and Reiss specification can be obtained when g = 0, and that of Sato and Suzawa
1984 results from setting g = 1, d = d 0 =0.
We assume monopolistic competition in the output market. This allows us to investigate the influence of product differentiation and the number of competitors
on technological change and welfare. We consider two kinds of goods: n differenti- ated products and one homogeneous product. The utility is quasi-linear, i.e. it adds
two kinds of sub-utility or two sectoral utility levels for the differentiated and the homogeneous goods. As in Grossman and Helpmann 1991, the utility of the
differentiated goods is a` la Dixit-Stiglitz, which means that there is linear homo- geneity among the n number of varieties. The optimal allocation of expenditures
across differentiated goods and homogeneous good yields the usual demand function for each differentiated good:
y
i
= p
i −
1
P
D a − b
X
b
7 where
4
a = 11 − r \ 1, b = 11 − z \ 1, with the following price index: P
D
=
n i = 1
p
i 1 − a
n
11 − a
8 Note that a is the elasticity of substitution across n differentiated goods, while b is
the overall price elasticity of demand. We then logically assume a \ b. The last hypothesis we need is the dynamic of exogenous 6ariables, i.e. scale of
demand, and in particular, the costs of N and K. As in Morrison and Berndt 1991, we assume that the exogenous variables increase at given constant rates X
0t
= X
00
e
− s
X
t
, c
nt
= c
n0
e
− s
n
t
, c
kt
= c
k0
e
− s
K
t
.
3. Dynamic profit maximisation and balanced growth rate
