Analysis of the steady state TFP and ITcommunication levels

Equating the dynamic equations to zero, we obtain the steady state value of A d and N d 7 : A d = X 00 b c K0 1 − b c n0 r + s a a P − 1 a P b n a − b1 − a S N S ´ N n 11 − g + d 1 b − 1 s a d 1 − 11 − g + d 1 b − 1 14 N d = X 00 b c K0 1 − b r + s a a P − 1 a P n a − b1 − a S ´ N c n0 n 11 − g + d 1 b − 1d 1 s a 2 − g − b1 − g + d 1 b − 1 S N d 1 b − g − 21 − g1 − g + d 1 b − 1d 1 15 where the externalities obtained by using a communication network are as follows: S N = 1 + en − 1 1 − e 2 n − 1 n d S ´ N = d + d 1 + en − 1 n 16

4. Analysis of the steady state TFP and ITcommunication levels

In this section, we focus on the impact of the parameters defining the network externality effect i.e. the number of firms, n, and the extent of the network effect, e on the steady state levels of TFP and telecommunications investment 8 . Several, and sometime contrasting, forces are at work. The term S N = {[1 + en − 1][1 − e 2 n − 1]} d represents the productivity level of the firm’s telecommunication expenditures or the pure network effect, while the term S N = {d + d 0 [1+en−1]} is the elasticity of the telecommunications invest- ment on the TFP dynamics at the symmetric equilibrium. A higher e andor an increased number of users n increase the pure network effect: this enhances the productivity of the firm’s own network usage which results in higher marginal benefits of communication technologies. However, a larger extent of spillovers as well as a larger number of users mean that the appropriability of the firm’s own 7 Note that in equilibrium A d and N d are constant and positive, but the original variables grow at a constant steady state growth rate, as defined by the FOC of the original non-deflated system. 8 As regards the other parameters, note that the interest rate r, c n have a negative effect on both TFP and telecommunications steady state levels. Since b B 1, c K has a negative influence on both the steady state levels. The autonomous parameter of scale of demand X has a positive influence on A d and N d . The depreciation rate s a has a negative impact on A d because d 1 B 1: the faster the depreciation rate, the lower the steady state total factor productivity, while its effect on N d depends on the ‘adjusted elasticity of demand’: if b + g B 2, s a has a positive impact on the steady state telecommunications usage, but if the elasticity of demand is high, the effect could be reversed. Remember that 1 − g + d 1 b − 1 is positive in order to have a stable dynamic system see the Appendix. communications usage declines or S N decreases. We therefore find two typical effects studied in the models on RD and spillovers. On the one side, when e andor n increase, the intra-industry spillover pool is fostered, which results in a benefit for the firm, but on the other side, less appropriability of knowledge spillovers has a disincentive effect on telecommunications investment, as free riding and exploiting incoming contacts becomes more appealing to the firms. Although these two effects are similar to those analysed by the RD models, they differ in the intensity: as we also noted in Section 2, in our model the impact of the parameters e and n on the intra-industry pool of knowledge is stronger than that considered by the standard RD spillovers models. Indeed, this will have substan- tial implications in the comparative statics analysis. The parameter n has also a positive impact on the steady state TFP and telecommunication investment level through the perceived price elasticity: a greater number of firms implies a higher perceived price elasticity, which increases the perceived change in demand by a productivity improvement. However, an increase of the number of users also exhibits a negative effect on A d and N d , as it increases what we call the competition effect, i.e. the term n a − b1 − a . This effect is driven by the Dixit-Stiglitz specification of the demand for differentiated goods, which at the symmetric equilibrium is a negative function of the number of available varieties. The Dixit-Stiglitz specification has been mainly used by the endogenous growth models and indeed differs from the linear demand specification, quite common to those RD models focusing on quantity competition. Both of these opposite effects are stronger when product differentiation is low the term a − b is high, andor there is a great difference between the elasticity of substitution among goods a and the inter-industry price elasticity b. As it is analytically quite difficult to disentangle the above-mentioned effects, we mainly use numerical simulations 9 . Whenever appropriate, we also compare our results with those of the literature on RD and spillovers. 4 . 1 . The extent of the network externality effect e : comparati6e statics 4 . 1 . 1 . The impact of the extent of network externality on N d The impact of the network extent parameter on N d is ambiguous, as the following derivative shows: sign N d e 9 The figures in this section are obtained from simulations performed using ‘Mathematica 3’. The values of the parameters and exogenous variables are: a = 2.5, b = 1.5, c no = 0.8, c Ko = 1.35, X 00 = 100, r = 0.007, s a = 0.005, g = 0.05, d 0 =0.1, d=0.3, e=0.2. Only if different values for some parameters are used, we report them. = sign − d 0 n−1S N d 1 b − g − 21 − g 1 + en − 1 2 B + d 0 S N d 1 b − g − 21 − gS N S N d d1b−g−21−g − 1 e 1 + en − 1 1 − e 2 n − 1 n \ Our simulations yield: Simulation result 1 : when the number of firms is low, an increase of the extent of network effects leads to a decrease of the steady state communication level. However, when the number of firms increases, a higher network effect causes telecommunications investment to decline, and then to rise. With a specification similar to that of Spence 1984 — which, in terms of our model, would imply at the symmetric equilibrium dAdt = N[1 + en − 1], S N = [1 + en − 1] − 1 and S N = 1 — the positive effect of the network spillovers disap- pears, while the negative one prevails. In our model, the possibility of a positive impact of network extent on telecommunications investment depends on the double counting method 10 , and more specifically on our modelling of the network external- ity effect. Another important determinant of the sign of the derivative is the general price elasticity b. The value of this elasticity is an indicator for the degree of product differentiation with regard to the homogeneous good. In our model, a higher level of b or less differentiated products increases the possibility of a positive influence of e on N d . This effect also differs from the findings of De Bondt et al. 1992, who conclude that a positive effect is more likely when product differentia- tion is moderate to high. In their model, moderate to high product differentiation implies that appropriability is larger. In our model, higher product differentiation has an opposite effect: it lowers the perceived price elasticity of demand and therefore it results in less competition, which in turns lowers the incentives to invest in cost-reducing innovation. Therefore, the positive effect of spillovers on the cost-reduction innovation is more likely to appear under low product differentiation. Our analysis confirms the results of the literature on RD that high technologi- cal opportunities i.e. high d and d 0 will cause a positive influence of e on N d . Summarising the results of this sub-section, we can say that, in our model, a higher number of firms in the product market raises the total volume of spillovers and, together with high technological opportunities linked to communication networks and low differentiation, creates the conditions for greater appropriability of telecommunications investment. These three conditions are therefore the prereq- uisites for a positive effect of network externality on the steady state telecommuni- cations level. ¿¹¹¹¹¹¹¹¹¹¹¹Ë¹¹¹¹¹¹¹¹¹¹¹À 10 It must be stressed that, in our model, the number of firms determines the stability of network effect: to have positive network effect we assume e 2 B n − 1. With many firms, the positive effect is then limited to a low range of the externality parameter. Í Ã Ã Ã Ã Ã Ã Á Ä Fig. 2. The impact of extent of network effect on productivity level. 4 . 1 . 2 . The impact of the extent of network externality on A d The technological performance of a firm can be measured by its steady state productivity level. In this sub-section, we investigate the relationship between technological performance and the extent of network effects. While the impact of d and d 0 on steady state TFP is always positive, the parameter e has again an ambiguous effect: sign A d e = sign − S N d 0 n−1 1 + en − 1 2 B + d 0 S N − 1 S N e 1 + en − 1 1 − e 2 n − 1 n \ This yields: Simulation result 2 : when the externality parameter is low, an increase of e lowers A d , but this effect is reversed when the externality is higher. Fig. 2 shows that the steady state productivity level first decreases then increases, until the ‘stability condition’ is reached. This effect appears regardless of the number of users. To our knowledge the impact of the spillover parameter on the technological performance of a firm has been neglected not only by the literature on RD, but also by empirical studies on productivity and usage of information technologies. The rationale for simulation result 2 is that, as long as the extent of the network effect is too low, there is no incentive to invest in ITtelecommunication usage, which exhibits a negative or zero impact on TFP. When the quality of the exchanges increases, namely when the information gathered by the community of users is more valuable to the firm, then a positive impact of network effect can be predicted. Another interesting explanation of our result should probably take into account the consideration of a learning function, because it is recognised that extensive experience is needed by firms and organisations to exploit IT gains, as it is for most radically new technologies. Probably, positive learning effects may cause an increase in the extent of the interaction among communication technologies Í Ã Ã Ã Ã Á Ä Í Ã Ã Ã Ã Ã Ã Á Ä users, thus endogenising the shift from the negative to the positive part of the curve we depicted in Fig. 2. The investigation on this latter point is left for further research. 4 . 2 . The number of users n : comparati6e statics 4 . 2 . 1 . The impact of the number of users on N d In this subsection, we discuss the impact of the club of users on the steady state ITtelecommunication level. When the number of firms increases, the cost-reduction investment is negatively affected by two effects: the lower appropriability and the competition effect. However, an increase of n has a positive impact on the network effect and on the perceived price elasticity: sign N d n = sign − S N eu 1 1 + en − 1 2 B + u 2 d S N d 1 b − g − 3 − 2g n 1 + en − 1 1 − e 2 n − 1 n \ +bu 3 n 1 − 1 a P \ + u 4 a − b 1 − a n a − b1 − a − 1 B u 1 = S N d 1 b − g − 21 − g 1 − 1a P n a − b1 − a u 2 = S N 1 − 1a P n a − b1 − a u 3 = S N d 1 b − g − 21 − g S N n a − b1 − a u 4 = S N d 1 b − g − 21 − g S N 1 − 1a P We then find two patterns: Simulation result 3 : when the extent of the externality effect is low, an increase of the number of users has a negative impact on N d ; when e is high, this effect is reversed. The increasing pattern is another element that does not appear in the standard literature on RD and RD spillovers. An increasing pattern is more likely to appear when products are less differentiated higher values of b, the technological opportunities linked to the communication network increase higher d 0 and the difference between the elasticity of substitution a and the inter-industry price elasticity b is high. 4 . 2 . 2 . The impact of the number of users on A d The impact of an increased number of users on the steady state productivity level has the same determinants as discussed in the Section 4.2.1: Í Ã Ã Ã Ã Á Ä Í Ã Ã Ã Ã Á Ä Í Ã Ã Ã Ã Á Ä Í Ã Ã Ã Ã Ã Ã Á Ä sign A n = sign − v 1 S N 1 + en − 1 2 B + v 2 d 0 S N n 1 + en − 1 1 − e 2 n − 1 n + v 4 n a P a P − 1 n \ + v 3 a − b 1 − a n a − b1 − a − 1 B v 1 = S N 1 − 1a P n a − b1 − a v 2 = S N 1 − 1a P n a − b1 − a v 3 = S N S N n a − b1 − a v 4 = S N S N 1 − 1a P A few simulations help to illustrate the complex interplay between market structure and technological change in our model. First, we analyse the impact of elasticity of substitution and inter-industry price elasticity. Simulation result 4 : when spillovers are low, the productivity level decreases with an increased number of users. This decreasing pattern is also found when the difference between a and b is very low. When spillovers are high, a duopoly always obtains the highest productivity level. The total factor productivity decreases, then increases with an increased number of users, until the stability condition has been reached. The higher the difference between a and b, the faster the decrease. The increasing pattern is an interesting one and, to our knowledge, a new pattern to the literature. With higher spillovers and less differentiation, entry determines first a decrease then an increase of the steady state productivity level. The intuition behind these results is that the lower market shares as a result of a higher number of users on the communication network drive the productivity level down. This negative effect decreases when the number of firms increases and at a certain intermediate level of rivalry, the positive influence of a larger investment in ITtelecommunication and then a larger intra-industry knowledge stock becomes more important. The positive pattern is then driven by the same forces that determine the positive impact of the number of users on the telecommunications steady state level: high network effect and low differentiation. If we combine all the results of these sub-sections, we can expect that the most fa6ourable condition for a firm to increase her in6estment in network technologies and to obtain a more efficient total factor producti6ity is: to be in a market with low product differentiation andor with a great difference between the elasticity of substitution among goods and the inter-industry price elasticity, an important number of users, an intensive network externality extent and considerable techno- logical opportunities linked to the telecommunication network. Í Ã Ã Ã Ã Á Ä Í Ã Ã Á Ä Í Ã Ã Ã Ã Ã Ã Á Ä

5. Consumer surplus, total profits and welfare