Consumer surplus, total profits and welfare

5. Consumer surplus, total profits and welfare

The last section of this paper concentrates on the impact of network externalities and number of users on consumer surplus, total profits and welfare. Using the FOC of the deflated system and the definition of the consumer utility, the consumer surplus can be written as: CS = nTC b − 1 a P a P − 1 17 where: TC = X 00 b c K0 1 − b n a − ba − 1 A d b − 1 a P a P − 1 − b Remembering that a, b \ 1, a \ b, a P \ 1, is it easy to see that the consumer surplus depends positively on the number of firms, reflecting love of variety, and on the perceived price elasticity, because if a P increases, the mark-up over costs decreases. The technological level or total factor productivity also has a positive impact on consumers’ surplus. Using FOC, total profits can be written as follows: np = TC 1 a P − 1 − s a d + d 1 + en − 1 r + 1 − gs a = 19 Note that, as for consumer surplus, through TC, the technological level of firms has a positive effect on total profits. In order to have a viable situation in monopolistic competition, the long run total profits have to be equal to zero. This condition defines the no-entry condition and the optimal number of firms present in the market n. The first term of Eq. 19 can be interpreted as the gross profit’s ratio, while the second one represents the IT fixed investment ratio. The impact of an increase of the number of users on total profit is ambiguous, because two opposite effects are present. On one side, the entry of new users increases the perceived price elasticity a P , which has a negative effect on profits; on the other side, it lowers the fixed cost ratio of the investment in the communication technology with network effects, which increases profits. We find that the first effect dominates the second one: Simulation result 5 : profits decrease with entry of new users and the appearance of a negative profit is more likely when technological opportunities d, d 0 are larger. This situation is analysed by the traditional literature on RD. The long-run equilibrium is attained at different optimal numbers of firms, depending on different values of elasticity of substitution a and the productivity of the network d. Once the no-entry condition is determined, the stability condition gives us a condition on network effect associated with that scenario: e = n−1. This link between the optimal number of firms and the extent of the network effect ensures the coherence of the model. We find a result similar to that of Dasgupta and Stiglitz 1980: industries with larger technological opportunities tend to have few firms. A higher extent of network effect decreases the second term in the brackets see Eq. 19 and thus reduces the probability of a negative profit rate. If network externality is high, then the number of viable users in a market will increase. A higher degree of product differentiation lower level of a, decreases the perceived elasticity and hence makes a negative profit less likely. When a decreases, the number of viable users increases. The model therefore predicts that industries with high differentiation have more ITtelecommunication users than the industries with more homogeneous goods. Combining these findings we can conclude that traditional industries with high technological opportunities, a low extent of communication spillover and a low degree of product differentiation allow a low equilibrium number of network technologies users. Highly differentiated industries with low technological opportunities and high network effects are characterised by a high equilibrium number of users. 5 . 1 . Welfare We now analyse the total impact of the number of users, and the extent and prod- uctivity of the network effect on total welfare, as the sum of consumer surplus and total profits. We easily see that technological opportunities increases welfare, because both consumer surplus and total profits depends on the productivity level A d . The impact of the network effect extent on welfare is not clear-cut. First, parameter e has a positive impact on total welfare, because it increases total profits. Second, in the previous section simulation result 2 we found that a positive impact of e on the steady state productivity level A d is likely to appear when this parameter is high, regardless the number of firms. When e is low, its positive effect on the total profit to total costs ratio does not easily counterbalance the negative impact on total costs, that enters both consumer surplus and total profits. The impact of the extent of network effects thus depends on its impact on the steady state technological level. This yields the following result: Simulation result 6 : when the extent of network effect is high, welfare is a positive function of the network externality extent. The influence of an increase in the number of users is again difficult to understand. First, new users increase the perceived price elasticity, which increases consumer surplus and decreases total profits. Second, the influence of new users on the productivity level is ambiguous see Section 4.1.2. The difference between a and b, and the extent of the network effect determines whether the influence is positive or negative. Third, when consumers show love of variety, entry directly increases the total surplus. Our simulations show that: Simulation result 7 : with a high differentiation, welfare increases with entry of new users. The degree of differentiation and extent of network externality effect are of crucial importance, because with low differentiation high inter-industry price elasticity a and low e, welfare decreases with the entry of new users. This result is coherent with the analysis of the impact of entry on the steady state TFP: in Section 4.2, we said that A d decreases with entry if the differentiation and the extent of spillover are low. The decreasing welfare is then driven by this negative effect on A d , which decreases consumer surplus and total profits. We obtain the following result: Simulation result 8 : when differentiation and extent of network effect are low, total welfare decreases with entry. 6. How is this model linked to empirical evidence?