Introduction to Modern Economic Growth Proof Most of the proof is given in the preceding analysis In Exercise 14.3 you are asked to check that the BGP equilibrium is unique and satisfies the transversality condition Ô The above analysis illustrates that the mathematical structure of the model is quite similar to those analyzed in the previous chapter Nevertheless, the feature of creative destruction, the process of incumbent monopolists being replaced by new entrants, is new and provides a very different interpretation of the growth process We will return to some of the applications of creative destruction below Before doing this, we can also analyze transitional dynamics in this economy Similar arguments to those used in the previous chapter establish the following result: Proposition 14.2 In the model of competitive innovations described above, starting with any average quality of machines Q (0) > 0, there are no transitional dynamics and the equilibrium path always involves constant growth at the rate g∗ given by (14.21) Proof See Exercise 14.4 Ô A notable feature of the model, which is again related to the functional form of the aggregate production function (14.3), is that only the average quality of machines, Q (t), matters for the allocation of resources Moreover, the incentives to undertake research are identical for two machine types ν and ν , with different quality levels q (ν, t) and q (ν , t), thus there is no incentive to undertake different R&D investments for more and less advanced machines This is again a feature of the functional forms chosen here, and Exercise 14.12 shows that in different circumstances this result may not apply Nevertheless, the specification chosen in this section is appealing, since research directed at a broad range of machines and products seems to be a good approximation to reality 14.1.4 Pareto Optimality This equilibrium, like that of the endogenous technology model with expanding varieties, is typically Pareto suboptimal The first reason for this is the appropriability effect, which results because monopolists are not able to capture the entire social gain created by an innovation However, 619