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					, 
						Antonella

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decreases, the market share and the demand of new and more productive varieties made availableincreases as long as they are on the technological frontier.5 Structural changes and the scale effectOne of the most striking characteristics of the moving equilibrium we have so far described is thatit allows us to represent the effects of ongoing patent innovations which take place together withprocess innovations. Considering both kinds of innovations gives a more complete picture of theeffects of R&D activities and it produces a setup in which the rate of growth of patent innovationsvaries across time according to workers’ distribution between the final and the innovative sectorsconsidered in the model.In the period in which technology of type i is available, we know from expression (12) that therate of innovation is proportional to the number of workers employed in the R&D sector, and thisnumber LR, derived from (33)-(34) when V˙i = 0, depends on the value of bi, that isLR =Lbi (1− α)− aρα(1− α) bi + α(36)As in Grossman and Helpman (1991), we assume that L is sufficiently large to allow patentinnovations to take place: this requires that L > aρα/bi (1− α). Once more, it is readily verifiablethat when bi = 1 we obtain the same results as in Grossman and Helpman (1991).Expression (36) shows that the number of workers employed in the innovative sector is anincreasing function of bi because∂LR∂bi=(1− α)α (L+ aρ)((1− α) bi + α)2> 0Therefore, when there are at least two different types of firms producing using different technolo-gies, and the innovative sector intensifies its research in finding new patents for the productionof new goods employing the more productive technologies, then any time a new patent is pro-duced and implemented the value of bi increases. As bi increases, the final sector in aggregate22becomes more productive and, therefore, more workers are made available to be employed in theR&D sector. Moreover, the growth rate of new varieties increases as it is shown by the followingexpressiongi = g =LRa=Lbi (1− α) /a− ρα(1− α) bi + α(37)The growth rate g is superiorly and inferiorly limited because 0 ≤ bi ≤ 1.In general, the model explains structural changes by means of workers’ distribution movementsbetween the two sectors. Indeed, changes in LR (and LC) reflect changes in bi, which are the resultsof product and process innovations. We know that as long as new patents are produced by meansof product innovations, bi continues to increase over time implying a continuous shift of workersfrom the sector in which final consumption goods are produced to the innovative sector, with anincreasing value of gi. However, once there is a process innovation which reduces γi, changes in biare more complex and they explain structural changes of different nature, which may end up alsowith workers shifted from the innovative sector towards the sector in which consumption goodsare produced if bi for the new type of varieties is larger than it was for previous varieties on thefrontier.Particularly, we may state that there is a redistribution of workers from the innovative (finalgood) toward the final good (innovative) sector when the value which bi takes once the processinnovation takes place is smaller (larger) than its value for previous varieties on the frontier. InAppendix A we show that when process innovations are relatively not too big, bi decreases afterprocess innovations take place with workers moving from the innovative sector to the final goodsector and, as a consequence, the growth rate of patents decreases.Once the process innovation has taken place, as long as there are further innovations whichincrease the number of patents with the same value of γ, workers move from the final to theinnovative sector. They are induced to move again to the final sector, once a subsequent processinnovation of limited impact takes place.Regarding the scale effect, we notice that it would still be present in this work if we had not23introduced the assumption in (19) that increases in L may produce process innovations. Thesecontinuous subsequent process innovations due to increases in L may contribute to continuouslylowering the value of bi and keeping g from increasing.In particular, this could not happen as long as subsequent patent innovations are related tovarieties characterized by the same value of γ. In fact, partially differentiating (36) with respectto LR, L and bi, after few steps we obtaindLRLR=(1− α) bi(Lbi (1− α)− aρα)µLdLL+α (L+ aρ)((1− α) bi + α)dbibi¶(38)From (38) we know that LR, and consequently g, would be constant only ifdbibi= −L ((1− α) bi + α)α (L+ aρ)dLL≡ b∗ < 0 (39)This is never the case when varieties of type i remain along the technological frontier given thatbi would continuously increase over time and, therefore, dbi/bi can only be positive.However, when L increases, continuous process innovations could continuously lower bi. If thesetwo effects on bi balance each other, bi will be constant implying that LR, in turn, is constantwith no change in the growth rate of the number of varieties. In appendix B we show that thiswould imply a constant growth of the real gross domestic product (GDP).Therefore, we may conclude that when process innovations are associated to product innova-tions, we can obtain equilibrium paths characterized by a stable distribution of workers betweenthe two sectors, which corresponds to a fixed growth rate, provided that bi continuously decreasesover time due to subsequent process innovations.6 ConclusionScholars in the field of international economics and economic growth have devoted great attentionto the subject of heterogeneity of firms in the last few years. Productivity differences across firmsare, for instance, analyzed in a general equilibrium framework by Melitz (2003) which analyzes24

Structural changes and the scale effect

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Structural changes and the scale effect

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Università del Salento: ESE - Salento University Publishing