Economic growth and economic development 695

Introduction to Modern Economic Growth 15.4 Directed Technological Change with Knowledge Spillovers We now consider the directed technological change model of the previous section with a different specification of the innovation possibilities frontier This is not only useful to show that the results can be generalized, but also enables us to understand the conditions leading to the strong bias result in Proposition 15.4 better The lab equipment specification of the innovation possibilities frontier is special in one respect: it does not allow for state dependence State dependence refers to the phenomenon in which the path of past innovations affects the relative costs of different types of innovations The lab equipment specification implied that R&D spending always leads to the same increase in the number of L-complementary and H-complementary machines We will now introduce a specification with knowledge spillovers, which allows for state dependence Recall that, as discussed in Section 13.2 in Chapter 13, when there are scarce factors used for R&D, then growth cannot be sustained by continuously increasing the amount of these factors allocated to R&D Therefore, in order to achieve sustained growth, these factors need to become more and more productive over time, because of spillovers from past research Here for simplicity, let us assume that R&D is carried out by scientists and that there is a constant supply of scientists equal to S (Exercise 15.18 shows that the results are identical when workers can be employed in the R&D sector) With only one sector, the analysis in Section 13.2 in Chapter 13 indicates that sustained endogenous ˙ growth requires N/N to be proportional to S With two sectors, instead, there is a variety of specifications with different degrees of state dependence, because productivity in each sector can depend on the state of knowledge in both sectors A flexible formulation is the following: (15.32) N˙ L (t) = η L NL (t)(1+δ)/2 NH (t)(1−δ)/2 SL (t) and N˙ H (t) = η H NL (t)(1−δ)/2 NH (t)(1+δ)/2 SH (t) , where δ ≤ 1, and SL (t) is the number of scientists working to produce L-complementary machines, while SH (t) denotes the number of scientists working on H-complementary machines Clearly, market clearing for scientists requires that (15.33) SL (t) + SH (t) ≤ S 681