Introduction to Modern Economic Growth Then the next proposition shows a negative result on the possibility of purely laboraugmenting technological change Proposition 15.13 Consider the baseline model of directed technological change with the knowledge spillovers specification and state dependence Suppose that δ < and capital accumulates according to (15.46) Then there exists no BGP Ô Proof See Exercise 15.22 Intuitively, even though technological change is more labor augmenting than capital augmenting, there is still capital-augmenting technological change in equilibrium, and this, combined with capital accumulation, is inconsistent with balanced growth In fact, even a more negative result can be proved (see again Exercise 15.22): in any asymptotic equilibrium, the interest rate cannot be constant, thus consumption and output growth cannot be constant In contrast to these negative results, there is a special case that justifies the basic structure of the neoclassical growth model This takes place when we have extreme state dependence, so that δ = In this case, it can be verified that technology market equilibrium implies the following relationship in BGP (see Exercise 15.23): r (t) K (t) = η −1 wL (t) L (15.47) Thus, directed technological change ensures that the share of capital is constant in national income This already gives the intuition for why steady capital accumulation should lead to purely-labor augmenting technological change (from our analysis in Chapter 2) This is indeed the case More specifically, recall from (15.19) that µ ¶ε µ ¶ σ−1 µ ¶− K (t) σ − γ σ NK (t) σ r (t) = , wL (t) γ NL (t) L therefore, r (t) K (t) = wL (t) L (t) µ 1−γ γ ¶ σε µ NK (t) NL (t) µ ¶ σ−1 σ In this case, (15.47) combined with (15.46) implies that (15.48) N˙ L (t) N˙ K (t) − = sK NL (t) NK (t) 690 K (t) L ¶ σ−1 σ