Economic growth and economic development 697

Introduction to Modern Economic Growth This is no longer true when δ > To characterize the results in this case, let us combine condition (15.36) with equations (15.15) and (15.18), we obtain the equilibrium relative technology as (see Exercise 15.9): ả à ả ả µ σ − γ H NH = η 1−δσ , (15.37) NL γ L where recall that η ≡ η H /η L This expression shows that the relationship between the relative factor supplies and relative physical productivities now depends on δ This is intuitive: as long as δ > 0, an increase in NH reduces the relative costs of H-complementary innovations, so for technology market equilibrium to be restored, π L needs to fall relative to π H Substituting (15.37) into the expression for relative factor prices for given technologies, which is still (15.19), yields the following longrun (endogenous-technology) relationship between relative factor prices and relative factor supplies: (15.38) wH wL ả = 1 ả (1) H L ¶ σ−2+δ 1−δσ It can be verified that when δ = 0, so that there is no state-dependence in R&D, both of the previous expressions are identical to their counterparts in the previous section The growth rate of this economy is determined by the number of scientists In BGP, both sectors grow at the same rate, so we need N˙ L (t) /NL (t) = N˙ H (t) /NH (t), or η H NH (t)δ−1 SH (t) = η L NL (t)δ−1 SL (t) Combining this equation with (15.33) and (15.37), we obtain the following BGP condition for the allocation of researchers between the two different types of technologies, (15.39) η 1−σ 1−δσ µ 1−γ γ µ ¶− ε(1−δ) 1−δσ H L ¶− (σ−1)(1−δ) 1−δσ = SL∗ , S − SL∗ and the BGP growth rate (15.40) below Notice that given H/L, the BGP researcher ∗ , are uniquely determined We summarize these results with allocations, SL∗ and SH the following proposition: 683