Introduction to Modern Economic Growth and η H VH (t) ≤ and η H VH (t) = if ZH (t) > (15.21) Finally, the consumer side is characterized by the same necessary conditions as usual: C˙ (t) = (r (t) − ρ) , C (t) θ (15.22) and (15.23) Z t ả r (s) ds (NL (t) VL (t) + NH (t) VH (t)) = 0, lim exp − t→∞ which uses the fact that NL (t) VL (t) + NH (t) VH (t) is the total value of corporate assets in this economy We are now in a position to characterize a balanced growth path (BGP) equilibrium Let us define the BGP equilibrium to be one in which consumption grows at the constant rate, g∗ , and the relative price p (t) is constant From (15.10) this implies that pL (t) and pH (t) are also constant Let VL and VH be the BGP net present discounted values of new innovations in the two sectors Then (15.9) implies that 1/β (15.24) VL = 1/β βpL L βpH H and V = , H r∗ r∗ where r∗ is the BGP interest rate, while pL and pH are the BGP prices of the two intermediate goods The comparison of these two values is of crucial importance As discussed intuitively above, the greater is VH relative to VL , the greater are the incentives to develop H-complementary machines, NH , rather than NL Taking the ratio of these two expressions, we obtain µ ¶ β1 H pH VH = VL pL L This expression highlights the two effects on the direction of technological change discussed in Section 15.1 (1) The price effect manifests itself because VH /VL is increasing in pH /pL The greater is this relative price, the greater are the incentives to invent technologies complementing the H factor Since goods produced by relatively 669