Economic growth and economic development 681

Introduction to Modern Economic Growth Similar to the demands for machines in Chapter 13, these are iso-elastic, so the maximization of the net present discounted value of profits implies that each monopolist should set a constant markup over marginal cost and thus a price of χL (ν, t) = χZ (ν, t) = for all ν and t Substituting these prices into (15.13) and (15.14), we obtain xL (ν, t) = pL (t)1/β L for all ν and all t, and xH (ν, t) = pH (t)1/β H for all ν and all t Since these quantities not depend on the identity of the machine, only on the sector that is being served, profits are also independent of the machine type In particular, we have (15.15) π L (t) = βpL (t)1/β L and π H (t) = βpH (t)1/β H This implies that the net present discounted values of monopolists only depend on which sector they are supplying and can be denoted by VL (t) and VH (t) Next, combining these with (15.5) and (15.6), we obtain derived production functions for the supply of the intermediate goods of the two types: (15.16) YL (t) = 1−β pL (t) β NL (t) L 1−β and (15.17) YH (t) = 1−β pH (t) β NH (t) H 1−β These derived production functions are similar to (13.12) in Chapter 13, except for the presence of the price terms 667