Introduction to Modern Economic Growth of quality q (ν, t) Note that the demand from the final good sector for machines in (14.4) is iso-elastic as in the previous chapter, so the unconstrained monopoly price is again a constant markup over marginal cost However, contrary to the situation in the previous chapter, there is now competition between firms that have access to different vintages of the machine This implies that, as in our discussion in Chapter 12, we need to consider two regimes, one in which the innovation is “drastic” so that each firm can charge the unconstrained monopoly price, and the other one in which limit prices have to be used Which regime we are in does not make any difference to the mathematical structure or to the substantive implications of the model Nevertheless, we have to choose one of these two alternatives for consistency Here we assume that the quality gap between a new machine and the machine that it replaces, λ, is sufficiently large, in particular, satisfies ¶ 1−β µ β , (14.5) λ≥ 1−β so that we are in the drastic innovations regime (see Exercise 14.6 for the derivation of this condition and Exercise 14.7 for the structure of the equilibrium under the alternative assumption) Let us also normalize ψ = − β as in the previous chapter, which implies that the profit-maximizing monopoly price is (14.6) χ (ν, t | q) = q (ν, t) Combining this with (14.4) implies that (14.7) x (ν, t | q) = L Consequently, the flow profits of a firm with the monopoly rights on the machine of quality q(v, t) can be computed as: π (ν, t | q) = βq (ν, t) L This only differs from the flow profits in the previous chapter because of the presence of the quality term, q (ν, t) Next, substituting (14.4) into (14.3), we obtain that total output is given by (14.8) Y (t) = Q (t) L, 1−β 614