Introduction to Modern Economic Growth (1) Larger countries not necessarily grow faster (though the larger market of the United States or European economies may have been an advantage during the early phases of the industrialization process We will return to this issue in Chapter 22) (2) The population of most nations has not been constant If we have population growth as in the standard neoclassical growth model, sample, L (t) = exp (nt) L (0), these models would not feature a balanced growth path Instead, growth would become faster and faster over time, eventually leading to an infinite output in finite time, violating the transversality condition (3) In the data, the total amount of resources devoted to R&D appears to increase steadily, but there is no associated increase in the aggregate growth rate These observations have motivated Jones (1995) to suggest a modified version of the baseline endogenous technological progress model While the type of modification to remove scale effect can be formulated in the lab equipment model (see Exercise 13.19), it is conceptually simpler to so in the context of the model with knowledge spillovers discussed in the previous section In particular, in that model the scale effect can be removed by reducing the impact of knowledge spillovers More specifically, consider the model of the previous section with only two differences First, there is population growth at the constant exponential rate n, so that L˙ (t) = nL (t) The economy admits a representative household, which is also growing at the rate n, so that its preferences can be represented by the standard CRRA form: (13.32) Z ∞ exp (− (ρ − n) t) C (t)1−θ − dt, 1−θ where C (t) is consumption of the final good of the economy at time t, which is produced as before (with the production function (13.2)) Second, in contrast to the knowledge-spillovers model studied in the previous section, the R&D sector only admits limited knowledge spillovers and (13.24) is replaced by (13.33) N˙ (t) = ηN (t)φ LR (t) 590