Economic growth and economic development 701

Introduction to Modern Economic Growth Let us also modify the baseline environment by assuming that total population, in particular, the population of scientists, grows at the exponential rate n With a similar arguments to that in Section 13.3 in Chapter 13, it can be verified that aggregate output in this economy will grow at the rate (see Exercise 15.15): n (15.42) g∗ = 1−λ Consequently, even with limited knowledge spillovers there will be income per capita growth at the rate λn/ (1 − λ) As usual, this is because of the amplification to the externalities provided by population growth It can also be verified that when λ = 1, there is no balanced growth and output would reach infinity in finite time (see Exercise 15.16) The important point for the focus here concerns the market size effect on the direction of technical change To investigate this issue, note that the technology market clearing condition implied by (15.41) is (see Exercise 15.17): (15.43) η L NLλ π L = η H NHλ π H , which is parallel to (15.36) Exactly the same analysis as above implies that equilibrium relative technology can be derived as ả ả µ ¶ σ−1 σ NH − γ 1−λσ H 1−λσ 1−λσ (15.44) =η NL γ L Now combining this with (15.19)–which still determines the relative factor prices given technologywe obtain ả à ả 2+ ả (1) 1−λσ σ−1 − γ H 1−λσ w H = η 1−λσ (15.45) ω∗ ≡ wL γ L This equation shows that even without scale effects we obtain exactly the same results as before Specifically: Proposition 15.10 Consider the directed technological change model with no scale effects described above Then there is always weak equilibrium (relative) bias, meaning that an increase in H/L always induces relatively H-biased technological change ¤ Proof See Exercise 15.8 687