Consider the model in Section 18.3.1, and suppose that all countries have the same labor force size Lj = 1, have the same ηj = η, and only differ in terms of ζj. Imagine that the cross-country range of ζj is the same as used in the quantitative evaluation of the neoclassical growth model in Chapter 8.
(a) Evaluate the impact of these differences in ζj on cross-country technology and income differences for different values of φ.
(b) What value of φ is necessary so that a 4-fold difference in ζj translates into a 30-fold difference in income per capita?
(c) How would you interpret the economic significance of such a value of φ? Is this a more satisfactory model of cross-country technology and income differences than the neoclassical growth model?