ECON 425 | ECONOMIC GROWTH FALL 2022 PROBLEM SET 4 The Solow model referred to below is "version 2" as presented in Chapter 4. That is, in what follows: (1) assume zero growth in total factor productivity A and (ii) unless directed otherwise, without loss of generality normalize A = 1. 1. There are two islands, called A and B. On both islands, output is produced with labor and land. The quantity of land is fixed so we can bundle it together with productivity, which is assumed to also be constant (just like we did in class). The two islands have the same level of productivity and the same production functions. People on both islands also enjoy the same "subsistence" level of consumption, o. However, the two islands differ in how the growth rate of population, L, is related to the real wage, w. These "G(.)" equations are as follows: Island A: L = (w-o) Island B: L = (w-0)/2 a. How do the steady-state levels of population on the two islands compare? Explain. b. Suppose that on each island, half the population was wiped out by a meteor shower in the year to (very gruesome, I know). Prior to this catastrophe, both islands were in their steady states. Draw a time-path graph showing the evolution of the real wage over time on the two islands (right before year to, immediately after, and in the long run). Use the same graph for both islands. You should clearly indicate how the levels of the real wage on the two islands compare to each other at any given point in time. Explain