Question

Consider the Solow growth model with depreciation rate and population growth rate n. The equation of motion for the capital stock and the per worker production function in this economy are given by: Ak= s(f(k) - (8 + n) k y= f(k) = k1/4 a). Suppose adoption of modern birth control methods in a developing country causes the population growth rate to decrease. What happens in the main Solow diagram: what curve(s) shin, what happens to the steady- state level of capital per worker (if anything), and explain the intuition regarding how a new equilibrium is reached b). If the rate of depreciation is .05, the population growth rate is .03, the saving rate is.30. solve for the steady-state level of capital per worker, output per worker, and consumption per worker. c). In the Solow model as formulated above, what is the growth rate of the standard of living in steady-state? Explain. How can the Solow model be augmented to explain the roughly 2% average growth rate in real per-capita GDP that the U.S. has experienced over many decades?

Answer 1

- 18+n) k. -y=f(k) (stn) Output / werke Ak - s. (fik) y = f(k)= (kily. a Decrease in population Growth The initial steady state (8tny equilibrium occurs at pant A decrease in population growth rate will shift the Klasy. (stn line downwards to (Stris and new steady state equilibrium & occurs at point Es, where both capital per worker and Output RiCapitakt P per worker have increased. This is per Worker (k) because as labor decreases the factors at production will be used more intensively (b d= 0.05 n = 0.03 s= 0.30 At the steady state lene : k = s . fck) Etn. k = 0.30 (kily o-osto-03 (ki 3/4 = 0.30 = 3.75. T** (2.75% 5.8. * = y*_ s.y = 0.70x1.55 - 1:08. (o At steady state, Granth rate of Output fer worker is zero. It can be explained by introduction of Technological progress which is considered as constant in sshow Model.