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2. Consider the Solow growth model. Suppose that the production function is constant returns to scale...
4. The table below shows a Markov matrix for the income levels of 40 countries over two centuries: Poor in 20h CE 20th CE Poor in 19th CE Middle Income in 19h CE 4 Rich in 19th CE 10 How has income inequality across these countries changed? Why?
Solow Growth Model D. Consider an economy with production characterized by function Y = AVKL, per capita output y = AVkt with rate of depreciation of capital 8, investment it = sy. = sAvky, capital transition function kt+1 - k = SAVk - Okt, where s is savings ratio. 1. Putting per capita output (income) y on the y-axis and k on the x-axis, graph the curves for depre- ciation and investment. Label steady state capital k* and steady state...
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...
Malthusian Model of Growth Notation: Yt Aggregate output; Nt Population size; L¯ Land (fixed); ct Per capita consumption Production: Aggregate production function is Yt = F(Nt , Lt) = zN2/3 t L 1/3 t Population Dynamics: Nt+1 = g(ct)Nt Population growth function: g(ct) = (3ct) 1/3 Parameter Values: Land: L¯ = 1000 for all t. Productivity parameter: z = 1 ...
Exercise 1: Solow model . Consider an economy whose production function is defined by Y (t) = F (K (t), L (t)) = K (t) 1 − α · L (t) α. with 0 <α <1. In this economy, the population grows at the following rate: L (t) = n + β where n and β are strictly positive constants and k (t) represents capital per capita: k (t) = L (t). Moreover, a constant part of the product is...
Suppose an economy follows the Solow growth model, with constant investment, depreciation, and population growth rates. Please explain your answers. (a) Suppose that the government withdraws an investment tax credit leading to a permanent drop in the investment rate. Discuss the effect on the level and growth of per capita income (PCI) in the short run. What happens to the level and growth of PCI in the long-run? (b) Suppose that the economy is below its steady state level per...
Consider a country described by the Solow model. The production function is y = 29, where 0 <a < 1. Assume that capital depreciates at a rate 8 € (0,1). a) Write down this production function in levels instead of in per capita terms. Does it display constant returns to scale? Show it. What about if a = 1? b) Find the value of c (per capita consumption) in steady state. c) Find the level of per capita capital that...
1. Consider the simple version of the Solow Growth Model discussed in class summarized by these four equations: Consumers save a fraction s of output: 1 = sy Capital grows as follows: K' = 1 + (1 - 8)K Firms use capital to make output: Y = AK 0.3 There is no government or trade: Y = C+/ where Y is GDP, / is investment, C is consumption, s is the savings rate, K is the capital stock this year,...
3. Transition Dynamics Consider the Solow growth model with constant population and no techno- logical progress as studied in class. Suppose the economy is initially in the steady state, with the level of per-capita capital stock of kss. The per-capita production function is given by y -f (k) - Akt, 0 < α < 1. In each of the following scenarios, plot the transition time path of per capita capital stock. kt, per-capita output, yt, and per-capita consumption, ct- (1-s...
Growth rates in the Solow model (II): Suppose an economy begins in steady state and is characterized by the following parameter values: s 0.2, d 0.1, A 1, L 100. Apply your answer to question 8 to calculate the growth of per capita GDP in the period immediately after each of the changes listed below. (Hint: Since the economy begins in steady state, its growth rate is initially zero and Kt K*.)(a) The investment rate doubles.(b) The productivity level rises...