Consider a version of the Solow growth model in which output is determined by the productionfunction Y = z(¾½³K + ¾½N) where z = 1. The depreciation rate and the savings rate are given byd = 0.13 and s 0.3. Assume that population N grows at a rate of n = 0.02. Calculate the=steady-state output per capita and consumption per capita, y* and c*, respectively.O (y*, c*) = (0.2, 0.06)○ (y*, c*) = (0.5, 0.35)○ (y*, c*) = (0.5, 0.21)○ (y*, c*) = (1.0, 0.70)

To determine the steady-state output per capita (𝑦∗) and consumption per capita (𝑐∗) in the given…

Answered: Consider a version of the Solow growth…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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Consider the Solow growth model with labor growth and no technology growth, i.e., n = 0, x = 0. Output is created by a Cobb-Douglas produc- n0,x tion function combining Labor, Lt, and capital, Kt, such that output, Y+is given by Y₁ = A+ KL Yt 1-a For a given time t, Given a level of Capital, and Investment, It, and a depreciation rate of capital, 8, the level of capital at time t+1 is given by the following law of motion of capital K++1 = Kt - 8Kt + It The labor growth rate in this economy is n = 2%, depreciation is 8 = 4%, the savings rate is s = 25%, and a = 0.3. Initial levels of capital, labor and technology are Ko = 10, Lo = 5, Ao = 1 respectively. The economy is assumed to be closed with no government spending. What is the value for capital per worker at time t = 1? (a) 2.22 (b) 2.57 (c)1.78 (d) 1.82
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Question 3 Suppose that the production function is given by: Y = 0.5 K0.3 N0.7 where Y is aggregate output, K is aggregate capital and N is the number of workers (labour). a) In the context of the Solow model, derive the steady-state levels of capital per worker, output per worker and consumption per worker in terms of the saving rate, s, and the depreciation rate, 6. Show clearly your calculations and workings. b) Graphically show and explain the effect of a fall of the saving rate on steady state output, capital and consumption per worker.
Consider an economy described by the Solow model with the following production function: Y = F(K, L) = K“ (L)'-« L grows at the rate n, the depreciation rate is 8, and the country saves a constant fraction s of its income. The change in capital per-worker is given by Ak = sy – (n+ 8)k. (a) Derive the per-worker production function. (b) Assuming population growth equals n and the depreciation rate equals 8, find the steady state level of capital per worker. It will depend on a, s, n and 8. Imagine the economy begins at the steady state you found in part b. Then there is a war that destroys a substantial amount of the economy's capital. The war does not affect the size of the labor force, population growth, the depreciation rate, or the saving rate. c) What is the immediate effect of the war on output per worker? Explain. d) After the war, is the growth rate of output per worker higher or lower than it was in steady state? Explain. e) How does the war affect steady state output per…
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Let 0 be the saving rate, n the population growth rate and d the depreciation rate. Which of the following conditions is consistent with steady state in the Solow-Swan model? Y = 0K K = (n + d)Y O OY/L = (n+ d)K/L о өК — (п +d)Y
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= 2. Consider a Solow growth model in which the production function is Yt AK²N₁¹/2, where A = 1. Moreover, assume that the depreciation rate is d = 0.02, the rate of population growth is n = 0.02, and the saving rate is s = = 0.2. a. Compute the value of the capital stock per worker in steady state. b. Draw a graph that represents the steady-state equilibrium of the model. c. Suppose that the capital-labor ration in year t is 90. What will the level of the capital- labor ratio be in year t+1? Will it increase or decrease in future periods? Explain. d. Compute the rate of change of the capital labor ratio between time t and t + 1. How does it compare to the rate of growth of the capital-labor ratio in steady state?
In this problem, we distinguish between labor and population in the Solow growth model. A proportion of the population, a, between zero and one, works. The production function is now written as Y = A(K^1/3)[(aL)^2/3] (a) How does an increase in a from 0.3 to 0.6 change steady state GDP? (b) Does it change the steady-state capital? Explain. (c) Suppose a rises steadily over time. How do you think would affect the growth rate of GDP?
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Q1 The steady state Consider the Basic Solow Model without exogenous growth: Y-AKOL-a C= (1-8)Y Y=C+I K' I (1-8)K where labor is constant. Assume the following values for the rest of this question: A=100 a = 0.35 s=0.12 8=0.10 L=25 For each question that follows, if the answer depends on the answer(s) to previous question(s), use unrounded answers in do calculations. If you do not, rounding error will accumulate. Q1.1 Compute steady state capital per worker. Round your answer to at least three decimal places.
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