Macroeconomics (Fourth Edition)
4th Edition
ISBN: 9780393603767
Author: Charles I. Jones
Publisher: W. W. Norton & Company
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Question
Chapter 6.A, Problem 5E
a)
To determine
Growth rate of output per person along a balanced growth path.
b)
To determine
Level of output per person along a balanced growth path.
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Consider the Solow-Swan model of growth. Imagine that the production function is
Y = AKªL²-a
1. Use the production function to compute output per capita, y = Y /L, as a function of capital
per person, k = K/L.
2. Derive the fundamental equation of the Solow-Swan model. Please show all the steps.
Furthermore, imagine that the savings, depreciation, and population growth rates take the
values s = 0.3, 8= 0.1 and n =0.01. You do not know the value of A.
3. Use the fundamental equation of the Solow-Swan model to compute the growth rate of
capital per person as a function of k.
4. In the steady-state, the growth rate of capital is zero. Using the parameters assumed above,
find the steady-state level of the capital stock, k_.
5. Calculate GDP per capita at the steady state.
6. Imagine that this country is in its steady state so its capital stock is k_. Imagine that the
country receives a gift of one unit of capital from the world bank (so, suddenly, the capital
stock is k_+1). Can you say…
Consider the Solow-Swan model of growth. Imagine that the production function is
Y = AKªL²-a
1. Use the production function to compute output per capita, y= Y /L, as a function of capital
per person, k = K/L.
2. Derive the fundamental equation of the Solow-Swan model. Please show all the steps.
Furthermore, imagine that the savings, depreciation, and population growth rates take the
values s = 0.3, 8= 0.1 and n =0.01. You do not know the value of A.
3. Use the fundamental equation of the Solow-Swan model to compute the growth rate of
capital per person as a function of k.
(a) Consider an economy that is initially in a steady state equilibrium. Assume that in this equilibrium it has a saving rate of 50 per cent and a depreciation rate of 2 per cent. Further assume that the population growth rate is 3% and that the level of output produced can be represented by the following production function: = where A = 1 and = 0.5. Use the Solow-Swan model to determine the level of capital per worker and output per worker in this economy. (1 mark) (b) Now suppose the government introduces a set of policies to improve the institutional set up as well as better production technique which increases total factor productivity by double. What is the new steady state level of capital per worker and output per worker? (1 mark) (c) Use a Solow-Swan diagram to show the qualitative effects of this new government policy upon steady state output per worker and capital per worker. Briefly describe the intuition behind this result. (1 mark) (d) Now suppose, population growth rate…
Chapter 6 Solutions
Macroeconomics (Fourth Edition)
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- Question II - Solow Model with Population or Technology Growth Consider the Solow growth model with population growth and technology growth. Suppose that x = 0.1 and that n = 0.02, i.e., At = (1+0.1) At-1, and Lt = (1 +0.02) Lt-1. 1 Output is created by a Cobb-Douglas production function combining Labor, Lt, and capital, Kt, such that output Yt is given by Recall that efficient units of labor are given by Y₁ = A+ KL-a ล Assume that 8 = 0.1, s = 0.2, and a = 0.3. 1-a 1. What is the growth rate x = (1 + x) ¹/(1-a) – 1 - 2. Using the answer to the previous question, what is capital per efficiency units in steady state? Ess = | S itn tử + nữ 1-a Replace the numbers for s, d, ã and a to find the value of capital per efficient worker in steady state. 3. Take the production function (2) and divide by efficient worker, t = Y₁/Lt. You would find: yt = kg. What is output per-efficient worker if capital per-efficient worker is at its steady-state value? 4. If capital per-efficient worker is at…arrow_forwardConsider the Swan-Solow model of economic growth. [Hint: Question (e) below goes beyond the subject matter discussed in the lecture and requires you to think independently.] It has been argued that corruption affects economic growth (e.g. Mankiw/Taylor, 5th ed., pp. 479-480). Explain which of the curves in your diagram is most plausibly affected by a reduction in corruption in an economy, and what this effect would be.arrow_forwardAssume an endogenous growth model with labour augmenting technology. The production function is Y=RK,AN), with A = 2(KIN) such that y = 2k. If the savings rate is s= 0.08, the rate of population growth is n = 0.03, and the rate of depreciation is d= 0.04, what is the growth rate of output per capita? Multiple Choice 1% 3% 4% 7% 9%arrow_forward
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