Macroeconomics
10th Edition
ISBN: 9781319105990
Author: Mankiw, N. Gregory.
Publisher: Worth Publishers,
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Question
Chapter 9, Problem 1PA
(a)
To determine
The capital.
(b)
To determine
The steady state value of income.
(c)
To determine
The steady state value of income.
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3) There are two countries, Anihc (country A) and Bapan (country B), with the same production
function f (k) = 5k0.5. However, country A has saving rates of 0.2, depreciation rate of 0.2 and
population growth of 0.2; while country B has saving rates of 0.1, depreciation rate of 0.15 and
population growth of 0.05. Using the Solow model:
a. Find the steady state capital-labor ratio for each country.
b. Find the steady state output per worker, and the steady state consumption per worker
for each country.
c. Which country produces the most per capita? Which country consumes the most per
capita?
Consider the Solow model with a production function Y(t) = A*K(t)^α*L(t)^(1-α), Where A is a fixed technological parameter.
Explicitly solve for the steady-state value of the per capita capital stock and per capita income.
How do these values change in response to a rise in (a) the technological parameter A, (b) the rate of saving s, (c) α , (d) δ, the depreciation rate, and (e) the population growth rate n?
Two countries, Richland and Poorland, are described by the Solow model. They have the same Cobb-Douglas production
function F(K, L) = AK"L¹-ª, but with different quantities of capital and labor. Richland saves 32% of its income, while
Poorland saves 10 percent. Richland has population growth of 1% per year, while Poorland has population growth of 3% per
year. (The numbers in this problem are chosen to be approximately realistic descriptions of rich and poor nations.) Both
nations have technological progress at a rate of 2% per year and depreciation at a rate of 5% per year. Answer the following
questions about Richland and Poorland.
a. What is the per worker production function ƒ(k)?
ƒ(k) =
b. Solve for the steady-state value of output y*.
y* :
=
units
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