Macroeconomics
10th Edition
ISBN: 9781319105990
Author: Mankiw, N. Gregory.
Publisher: Worth Publishers,
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Question
Chapter 8, Problem 8PA
(a)
To determine
The output per worker.
(b)
To determine
The steady state of the economy.
(c)
To determine
Change in profit due to reduction in production.
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Consider a Solow-Swan economy with a Cobb-Douglas production function. Imagine that the savings rate "s" is an increasing
function of capital and it has the following functional form: for low values of k the savings rate is constant at some low level. For
intermediate levels of k, the savings rate increases rapidly. For high values of k the savings rate is constant again. In other words,
the savings rate looks like:
Does a steady state necessarily exist?
b. Will the steady state be necessarily unique?
а.
Will the steady state(s) be stable?
d. Will there be a "poverty trap"? (define poverty trap)
С.
How can this model be used (and how has this model been used) to justify large increases in foreign development aid?
Discuss THREE potential flaws of the "savings poverty trap" model.
е.
f.
Suppose that output is produced according to the production function Y = Kα[(1 - u)L]1-α, whereK is capital, L is the labor force, and u is the natural rate of unemployment. The national savingrate is s, the labor force grows at rate n, and capital depreciates at rate d.a. Express output per worker (y = Y/L) as a function of capital per worker (k = K/L) and thenatural rate of unemployment (u).b. Write an equation that describes the steady state of this economy. Find the steady state capitalper worker and steady state output per worker.c. Does this production function have constant returns to scale? Explain.
Consider a numerical example of the Solow model:
Assume that
n=0.2
s=0.3
d=0.1
F(K,N)=K12N12
Initially, in period t=0, that
z=3
N=1
and the economy is in a steady state:
Suppose that at t=1, total factor productivity falls to z=1
and then returns to
z=3 for periods t=2,3,4....
What is the value of per person aggregate output at period t=1?
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