Question

c. How will simultaneous increases in the population growth rate and the savings rate effect per-capita income in the “standard” (constant returns to scale) Solow growth model? Show graphically, and briefly explain. This is a “qualitative”, not a quantitative question.

Answer #1

The simultaneous increase in population growth rate and saving rate will interact with each other to keep the per capita income at the same level.

We know that the population growth rate decreases the steady state level of output. This in turn decreases the per capita income. On the other hand, increase in saving rate will increase the steady state level of output, thus increasing the per capita income.

If both these forces interact in such a way that the negative impact is exactly balanced by the positive impact, the steady state level of output will stay the same and there will be no change in per capita income.

True or false or uncertain?
In the Solow model, a change in population growth rate affects
the level of per capita income, but it has no effect on the
long-run growth rate of per capita income.

In the Solow model, increases in the rate of population growth
and increases in the rate of technological progress both lower the
steady state values of capital and output per efficiency unit. True
or false: Therefore both are undesirable. If false, explain how
they differ in their consequences for levels and growth rates of
Y/L.

Why do both the overall population growth rate and the per
capita growth rate decrease as the size of the population
increases? Furthermore, if resources are limited, how would the per
capita share of resources change as population size increases?

Time
Current per capita capital
Per capita income
Savings per capita
Rate of deterioration of capital per capita
Next period per capita capital
Capital-Output Ratio
Growth rate of per capita income
t
k(t)
y(t)
sy(t)
(δ+n)k
k(t+1)
θ=k(t)/y(t)
(g*)
0
2.0
---
1
2
3
4
5
6
7
8
9
10
Population growth rate = .03
Savings rate = .5
capital depreciation rate = .2
capital share = .5
K(0) = 2
must be done by calculator, please show...

What will happen to the annual rate of growth of per capita real
GDP if the annual rate of population growth increases and the
annual rate of growth of real GDP goes down?
A.
The effect will depend upon whether the rate of population
growth is greater than or less than the rate of growth of real
GDP.
B.
It will increase since the annual rate of growth of real GDP
does not influence the growth rate of per capita...

1). Given the following law of motion for capital per capita ˙k
= sk^α − δk
find the steady state value of k.
Consider the Solow Growth Model with the following production
function
Y = AF(K, L) = AK^(1/2)L^(1/2)
where savings rate, s = 0.2, the depreciation rate, δ = 0.1, and
TFP, A = 2. Both population growth, n and technological growth are
0.
Problem 10. (10 Points) Derive the per worker production
function, y, and show that it...

1. For the following, assuming that there is no population
growth or technological progress.
a) What is the equation that defines the steady-state level of
capital per worker?
b) How would you determine the steady state level or output per
worker (i.e., real GDP per capita) from (a).
c) Explain, in words, how an economy that starts with too much
capita per worker gets to its steady state.
2. Many demographers predict that the United States will have
zero annual...

Why developed countries have income per capita much higher than
developing countries? Use economic growth Solow model to
explain.

Use the H-augmented Solow model to determine the a)
instantaneous impact on GDP per capita, b) instantaneous impact on
consumption per capita, c) long-run impact on GDP per capita, d)
long-run impact on consumption per capita, e) impact on long-run
GDP per capita growth rate, and f) impact on long-run GDP growth
rate of a permanent and instantaneous increase in the fraction of
national resources devoted to investment in human capital, sh.
Assume the country begins at its steady state...

What are the solow growth model equations which involves an initial
population growth (n), and technological advances (g), savings
(s),consumption (c), investment (I), depreciation of capital value
(delta). Also, can someone explain how to intuitively explain what
is happening in the growth model when certain variables change.
Also, if n increases due to immigration policy and the government
condsiders changing incentives to increase the savings rate, what
is the intuition of why this will work? Thank you!

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