Question

Consider the simple version of the Solow model, with no population growth and no technological change. Suppose that, due to an aging capital stock, an economy experiences a sudden increase in its depreciation rate.

a. Show the impact of an increase in the depreciation rate to ? ′ > ? on the diagram.

b. What happens to the steady-state level of capital? _______

c. What happens to the level of output in the steady state? _______

d. Assuming that the depreciation rate stays at its new, higher level, what action could the economy undertake to restore the initial steady-state level of capital and output?

Answer #1

Consider a version of the Solow model where population grows at
the constant rate ? > 0 and labour efficiency grows at rate ?.
Capital depreciates at rate ? each period and a fraction ? of
income is invested in physical capital every period. Assume that
the production function is given by:
?t =
?ta(?t?t
)1-a
Where ??(0,1), ?t is output, ?t is
capital, ?t is labour and ?t is labour
efficiency.
a. Show that the production function exhibits constant...

In the Solow growth model of an economy with population growth
and technological progress, the steady-state growth rate in output
per worker is equal to:
(a) zero
(b) the rate of technological progress g.
(c) the growth rate of population n plus the rate of technological
progress g. (d) the rate of technological progress g minus the
growth rate of population n.
In the Solow growth model of an economy with population growth
and technological progress, the steady-state growth rate...

In the Solow growth model with population growth but no
technological progress, if in the steady state the marginal product
of capital equals 0.10, the depreciation rate equals 0.05, and the
rate of population growth equals 0.03, then the capital per worker
ratio ____ the Golden Rule level.
A) is above
B) is below
C) is equal to
D) will move to

Answer the following questions using the basic Solow growth
model, without population growth or technological progress.
(a) Draw a diagram with per worker output, y, consumption, c,
saving, s and investment, i, on the vertical axis and capital per
worker, k, on the horizontal condition. On this diagram, clearly
indicate steady-state values for c, i, and y. Briefly outline the
condition that holds in the steady- state (i.e. what is the
relationship between investment and the depreciation of
capital?).
(b)...

Question #1: The Basic Solow Model
Consider an economy in which the population grows at the rate of
1% per year. The per worker production function is y = k6, where y
is output per worker and k is capital per worker. The depreciation
rate of capital is 14% per year. Assume that households consume 90%
of their income and save the remaining 10% of their income.
(a) Calculate the following steady-state values of
(i) capital per worker
(ii) output...

1. In the Solow model without exogenous technological change,
per capita income will grow in the long term as
long as the country has an initial level of capital below the
steady state level of capital (k o < k ⋅)
TRUE OR FALSE?
2. In the Solow model without exogenous technological change, per
capita income will grow in the short term as long
as the country has an initial level of capital below the steady
state level of capital...

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...

1) In the steady state of the Solow model with technological
progress, which of the following variables is not
constant?
(a) capital per effective worker
(b) the real rental price of capital
(c) the real wage
(d) the capital-output ratio
2) The U.S. economy has more/less capital than at
the Golden Rule steady state, suggesting that it may be desirable
to
increase/decrease the rate of saving.
3) The purpose of exogenous/endogenous
growth theory is to explain technological progress. Some of these...

Consider an economy that is characterized by the Solow Model.
The (aggregate) production function is given by:
Y =
1.6K1/2L1/2
In this economy, workers consume 75% of income and save
the rest. The labour force is growing at 3% per year
while the annual rate of capital depreciation is 5%.
Initially, the economy is endowed with 4500 units of
capital and 200 workers.
Is the economy in its steady state? Yes/no,
explain. If the economy is not in its steady state,
explain what...

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.

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