Question

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 per worker

(iii) consumption per worker

(iv) investment per worker

(b) Suppose that the savings rate in the economy increases to 12%. Assume that all other variables are held constant. Calculate the following steady-state values of

(i) capital per worker

(ii) output per worker

(iii) consumption per worker

(iv) investment per worker

(c) Suppose that the country wants to increase its steady-state level of output per worker. What would the steady-state level of capital per worker would be needed in order to double the level of output per worker that you found in Part (a)?

(d) What would the savings rate have to be in order to double the level of output per worker that you found in Part (a)?

Question #2: Solow Model (Graphing Examples)For each of the following examples use the basic Solow Model to graphically illustratehow each of the following would affect capital per worker in the long-run (the steady-state level).

(a) A tsunami destroys a portion of a nation’s capital stock, but has no effect on the population (L) or on the growth rate of the population (n).

(b) A country experiences an increase in the birth rate.

(c) There is a decrease in the savings rate.

(d) Because of an increase in pollutants in the air, the rate of capitaldepreciation rises.

Answer #1

Answering only question 1)

2. The Solow-Swan Model
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 is constant and that the level of output
produced can be represented by the following production function: Y
= AKαL 1−α where A = 1 and α = 0.5. Use the Solow-Swan model to
determine the level...

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)...

Assume that an economy is described by the Solow growth model as
below:
Production Function: y=50K^0.4 (LE)^0.6
Depreciation rate: S
Population growth rate: n
Technological growth rate:g
Savings rate: s
a. What is the per effective worker production function?
b. Show that the per effective worker production function
derived in part a above exhibits diminishing marginal returns in
capital per effective worker
C.Solve for the steady state output per effective worker as a
function of s,n,g, and S
d. A...

Use the Solow model to solve. Suppose, you are the chief
economic advisor to a small African country with an aggregate per
capita production function
of y=2k1/2. Population grows at a
rate of 1%. The savings rate is 12%, and the rate of depreciation
is 5%.
(a) On a graph, show the output, break-even investment, and
savings functions for this economy (as a function of capital per
worker). Denote steady-state capital per worker k* and
steady-state output per worker y*. Label...

Use the Solow model to solve. Suppose, you are the chief
economic advisor to a small African country with an aggregate per
capita production function
of y=2k1/2. Population grows at a
rate of 1%. The savings rate is 12%, and the rate of depreciation
is 5%.
(a) At the steady-state level of output, what is the numerical
value of consumption? Identify the amount of consumption in your
graph in part a. Show your work.
(b) Say that population growth decreases in...

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...

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...

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 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...

As an economy adjusts to a decrease in the saving rate,
according to Solow model, we would expect output per worker
-none of the other answers is correct.
-to decrease at a permanently higher rate.
-to return to its original level.
-to increase at a permanently higher rate.
-to decrease at a constant rate and continue decreasing at that
rate in the steady state.

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