Question

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 of capital per worker and output per worker in this economy.

Answer #1

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...

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...

Consider how unemployment would affect the Solow growth model.
Suppose that output is produced according to the production
function Y = Kα [(1 – u)L]1-α where K is
capital, L is the labor force, and u is the natural rate of
unemployment. The national saving rate is s, the labor force grows
at rate n, and capital depreciates at rate δ.
a. Write a condition that describes the golden rule
steady state of this economy.
b. Express the golden rule...

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...

Use the Solow-Swan model to explain what would happen to steady
state capital per
effective worker resulting from:
a. A decrease in the population growth rate.
b. An increase in labor productivity.
c. An increase in the investment share of GDP.

17. Solow growth The production function in your country is: Y =
K^0.5(LE)^0.5.
Your economy saves 24% of output each period, and 5% of the
capital stock depreciates each period. The population grows 2%
annually. Technology grows 1% annually. You begin with 1000 workers
and 1 unit of capital, and a tech- nology level equal to 1.
a) Write the production function in per-eective-worker terms, so
that per-effective-worker output (y = Y/LE ) is a function of
per-effective-worker capital (k=...

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...

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...

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...

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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