Question

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Consider a version of the Solow model where the population growth rate is 0.05. There is no technological progress. 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} = ?_{t}^{1/2}
?_{t}^{1/2} ,

where ?_{t} is output, ?_{t} is capital and
?_{t} is labour.

a. Derive an expression for the accumulation of capital per worker in this economy, i.e.

∆?_{t+1} where ?_{t} ≡
?_{t}/?_{t} .

b. What is the steady-state condition in this economy? Explain the intuition behind the equilibrium condition and illustrate the steady state in a diagram.

c. What happens to capital and output per worker if the saving rate decreases? Illustrate your answer in a diagram and explain the mechanisms behind the transition to the new steady state.

d. What is the main criticism of the Solow model?

Answer #1

b) Steady state output per worker depends positively on the saving (investment) rate and negatively on the population growth rate and depreciation rate.

c) If the saving rate decreases to say s',the saving curve shifts downwards to s'y and capital and output per worker falls since both the parameters depend positively on the saving (investment) rate. New steady state has lower capital per worker and output per worker.

d) Solow assumes technology as central for explaining the growth process but takes it as exogenous and does not offer any explanations for the same. His convergence hypothesis is majorly flawed and has no empirical validation.

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...

Hi. i need answer for this question as quickly as possible.
Consider the AS-AD model:
Y˜ t = α − βµ(πt − π¯),
where Y˜ t is short-run output, πt is current inflation and ¯π
is an inflation target pursued by the central bank. The AS curve
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πt = πt−1 + νY˜ t + σ.
a. Explain where the two equations come from and explain the
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Consider the simple version of the Solow model, with no
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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...

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
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Answer the following questions using the basic Solow growth
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(a) Draw a diagram with per worker output, y, consumption, c,
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worker, k, on the horizontal condition. On this diagram, clearly
indicate steady-state values for c, i, and y. Briefly outline the
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relationship between investment and the depreciation of
capital?).
(b)...

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...

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...

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
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capital and labor individually. Economy works under assumption that
technology is constant over time. The economy is in the
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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
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d. A...

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