Question
In: Economics
Consider the standard Solow growth model. Let productivity be denoted by A and let the production...
Consider the standard Solow growth model. Let productivity be denoted by A and let the production function be Y=AF(K,N). For simplicity, assume that there is no population growth (n=0 so that N'=N). Let depreciation be denoted by d and the savings rate by s.
a. Derive the per capita capital accumulation equation for k=K/N and the steady state level of capital per worker, kss. Please show the details of your derivation to earn points. Draw the Solow model graph showing the savings line and the depreciation line and marking the steady state level of k.
b. Now, consider the “AK model” with production function Y=AK, where A is the exogenous productivity level. Again, assume that there is no population growth in the economy. Follow the similar steps in part a. to derive the capital accumulation equation in terms of capital per capita k.
c. Based on the equations you derived in part b, draw a graph similar to that of the Solow growth model to show the steady state of the model in part b. If you cannot find such a steady state, please explain why. d. Recall that Solow growth model implies convergence in capital per capita. Does the model in part b has this feature?
Solutions
Rahul Sunny answered 1 year agoRelated Solutions
Consider the standard Solow growth model. Let productivity be denoted by A and let the production...
Consider the standard Solow growth model. Let productivity be
denoted by A and let the production function be Y=AF(K,N). For
Simplicity, assume that there is no population growth (n=0 so that
N' = N). let depreciation be denoted by d and the savings rate by
s.
a) Derive the per capita capital accumulation equation for k=K/N
and the steady state level of capital per worker, ??^ss . Please
show the details of your derivation to earn points. Draw the Solow...
Let us consider a Solow growth model in which the aggregate production function at time t...
Let us consider a Solow growth model in which the aggregate
production function
at time t for country i is given by:
Yit
=Ai(Kit)1-βi(ei
Lit) βi
Where Yit is the aggregate real GDP in
country i, Kit is the aggregate
physical capital in country i,
Lit is the aggregate
number of workers in country i, ei is the average
working time of a worker parameter in country i, Ai
>0 is the total factor productivity parameter in country i and...
Let us consider a Solow growth model in which the aggregate production function at time t...
Let us consider a Solow growth model in which the aggregate
production function
at time t for country i is given by:
Yit
=Ai(Kit)1-βi(ei
Lit) βi
Where Yit is the aggregate real GDP in
country i, Kit is the aggregate
physical capital in country i,
Lit is the aggregate
number of workers in country i, ei is the average
working time of a worker parameter in country i, Ai
>0 is the total factor productivity parameter in country i and...
Consider the Solow Growth model, and assume there is no technological change. The production function is...
Consider the Solow Growth model, and assume there is no
technological change. The production function is F(K,L) = K^aN^1−α,
α = 1/3. Population growth rate n = 0.01. Capital depreciation δ =
0.09. Savings rate s = 0.4.
(a) Write down the law of motion for capital per worker.
(b) Compute the steady state capital per worker and output per
worker.
(c) Suppose a book called Let’s Party Like There is No Tomorrow
reduces the nation’s savings rate to 0.35....
In the Solow growth model, if we assume the standard properties of the production technology, which...
In the Solow growth model, if we assume the standard properties
of the production technology, which are discussed in class, the
economy tends to move toward the steady state with positive capital
stock per worker.
One of key predictions of the Solow Growth Model is that growth in total factor productivity...
One of key predictions of the Solow Growth Model is that growth
in total factor productivity will ensure long run economic growth.
While Canada has been making progress in terms of a growing
technology sector due to many factors, some of which include:
strong economic base and rising standard of living highly educated
work force multi-cultural mix and friendly business environment
universal health care foreign immigration policies friendly
domestic immigration policy and foreign anti-immigration
policies
Discuss some public policies that...
One of key predictions of the Solow Growth Model is that growth in total factor productivity...
One of key predictions of the Solow Growth Model is that growth
in total factor productivity will ensure long run economic growth.
While Canada has been making progress in terms of a growing
technology sector due to many factors, some of which include:
strong economic base and rising standard of living
highly educated work force
multi-cultural mix and friendly business environment
universal health care foreign immigration policies
friendly domestic immigration policy and foreign
anti-immigration policies
Discuss three public policies (in...
2. Consider the Solow growth model. Suppose that the production function is constant returns to scale...
2. Consider the Solow growth model. Suppose that the production
function is constant returns to scale and it is explicitly given
by: Y = KaL1-a
a. What is the level of output per capita, y, where y = Y/L?
b. Individuals in this economy save s fraction of their income.
If there is population growth, denoted by n, and capital
depreciates at the rate of d over time, write down an equation for
the evolution of capital per capita, k,...
2) Imagine a Solow Growth Model with a standard Cobb-Douglas production function and the following parameters:...
2) Imagine a Solow Growth Model with a standard Cobb-Douglas
production function and the following parameters: α = 0.4; d =
0.05; A = 1; s = 0.75; n = 0.4 a) Calculate the rate of capital
accumulation (law of motion) b) Calculate the steady state level of
capital? c) Calculate the steady state level of real output/income?
d) Calculate the steady state level of investment? e) Calculate the
steady state level of consumption? f) What effect does a higher...
Consider the Solow growth model with population growth and growth in the efficiency of labor. Suppose...
Consider the Solow growth model with population growth and
growth in the efficiency of labor. Suppose that 2 countries A and B
have the same production function given by Yt = Ktα(LtEt)1−α, the
same rate of growth of E (g), the same depreciation rate of
physical capital (δ) and the same saving rate s. The initial level
of E, E0, is lower in country A than in country B.
(a) Compare the steady-state levels of output per effective
worker of...
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