Question

Consider a numerical example using the Solow growth model: The production technology is Y=F(K,N)=K0.5N0.5 and people consume after saving a proportion of income, C=(1-s)Y. The capital per worker, k=K/N, evolves by (1+n)k’=szf(k)+(1-d)k.

(a) Describe the steady state k* as a function of other variables.

(b) Suppose that there are two countries with the same steady state capital per worker k* and zero growth rate of population(n=0), but differ by saving rate, s and depreciation rate, d. So we assume that s1/d1=s2/d2 where s2>s1 and d2>d1. Compare two countries’ consumption per worker(C/N). Is it different? Why?

(c) Now we learn that that d=0.1, s=0.1, z=1, and n=0. Calculate the steady state k*. Suppose that the saving rate, s, is doubled into s=0.2. Find out the new steady state k**.

(d) Now suppose that d=0. Can you describe the steady state? If not, explain why.

Answer #1

2. Consider a numerical example using the Solow growth model:
The production technology is Y=F(K,N)=K0.5N0.5 and people consume
after saving a proportion of income, C=(1-s)Y. The capital per
worker, k=K/N, evolves by (1+n)k’=szf(k)+(1-d)k.
(a) Describe the steady state k* as a function of other
variables
(b) Suppose that there are two countries with the same steady
state capital per worker k* and zero growth rate of
population(n=0), but differ by saving rate, s and depreciation
rate, d. So we assume...

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 the Solow growth model. The production function is
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capital per worker k0 = 1
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0.02, and savings rate s = 0.3. Country Y starts with capital per...

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a. Write a condition that describes the golden rule
steady state of this economy.
b. Express the golden rule...

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
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(b)...

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 the production function Y = F (K, L) = Ka *
L1-a, where 0 < α < 1. The national saving rate is
s, the labor force grows at a rate n, and capital depreciates at
rate δ.
(a) Show that F has constant returns to scale.
(b) What is the per-worker production function, y = f(k)?
(c) Solve for the steady-state level of capital per worker (in
terms of the parameters of the model).
(d) Solve for the...

Assume that an economy described by the Solow model has the
production function Y = K 0.4 ( L E ) 0.6, where all the variables
are defined as in class. The saving rate is 30%, the capital
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rate of change in labor effectiveness (E) is 1%.
For this country, what is f(k)? How did you define lower case
k?
Write down the equation of motion for k....

Consider an economy described by the production function:
Y = F(K, L) = K0.3L0.7.
Assume that the depreciation rate is 5 percent per year.
Make a table showing steady-state capital per worker, output per
worker, and consumption per worker for saving rates of 0 percent,
10 percent, 20 percent, 30 percent, and so on. Round your answers
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spreadsheet then transfer your answers to this table.)
Steady State...

In a solow-type economy with Cobb-Douglas production, assume
that the population growth rate depends on the current level of
output per worker, y, so that n=my, where m is a positive constant.
For simplicity, assume d=0
a) Find an expression for the growth rate of the capital-labor
ratio, k̇ / k
b) Find expressions for the steady states of y and k
c) Find an expression for the growth rate of Y in steady state

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