Question

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 developed country has a saving rate of 28 percent and a
population growth rate of 1 percent per year. A less developed
country has a saving rate of 10 percent and a population growth
rate of 4 percent per year. In both countries, *g* = 0.02
and S = 0.04. Find the steady state value of output per effective
worker, y^steady state for each country. Illustrate your answer
with a graph showing steady state capital per effective worker,
output per effective worker and consumption per effective
worker.

Answer #1

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=...

Intermediate Macroeconomics! Thank you!!
Suppose that the economy is summarized by the Solow economy with
technological progress:
Production Function: Y=10K.3(LE).7
Savings rate: s= .2
Depreciation rate: δ= .1
Population Growth rate: n= .02
Technological growth rate: g= .01
a) Derive the per effective worker production function for this
economy.
b) Based on your answer in part (a), derive the formula for
marginal product of capital (MPK) and show that the per effective
worker production function exhibits diminishing marginal product of...

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
depreciation rate is 3%, the population growth rate is 2%, and the
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....

An economy has a Cobb–Douglas production function:
Y=Kα(LE)1−αY=Kα(LE)1−α
The economy has a capital share of 0.30, a saving rate of 42
percent, a depreciation rate of 5.00 percent, a rate of population
growth of 2.50 percent, and a rate of labor-augmenting
technological change of 4.0 percent. It is in steady state.
Solve for capital per effective worker (k∗)(k∗), output per
effective worker (y∗)(y∗), and the marginal product of capital.
k∗=k∗=
y∗=y∗=
marginal product of capital =

Consider the Solow growth model. The production function is
given by Y = K^αN^1−α, with α = 1/3. There are two countries: X and
Y. Country X has depreciation rate δ = 0.05, population growth n =
0.03, and savings rate s = 0.24. Country X starts with initial
capital per worker k0 = 1
Country Y has depreciation rate δ = 0.08, population growth n =
0.02, and savings rate s = 0.3. Country Y starts with capital per...

3- Growth Model
Suppose that the output (Y) in the economy is given by
the following aggregate production function.
Yt = Kt +Nt
where the Kt is capital and Nt is population.
Furthermore assume that the capital depreciate at the rate of ẟ and
That saving constant and proportion s of income you may assume that
ẟ>s
1-suppose that the population remains constant . solve
for the steady state level of capital per worker
2- now suppose that the population...

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...

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...

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...

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
to two decimal places. (You might find it easiest to use a computer
spreadsheet then transfer your answers to this table.)
Steady State...

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