Question

Consider the production function Y = F (K, L) = K^{a} *
L^{1-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 golden-rule steady-state level of capital per worker. (in terms of the parameters of the model).

Answer #1

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...

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=...

Suppose that output (Y ) in an economy is given by the following
aggregate production function: Yt = Kt + Nt
where Kt is capital and Nt is the population. Furthermore,
assume that capital depreciates at rate δ and that savings is a
constant proportion s of income. You may assume that δ > s.
Suppose that the population remains constant. Solve for the
steady-state level of capital per worker.
Now suppose that the population grows at rate n. Solve...

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...

Answer the following
Y = f(k) = ka, where a = 0.25
S = 0.3
δ = 0.2
n = 0.05
g= 0.02
a. Find the steady state capital per effective worker, output
per effective worker, investment per effective worker, and
consumption per effective worker.
b. Find the steady state growth rate of capital per worker,
output per worker, investment per worker, and consumption per
worker.
c. Find the steady state growth rate of capital, output,
investment, and consumption.
d....

Assume that the production function in an economy is given by
y=k1/2, where y and k are the per-worker levels of output and
capital, respectively. The savings rate is given by s=0.2 and the
rate of depreciation is 0.05. What is the optimal savings rate to
achieve the golden-rule steady state level of k?

Solow Growth Model Question: Consider an economy where output
(Y) is produced according to function Y=F(K,L). L is number of
workers and Y is the capital stock. Production function F(K,L) has
constant returns to scale and diminishing marginal returns to
capital and labor individually. Economy works under assumption that
technology is constant over time. The economy is in the
steady-state capital per worker. Draw graph. Next scenario is that
the rate of depreciation of capital increases due to climate change...

Use information to answer questions below.
Y = f(k) = ka, where a = 0.25
S = 0.3
δ = 0.2
n = 0.05
g= 0.02
a. Find the steady state capital per effective worker, output
per effective worker, investment per effective worker, and
consumption per effective worker.
b. Find the steady state growth rate of capital per worker,
output per worker, investment per worker, and consumption per
worker.
c. Find the steady state growth rate of capital, output,
investment,...

Question 1
Production is given by:
? 1−? ?≡?(?,?)=?? ?
where ??+1 = (1 + ?)?? and ??(0,1)
Show that F exhibits a constant return to scale technology.
Express output as a function of the capital labor ratio ?? = ??
∕ ??.
Find the dynamical system (describing the evolution of ?? over
time) under the assumption
that the saving rate is ? ?(0,1) and the depreciation rate is ?
∈ (0,1].
What is the growth rate of ??, ???≡(??+1...

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....

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