Question

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
worker k0 = 1.5.

(a) Which country has higher output per worker in the short run? in
the long run? Explain your answers.

(b) Which country has higher growth of output per worker in the short run? in the long run? Explain your answers.

Answer #1

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...

Suppose Canada’s aggregate production function is given by the
following:
Y = K^1/3 *(AN)^2/3
Variables are deﬁned as they were in class. Suppose the savings
rate in Canada is 20% (s = 0.2), the depreciation rate is 5% (δ =
0.05), the population growth rate is 2% (gN = 0.02), and the growth
rate of technology is 4% (gA = 0.04).
a) Solve for the equilibrium level of capital per eﬀective worker (
K/AN ) and output per eﬀective worker...

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...

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...

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...

(Neoclassical Growth Model). Consider the production function
f(k) = Ak0.25, with A = 1, the saving rate s = 0.25, and
the depreciation and population growth rates rates d = 0.15 and n =
0.10. The steady state level of capital per capita is k*
= 1. For k0 = 0.5 and k0 = 1.5, as initial capital per capita, ll
the values of per capita capital, output, the MPK, savings,
required investment and the net capital accumulated (△k) in...

Consider the Basic growth model from your text and lecture as
defined below: Production function: GDP = f(At, Kt, Lt); where
capital (K) and labor (L) are substitutes and technology (A) aids
production
Demographic Behavior: Lt+1= Lt(1+n) = Nt+1; where n is the
population growth rate, N is the total population and there is no
unemployment
Capital and Savings/Investment Dynamics: Kt+1 = It + Kt(1-δ); It
= St = s*Y; where δ is the depreciation rate of capital, s is...

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...

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=...

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....

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 6 minutes ago

asked 12 hours ago

asked 4 months ago

asked 4 months ago

asked 17 minutes ago

asked 18 minutes ago

asked 18 minutes ago

asked 18 minutes ago

asked 4 months ago

asked 20 minutes ago

asked 20 minutes ago