Question

Consider how unemployment would affect the Solow growth model.
Suppose that output is produced according to the production
function Y = K^{α} [(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 levels of capital per worker,
k* _{G}, and output per worker, y*_{G}, as functions
of the parameters, s, n, δ, α, and u.**

Answer #1

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...

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...

Suppose output is given by
Y = K 1/2 (AN) 1/2
As in the basic model, the workforce grows at rate n, capital
depreciates at rate d and the savings rate is s. In addition,
suppose that TFP grows at a constant rate g. That is:
∆A/A = g
We will refer to the product AN as the “effective workforce”. It
follows that the effective workforce grows at rate n + g.
a. Express the production in per “effective worker”...

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...

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...

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...

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...

Which of the following statements about the Solow growth model
is FALSE?
A. The higher steady-state capital per capita, the higher the
output/income per capita.
B. The higher output/income per capita, the higher consumption
per capita.
C. Golden-rule capital per capita must be a steady state, but
not all steady-state is also a golden-rule.
D. Golden-rule capital per capita can be achieved by setting
the saving rate at the appropriate level.

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