Question

Consider the following Cobb-Douglass production function?≡??(?,?):?=??1/3?2/3

where Y is output, the constant z measures productivity, K is physical capital, and N is labor. Suppose ?=2, ?=0.16, ?=0.06, and ?=0.02.

a. What are the steady-state (numerical) values of ?, ?, and ??

b. What is the golden-rule (numerical) level of capital per worker?

c. If the government wants to achieve the golden rule level of k, should savings increase, decrease or remain unchanged? Solve for/obtain its (numerical) value. Explain briefly.

Answer #1

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?

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...

An economy has the following Cobb-Douglas production
function:
Y = Ka(LE)1-a
The economy has a capital share of 1/3, a saving rate of 24
percent, a depreciation rate of 3 percent, a rate of population
growth of 2 percent, and a rate of labor-augmenting technological
change of 1 percent. It is in steady state.
a. Does the economy have more or less capital than at the Golden
Rule steady state? How do you know? To achieve the Golden Rule
steady...

Assuming the following Cobb-Douglas production
function is given for a closed economy without government.
i. Where returns to capital = 0.5; and rate of
depreciation of physical capital
Determine the steady-state level of capital per worker. What is the
savings rate at which the steady-state level of capital is
achieved?
[6marks]
ii Prove that the steady-state level of output is the
ratio of the saving rate to the rate of
depreciation
[6 marks]
iii. Assuming that , what will be...

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...

Consider two countries: Country A and Country B. Each country
has the following Cobb-Douglas type production function:
Country A: Y = (K0.5)(EL)0.5 Country B: Y =
(K0.7)(EL)0.3
Unfortunately, your knowledge of Country A is a bit limited.
You have pieces of information, but you don’t know the entire
picture.
o Savings rate (s): unknown for Country A and 14.29% for
Country B
o Steady-state value of capital per effective worker: unknown
for both countries, but you have
heard that Country...

Consider the following production function Y=z*(a*K + (1-a)*N)
where z represents total factor productivity, a is a parameter
between 0 and 1, K is the level of capital, and N is labor. We want
to check if this function satisfies our basic assumptions about
production functions.
1. Does this production function exhibit constant returns to
scale? Ex- plain
2. Is the marginal product of labor always positive? Explain
3. Does this function exhibit diminishing marginal product of
labor? Ex- plain...

A closed economy has the following Cobb-Douglas production
function: F(KL) = K2/5 (EL)3/5, where the notation is as in class.
The depreciation rate is 1.5% and the saving rate is 20%. The
economy is in steady state, where the population decreases at a
rate 1% and capital K increases at a rate 1%. (a) Find the growth
rates of the following variables (i) labor efficiency, E (ii) the
number of workers per machine, L/K (iii) the average productivity
of capital,...

. Let the production function be Y=AL^1/2*K^1/2 where Y is
output, K is capital, L is labor and A represents the level of
technology.
a. What happens to the marginal product of capital as the level
of capital increases?
b. If L=100, A=5, the savings rate is 1/2 and the depreciation
rate is 1/3, what will the steady-state levels of capital, output
and consumption be?

Consider an economy described by the following production
function: ? = ?(?, ?) = ?^1/3 ?^2/3
depreciation rate is 5 percent (? = 0.05)
the population grows at 2 percent (n = 0.02)
savings rate is 20 percent (s = 0.20)
f) At what rates do the following grow at in the steady state:
[3 points]
a. Capital per worker, k:
b. Output per worker, y:
c. Total output, Y:

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