Question

In a solow-type economy with Cobb-Douglas production, assume
that the population growth rate depends on the current level of
output per worker, y, so that n=my, where m is a positive constant.
For simplicity, assume d=0

a) Find an expression for the growth rate of the capital-labor
ratio, k̇ / k

b) Find expressions for the steady states of y and k

c) Find an expression for the growth rate of Y in steady state

Answer #1

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 =

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...

QUESTION 1
Suppose an economy can be characterized by a Cobb-Douglas
production function with capital share of 1/3, and A =
200. The investment rate is 0.12 (12%), the annual rate of growth
of the labor force is 0.02 (2%), and the annual depreciation rate
of capital is 0.04 (4%). According to the Solow growth model, this
economy's steady state capital/labor ratio (capital per worker,
k) is
4,000
8,000
10,000
12,000
None of the above.
QUESTION 2
The steady state...

An economy has the following Cobb-Douglas production
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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
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i. Where returns to capital = 0.5; and rate of
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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%
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(a) Calculate the following steady-state values of
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(ii) output...

Assume that a competitive economy can be described by a
constant-returns-to-scale Cobb-Douglas production function and all
factors of production are fully employed. Holding other factors
constant, including the quantity of capital and technology,
carefully explain how a one-time, 10 percent increase in the
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The level of output produced
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Labor share of total...

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