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# Econ 304 Fall 2012 Problem Set #4 Due by 11:59 PM MDT October 12 1. (6 points each part) Consider an economy described by the production function: a. What is the per worker production function? b....

Econ 304 Fall 2012 Problem Set #4 Due by 11:59 PM MDT October 12 1. (6 points each part) Consider an economy described by the production function: a. What is the per worker production function? b. Assuming no population growth or technological progress, find the steady state capital stock per worker , output per worker, and consumption per worker as a function of the savings rate and the depreciation rate. c. Assume that the depreciation rate is 10% per year.
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Econ 304 Fall 2012 Problem Set #4 Due by 11:59 PM MDT October 12 1. (6 points each part) Consider an economy described by the production function: Y=FK,L=K.3L.7 a. What is the per worker production function? b. Assuming no population growth or technological progress, find the steady state capital stock per worker , output per worker, and consumption per worker as a function of the savings rate and the depreciation rate. c. Assume that the depreciation rate is 10% per year. Make a table showing steady state capital per worker, output per worker, and consumption per worker for savings rates of 0%, 10%, 20%, 30%, and so on. What saving rate maximizes output per worker? What saving rate maximizes consumption per worker? 2. (7 points each part) Consider how unemployment would affect the Solow growth model. Suppose that output is produced according to the production function =Ka[1-uL1-a , 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 d. a. Express output per worker (y=Y/L) as a function of capital per worker and the natural rate of unemployment. b. Write an equation that describes the steady state of this economy. c. Suppose that some change in government policy reduces the natural rate of unemployment. Describe how this change affects output both immediately and over time. Is the steady state effect on output larger or smaller than the immediate effect? 3. (6 points each part) Suppose and economy described by the Solow model has the following production function: Y=K1/2(LE)1/2 a. For this economy, what is f(k)? b. Use your answer to part a to solve for the steady state value of y as a function of s, n, g, and d. c. Two neighboring economies have the above production function, but they have different parameter values. Atlantis has a saving rate of 28% and a population growth rate of 1% per year. Xanadu has a saving rate of 10% and...

Answered Same Day Dec 31, 2021

## Solution

David answered on Dec 31 2021
Econ 304 Fall 2012
Problem Set #4 Due by 11:59 PM MDT October 12
1. (6 points each part)
Consider an economy described by the production function:
( )
a.
What is the per worker production function?
Per worker production function :
y=Y/L= K
.3
L
.7
L
Thus, y=K
.3
L
.3
Thus y=k
0.3
where y=Y/L and k=K/L
.
Assuming no population growth or technological progress, find the steady state capital stock per
worker , output per worker, and consumption per worker as a function of the savings rate and the
depreciation rate.
Steady state= change in k is 0
Thus sf(k)=dk
s=savings rate
d = depreciation
s*k
0.3
=dk
k
0.7
=s/d
Capital per worker : k=(s/d)
1/0.7

y=k
0.3
=(s/d)
0.3/0.7
Output per worker : y=(s/d)
3/7
Consumption per worker : c=(1-s)y
=(1-s) (s/d)
3/7
c.
Assume that the depreciation rate is 10% per year. Make a table showing steady state capital per
worker, output per worker, and consumption per worker for savings rates of 0%, 10%, 20%,
30%, and so on. What saving rate maximizes output per worker? What saving rate maximizes
consumption per worker?
Now we assume d =0.1
Savings
ate
capital per
worker
output per
worker
consumption per
worker
0.1 1 1 0.9
0.2 2.691800385 1.345900193 1.076720154
0.3 4.803986657 1.601328886 1.12093022
0.4 7.245789314 1.811447329 1.086868397
0.5 9.966176578 1.993235316 0.996617658
0.6 12.93137313 2.155228856 0.862091542
0.7 16.11695207 2.302421724 0.690726517
0.8 19.50421847 2.438027308 0.487605462
0.9 23.0782878 2.5642542 0.25642542
1 26.82695795 2.682695795 0
Savings rate for which output per worker is maximized =100%
Consumption per worker...
SOLUTION.PDF