a)
To describe: The steady state values of capital-labor ratio, output per worker and consumption per worker is to be calculated.
a)
Answer to Problem 5NP
The steady-state values are −
Capital-labor ratio =
Output per worker =
Consumption per worker =
Explanation of Solution
Given that −
Output per worker =
Consumption per worker =
Capital stock per worker =
When the all above values of economy is constant then it is known as steady state condition.
The following equation will be used to represent the steady state value of the capital-labor ratio −
Given values −
s = 0.3
n = 0.05
d = 0.1
Put the above values in Equ (1) −
Divide the above equation by
Square on both sides −
Now, the capital-labor ratio = 36
The output per worker is calculated by using the following equation −
Now, put the calculated value in above equation −
Now, the steady state value for the output per worker = 18
The following equation will be use to represent the consumption per worker −
Also given that −
Population growth rate, n = 0.05
Depreciation rate, d = 0.1,
Now, put the given and calculated values in Equ (2) −
The consumption per worker,
Introduction:
The ratio between capital and labor is known as capital-labor ratio and the ratio between the output and labor is known as output per worker.
b)
To describe: The steady state values of capital-labor ratio, output per worker and consumption per worker is to be calculated with saving rate 0.4 instead of 0.3.
b)
Answer to Problem 5NP
The steady-state values are −
Capital-labor ratio =
Output per worker =
Consumption per worker =
Explanation of Solution
Given values −
s = 0.4
n = 0.05
d = 0.1
The following equation will be used to represent the steady state value of the capital-labor ratio −
Now, put the given values in above Equ (1) −
Divide the both side of above Equ by
Square both sides −
The capital − labor ratio =
The output per worker is calculated by using the following equation −
Now, put the calculated value in above equation −
Now, the steady state value for the output per worker = 24
The following equation will be use to represent the consumption per worker −
Also given that −
Population growth rate, n = 0.05
Depreciation rate, d = 0.1,
Now, put the given and calculated values in Equ (2) −
The consumption per worker,
Introduction: The ratio between capital and labor is known as capital-labor ratio and the ratio between the output and labor is known as output per worker.
c)
To describe: The steady state values of capital-labor ratio, output per worker and consumption per worker is to be calculated with 0.8 population growth rate.
c)
Answer to Problem 5NP
The steady-state values are −
Capital-labor ratio =
Output per worker =
Consumption per worker =
Explanation of Solution
Given values −
s = 0.4
n = 0.08
d = 0.1
The following equation will be used to represent the steady state value of the capital-labor ratio −
Now, put the given values in above Equ (1) −
Divide the both side of above Equ by
Square both sides −
The capital − labor ratio =
The output per worker is calculated by using the following equation −
Now, put the calculated value in above equation −
Now, the steady state value for the output per worker = 15
The following equation will be use to represent the consumption per worker −
Also given that −
Population growth rate, n = 0.08
Depreciation rate, d = 0.1,
Now, put the given and calculated values in Equ (2) −
The consumption per worker,
Introduction:
The ratio between capital and labor is known as capital-labor ratio and the ratio between the output and labor is known as output per worker.
d)
To describe: The steady state values of capital-labor ratio, output per worker and consumption per worker is to be calculated with following production function −
d)
Answer to Problem 5NP
The steady-state values are −
Capital-labor ratio =
Output per worker =
Consumption per worker =
Explanation of Solution
Given values −
s = 0.3
n = 0.05
d = 0.1
The following equation will be used to represent the steady state value of the capital-labor ratio −
Now, put the given values in above Equ (1) −
Divide the both side of above Equ by
Square both sides −
The capital-labor ratio =
The output per worker is calculated by using the following equation −
Now, put the calculated value in above equation −
Now, the steady state value for the output per worker = 32
The following equation will be use to represent the consumption per worker −
Also given that −
Population growth rate, n = 0.05
Depreciation rate, d = 0.1,
Now, put the given and calculated values in Equ (2) −
The consumption per worker,
Introduction: The ratio between capital and labor is known as capital-labor ratio and the ratio between the output and labor is known as output per worker.
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