
Sub part (a):
Steady state level of output.
Sub part (a):

Explanation of Solution
The steady state level of output is calculated as follows:
The steady state level of output is 200 units.
Concept introduction:
Sub part (b):
Solow diagram to show short run impact.
Sub part (b):

Explanation of Solution
Figure 1 depicts Solow diagram which shows the short run impact of a 21% increase in the amount of labor available.
In figure 1, the horizontal axis represents the capital (K) and the vertical axis represents the output (Y). The initial production function
Concept introduction:
Economic growth: The economic growth is the increase in the overall goods and services produced per head in the economy over a specific period of time.
Solow growth rate The Solow growth rate is the rate of economic growth with given flexible price, and the existing real factors of capita, labor and knowledge. The Solow growth rate is an economy’s potential growth rate.
Sub part (c):
Steady state level of output.
Sub part (c):

Explanation of Solution
The new steady state level of output is calculated as follows:
The new steady state level of output is 220 units.
Concept introduction:
Economic growth: The economic growth is the increase in the overall goods and services produced per head in the economy over a specific period of time.
Sub part (d):
The new steady state level of output in the diagram.
Sub part (d):

Explanation of Solution
The new steady state level of output is 220 units which is depicted in the figure 1.
Sub part (e):
Action to gain long lasting benefits from the increase in capital stock.
Sub part (e):

Explanation of Solution
The initial production function is algebraically represented as follows:
Squaring both sides,
And solving for K, we get
Substitute K into the steady-state condition
And solve for Y by multiplying L and dividing by
Similarly, the new production function can be algebraically represented as follows:
Substitute K into the steady-state condition
And solve for Y by multiplying L and dividing by
Equating (1) in (2) we get
Substituting the values in equation (3) we get
Further, the percentage change in the output is depicted as follows:
This implies the steady-state level of output will grow by 21% per cent in the long run.
Concept introduction:
Production function: It is the relationship between the inputs employed by a firm and the maximum output the firm can produce with those inputs.
Sub part (f):
Output per worker.
Sub part (f):

Explanation of Solution
The output per worker in the initial steady state is calculated as follows:
The output per worker in the initial steady state is 2 units per labor.
The output per worker in the short run is calculated as follows:
The output per worker in short run is 1.82 units per labor.
The output per worker in the initial steady state is calculated as follows:
The output per worker in the long run is 2 units per labor.
Sub part (g):
New immigration policy and its effect.
Sub part (g):

Explanation of Solution
The citizens of the country are neither made worse off nor better off in the long run by a new immigration policy. This is because the new long-run level of output per worker compare with the initial level of output per worker remains unchanged which is 2 units per labor. This is unlike the short run effect which has lower output per worker. In the long run, the steady output level is determined largely by the
Concept introduction:
Depreciation: Depreciation is the process of decreasing the value of an asset over time especially due to wear and tear.
Investment: The investment is the money invests in terms of assets and building by the individual for the future consumption and profit making.
Sub part (h):
New steady state level of capital.
Sub part (h):

Explanation of Solution
The new steady state level of capital is calculated as follows
We know
Also
Equating all these we get,
Substituting the values we get
Thus the new steady state level of capital is 484, so that
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Chapter 8 Solutions
Modern Principles: Macroeconomics
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