a
To calculate:Steady state values of Output per worker, Capital per worker, Consumption per worker, Investment per worker
a
Answer to Problem 6NP
the steady-state value of the capital per worker is
the steady-state value of output per worker is
the steady-state value of consumption per worker is
Explanation of Solution
Given Information:
Households save 10% of income, so savings,
At steady stae:
Output per worker
Capital per worker
Consumption per worker are equal.
To determine the steady-state value of the capital per worker, use the equation
Households save 10% of income, so savings,
Substitute the given values
Continue solving for k by dividing both sides by
Therefore, the steady-state value of the capital per worker is
To find the steady-state value of output per worker, substitute the calculated value for capital-labor ratio from the previous step into the given per-worker production function,
Hence, the steady-state value of output per worker is
To find the steady-state value of consumption per worker, use the equation
Therefore, the steady-state value of consumption per worker is
To fund the steady-state value of investment per worker, use the equation
Hence, the steady-state value of investment per worker is
Introduction:
Steady state is a situation at which investment is equal to depreciation. It implies all the investment done is used to replace the depreciating capital.
b)
Value of capital-labor ratio required to double steady state value of output per capita, Amount of savings to achieve output per worker.
b)
Answer to Problem 6NP
The steady-state value of capital-labor ratio needed is
Households would need to save
Explanation of Solution
Given Information:
Households save 10% of income, so savings,
To determine the steady-state value of the capitallabor ratio needed to double the steady-state value of output per capita, double the value for y in part a,
So to double the steady-state value of output per capita, the steady-state value of capital-labor ratio needed is
To determine the fraction of income households would need to save to have a double steady-state value of output per capita than in part a, use the steady-state value of capitaI-Iabor ratio from the previous step,
Solve for s.
Continue solving for
So households would need to save
Introduction:
Steady state is a situation at which investment is equal to depreciation. It implies all the investment done is used to replace the depreciating capital.
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