A natural disaster destroys half the capital of a country without affecting labor force.?
Suppose the economy was at its steady state equilibrium b4 the event.Explain how the economy will adjust to the fall in capital,assuming the saving rate is 20%,depreciation rate is 10% and population growth is 5%.The production function is
Y = K1/4 L ¾.Suppose the size of the
population (labour force) is equal to 2.
Describe and explain how the following variables will evolve: Output, output per
worker, capital and capital per worker. Make sure you describe both the short-run and long-run effects of the catastrophe.
Answer:
output, capital (both total and per-worker) will increase back to steady state over the years.
In the short run, firms will shift to using more labor, because the marginal cost for workers will be less expensive than the marginal cost for capital. This should be fairly intuitive, as there are the same number of workers, but the capital, factories, etc, have decreased. Thus, to achieve the highest output, more workers must be utilized. Output will likely fall, as capital seems to have been more productive than workers from the production function. Output per worker will decrease, as output will decrease but workers will increase. Capital per worker will increase, as less capital is being utilized.
In the long run, things will return to the equilibrium state, as the capital will be reinvested into in order to bring the return to capital back in line with the production function.
The intuitive piece is, well, intuitive! Recall your concept of declining marginal benefit -> a sharp decrease in the current amount of capital increases the return on capital, decreases the return to labor. Interest rate will go WAY up (due to increased demand for investment) which will increase savings.
Now, quantitatively; you need to take the derivative of your equation to get the slope; dY/dK to find the return to capital before & after the disaster.
Additionally, you'll need to use a basic Solow equation to plug in the depretiation, savings, population growth etc.
Sounds like you guys might be using the Mankiw text?
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Y = K1/4 L ¾.Suppose the size of the
population (labour force) is equal to 2.
Describe and explain how the following variables will evolve: Output, output per
worker, capital and capital per worker. Make sure you describe both the short-run and long-run effects of the catastrophe.
Answer:
output, capital (both total and per-worker) will increase back to steady state over the years.
In the short run, firms will shift to using more labor, because the marginal cost for workers will be less expensive than the marginal cost for capital. This should be fairly intuitive, as there are the same number of workers, but the capital, factories, etc, have decreased. Thus, to achieve the highest output, more workers must be utilized. Output will likely fall, as capital seems to have been more productive than workers from the production function. Output per worker will decrease, as output will decrease but workers will increase. Capital per worker will increase, as less capital is being utilized.
In the long run, things will return to the equilibrium state, as the capital will be reinvested into in order to bring the return to capital back in line with the production function.
The intuitive piece is, well, intuitive! Recall your concept of declining marginal benefit -> a sharp decrease in the current amount of capital increases the return on capital, decreases the return to labor. Interest rate will go WAY up (due to increased demand for investment) which will increase savings.
Now, quantitatively; you need to take the derivative of your equation to get the slope; dY/dK to find the return to capital before & after the disaster.
Additionally, you'll need to use a basic Solow equation to plug in the depretiation, savings, population growth etc.
Sounds like you guys might be using the Mankiw text?
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