6. Compute the evolution of economic variables over time (capital, output, consumption, investment, depreciation, all in per-capita terms), for 100 periods, assuming that the initial level of capital is k₁ = 1 in the first period and that e = 1 for every t. Create a graph that has time in the x-axis and the evolution of the variables output, consumption, investment, depreciation (all in per-capita terms) in the y-axis. Do variables grow or decline over time?

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i need Question 6 solution

6. Compute the evolution of economic variables over time (capital, output, consumption,
investment, depreciation, all in per-capita terms), for 100 periods, assuming that the
initial level of capital is ki = 1 in the first period and that e = 1 for every t.
Create a graph that has time in the x-axis and the evolution of the variables output,
consumption, investment, depreciation (all in per-capita terms) in the y-axis. Do
variables grow or decline over time?
Transcribed Image Text:6. Compute the evolution of economic variables over time (capital, output, consumption, investment, depreciation, all in per-capita terms), for 100 periods, assuming that the initial level of capital is ki = 1 in the first period and that e = 1 for every t. Create a graph that has time in the x-axis and the evolution of the variables output, consumption, investment, depreciation (all in per-capita terms) in the y-axis. Do variables grow or decline over time?
Solow Model
Consider a Solow growth model like the one discussed in class, but incorporating the
possibility of less than full employment. Let t denote a period. The production function is
Y; = zK; [e,L]*¬,
so that given the current TFP z4, the capital input K, and the labor input N = eL, firms
produce output Y; in period t. Here e € [0, 1] denotes the proportion of the labor force L
that is employed at each point in time. If e = 1 the economy is at full employment, with
e = 0, on the other hand, everyone is unemployed. Total resources satisfy
Y; = C; + I,
where C; denotes aggregate consumption, I aggregate investment, and Y; is GDP. Assume
that people invest a constant proportion s of their income, so that aggregate investment
satisfies
It = sY;
and capital evolves according to
K+1 = K,(1 – 8) + I,
%3D
where ổ denotes depreciation. This function tells us how capital next period is related to
current capital, investment, and depreciation. In the book, you have seen the expression
written as
AK = I – 8K,
note that the two are equivalent.
Transcribed Image Text:Solow Model Consider a Solow growth model like the one discussed in class, but incorporating the possibility of less than full employment. Let t denote a period. The production function is Y; = zK; [e,L]*¬, so that given the current TFP z4, the capital input K, and the labor input N = eL, firms produce output Y; in period t. Here e € [0, 1] denotes the proportion of the labor force L that is employed at each point in time. If e = 1 the economy is at full employment, with e = 0, on the other hand, everyone is unemployed. Total resources satisfy Y; = C; + I, where C; denotes aggregate consumption, I aggregate investment, and Y; is GDP. Assume that people invest a constant proportion s of their income, so that aggregate investment satisfies It = sY; and capital evolves according to K+1 = K,(1 – 8) + I, %3D where ổ denotes depreciation. This function tells us how capital next period is related to current capital, investment, and depreciation. In the book, you have seen the expression written as AK = I – 8K, note that the two are equivalent.
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