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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?

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?

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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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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