Education has been demonstrated to be an important contributor to economic growth. In- vestment in human...

  

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Education has been demonstrated to be an important contributor to economic growth. In- vestment in human capital through education can be easily introduced into the Solow model. To do so, it is useful to review the simple version of the Solow model seen in class. We can introduce human capital into the model in a straightforward manner. Suppose we modify the Solow model by allowing people to invest in education and accumulate human capital, H, and also by allowing long-run technological progress. That is, suppose that z = 1 and that there is labor-augmented technological progress, AN: Y = K&H (AN)¹-a-x where Y is output, K is physical capital, H is human capital, A is the efficiency of labor and N is labor, so that AN measures the effective number of workers. That is, output Y depends not only on the number of workers, N, but also on how effective they are L. Assume that a > 0, λ > 0, and a + >> 0. Further, suppose that labor and the efficiency of labor (i.e.,technology) grow at constant rates n and g, respectively. That is, 1+ g. Also, assume that both types of capital depreciate at rate d and that gross investment in physical capital is a fraction Sk of output and that gross investment in human capital is a fraction sh of output. 1+n and A' A H AN N' N K AN (a) Let k = and h = Obtain the law of motion for capital accumulation (both, physical and human). (Hint: Determine each law of motion individually. Derive the law of motions in the same way they were derived in class. Note, however, that you should be interested in per unit of effective worker variables, not per worker variables.) . = (b) Determine the steady-state values of physical capital, human capital and output, all per unit of effective workers. (c) Is the steady-state in this version of the Solow model a balanced growth path? Deter- mine what the growth rate of aggregate output, Y, and both types of capital, K and H. (d) What is the effect of an increase in investment rate of human capital, sʼn on per-capita physical and human capital, output and consumption? Education has been demonstrated to be an important contributor to economic growth. In- vestment in human capital through education can be easily introduced into the Solow model. To do so, it is useful to review the simple version of the Solow model seen in class. We can introduce human capital into the model in a straightforward manner. Suppose we modify the Solow model by allowing people to invest in education and accumulate human capital, H, and also by allowing long-run technological progress. That is, suppose that z = 1 and that there is labor-augmented technological progress, AN: Y = K&H (AN)¹-a-x where Y is output, K is physical capital, H is human capital, A is the efficiency of labor and N is labor, so that AN measures the effective number of workers. That is, output Y depends not only on the number of workers, N, but also on how effective they are L. Assume that a > 0, λ > 0, and a + >> 0. Further, suppose that labor and the efficiency of labor (i.e.,technology) grow at constant rates n and g, respectively. That is, 1+ g. Also, assume that both types of capital depreciate at rate d and that gross investment in physical capital is a fraction Sk of output and that gross investment in human capital is a fraction sh of output. 1+n and A' A H AN N' N K AN (a) Let k = and h = Obtain the law of motion for capital accumulation (both, physical and human). (Hint: Determine each law of motion individually. Derive the law of motions in the same way they were derived in class. Note, however, that you should be interested in per unit of effective worker variables, not per worker variables.) . = (b) Determine the steady-state values of physical capital, human capital and output, all per unit of effective workers. (c) Is the steady-state in this version of the Solow model a balanced growth path? Deter- mine what the growth rate of aggregate output, Y, and both types of capital, K and H. (d) What is the effect of an increase in investment rate of human capital, sʼn on per-capita physical and human capital, output and consumption?

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a The law of motion for the physical capital per effective worker is Kt1 1dKt SkYt 1dKt SkYt1 1n1g The law of motion for the human capital per effecti... View the full answer