2. Solow Model with Human Capital. Consider the following production function: Y = K LH (1)...

 

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2. Solow Model with Human Capital. Consider the following production function: Y = K L³H₂ (1) where Y, is output, K, is physical capital stock, L, is labor and He is human capital stock. Parameters in the production function (a, B and 7) add up to 1. Households save a constant fraction s of their income for physical capital investment and a constant fraction sh of their income for human capital investment. Law of motion for physical capital and for human capital given as follows: Kt+1=(1-8k) K + I Ht+1=(1-8h) H₂ + I (3) where 5 and 6, are depreciation rate for physical and human capital, I and I are investment in physical and human capital, respectively. We assume that population grows exogenously with a constant rate n: Lt+1=(1+n) Lt (4) I For the questions below, show your work. Answers with no work won't get any credit. (2) Explain the model in words. That is, give economic intuition about the equations in the model and explain whether you expect differ- ent predictions compared to the benchmark Solow model analyzed in class (Writing the English version of the equations is not an accept- able answer). • What is the expression for aggregate savings? What is the expression for aggregate consumption? What is the equilibrium condition of this model? Explain. How is per capita output (or income) related to per capita physical and human capital? Explain. 2. Solow Model with Human Capital. Consider the following production function: Y = K L³H₂ (1) where Y, is output, K, is physical capital stock, L, is labor and He is human capital stock. Parameters in the production function (a, B and 7) add up to 1. Households save a constant fraction s of their income for physical capital investment and a constant fraction sh of their income for human capital investment. Law of motion for physical capital and for human capital given as follows: Kt+1=(1-8k) K + I Ht+1=(1-8h) H₂ + I (3) where 5 and 6, are depreciation rate for physical and human capital, I and I are investment in physical and human capital, respectively. We assume that population grows exogenously with a constant rate n: Lt+1=(1+n) Lt (4) I For the questions below, show your work. Answers with no work won't get any credit. (2) Explain the model in words. That is, give economic intuition about the equations in the model and explain whether you expect differ- ent predictions compared to the benchmark Solow model analyzed in class (Writing the English version of the equations is not an accept- able answer). • What is the expression for aggregate savings? What is the expression for aggregate consumption? What is the equilibrium condition of this model? Explain. How is per capita output (or income) related to per capita physical and human capital? Explain.