Question:

1 Solow Growth Model with Human Capital In this question we consider the coevolution of output and human capital using a Solow growth framework. To do so, we simply augment our aggregate production function to include an element of human capital. Suppose that the smarter people are (the more human capital they have), the more efciently they can produce output. Suppose further that we can measure human capital at time t with one composite number Ht. We then assume the following neoclassical production function )2 = K311? (AtLal-a-f' (1) We further assume that the labor supply is exogenously increasing at a constant rate 11. and that TFP is increasing at the constant rate 9: L,g = (1 + n)Lt_1 = (1 + n)'L0 A. = (1 + 9)A._1 = (1 + 90540 As before, we assume that a constant fraction of output 3K is saved and invested in capital, while a constant fraction 6 of capital depreciates each period. This yields the usual law of motion for capital Kt+1 = (1 (\"Kt + SKY} The new twist to the model is that a constrant fraction of output SH is invested in human capital. Think of this as though the fraction SH of output is spent on education services. Human capital also depreciates at the rate :5: the same as the depreciation rate on capital. 1. Write down the law of motion for human capital. 2. Divide all requisite variables by AtLt to get the intensive form versions of human capital, physical capital, output, and consumption. Denote these intensive form versions with lower case letters ht, kt, gt, 0:. 3. Solve for the steady state values of the intensive forms of physical and human capital in terms of model parameters (6, a, ,8, 3K, .53, n, g). 4. Will physical and human capital both converge to these steady state values in the long run? Why? A picture or two might be helpful here. 5. Discuss the comparative statics of the model. Does steady state human capital increase in ex, $536,104, and for 9? Please give a brief intuitive explanation for each. 6. What are the sources of long run growth in output per capita in this model