2 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 Y: = KsHAaLal-a- (1) We further assume that the labor supply is exogenously increasing at a constant rate at and that TFP is increasing at the constant rate g: Lt = (1 + n)Lt1 = (1 + n)tLo At = (1 + 9')At1 = (1 + gltAo 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 6)Kt + SKYt The new twist to the model is that a constrant fraction of output 3H 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 6: the same as the depreciation rate on capital