1. [40 points] Consider a simple model of human capital in which production is given by Y=K1(AL) and A is a measure of the efficiency of labor, such that the productive capacity of the stock of labor, or level of human capital is H=AL.Then Y=K1H. A proportion sk of income is invested in physical capital, and a proportion sh in human capital. The depreciation rates are respectively k and h. The population does not grow. (a) Find the equilibrium physical capital to human capital ratio K/H, using the condition that both investments must yield the same return and depreciate at the same rate. (b) Show that the production function can be written as an AK function letting =(H/K), and show that the growth rate of output is constant and depends on model parameters. 1. [40 points] Consider a simple model of human capital in which production is given by Y=K1(AL) and A is a measure of the efficiency of labor, such that the productive capacity of the stock of labor, or level of human capital is H=AL.Then Y=K1H. A proportion sk of income is invested in physical capital, and a proportion sh in human capital. The depreciation rates are respectively k and h. The population does not grow. (a) Find the equilibrium physical capital to human capital ratio K/H, using the condition that both investments must yield the same return and depreciate at the same rate. (b) Show that the production function can be written as an AK function letting =(H/K), and show that the growth rate of output is constant and depends on model parameters