II. A Solow Model of Economic Growth with Human Capital Accumulation (50 Points) Let us consider a Solow growth model augmented with human capital. The aggregate output Y, is produced according to the following production function at time t. Y = AK, 1-*-B HLR where x, (0,1) are production parameters, A stands for the total factor productivity parameter, K+ stands for the aggregate physical capital, Ht represents the aggregate human capital, L+ denotes the aggregate labour input that corresponds to the aggregate population size which grows at a constant rate n =(-1,+0): Nt+1 - Nt Nt = n The equilibrium law of motions of physical capital and human capital are given by: Kt+1yY Ht+1 EY = (1-8)Kt (1-8)Ht where y = (0,1) stands for the investment rate in physical capital, & E (0,1) stands for the investment rate in human capital and 8 (0,1) represents the depreciation rate. The aggregate level of consumption is a fraction of the total output: 2 C = (1-y) Yt a. Write-down the production function, the aggregate consumption function and the equilibrium law of motions of both types of capital in per capita units. (20 points) b. What would happen over time to the economy if = 0? (5 points) c. Derive the steady-state physical capital per capita: kss, the steady-state human capital per capita: hss and the steady-state income per capita: Yss. (15 points) d. Derive the investment rates: , & that maximize the steady-state consumption per capita: Css (10 points)