Write-down the production function, the aggregate consumption function and the equilibrium law of motions of both types of capital in per capita units.

Let us consider a Solow growth model augmented with human capital. The aggregate output Yt is produced according to the following production function at time t. Yt=AKt1HtLt where ,(0,1) are production parameters, A stands for the total factor productivity parameter, Kt stands for the aggregate physical capital, Ht represents the aggregate hum capital, Lt denotes the aggregate labour input that corresponds to the aggregate populatio size which grows at a constant rate n(1,+) : NtNt+1Nt=n The equilibrium law of motions of physical capital and human capital are given by: Kt+1=Yt+(1)KtHt+1=Yt+(1)Ht where (0,1) stands for the investment rate in physical capital, (0,1) stands for t investment rate in human capital and (0,1) represents the depreciation rate. The aggregate level of consumption is a fraction of the total output: Ct=(1)Yt Let us consider a Solow growth model augmented with human capital. The aggregate output Yt is produced according to the following production function at time t. Yt=AKt1HtLt where ,(0,1) are production parameters, A stands for the total factor productivity parameter, Kt stands for the aggregate physical capital, Ht represents the aggregate hum capital, Lt denotes the aggregate labour input that corresponds to the aggregate populatio size which grows at a constant rate n(1,+) : NtNt+1Nt=n The equilibrium law of motions of physical capital and human capital are given by: Kt+1=Yt+(1)KtHt+1=Yt+(1)Ht where (0,1) stands for the investment rate in physical capital, (0,1) stands for t investment rate in human capital and (0,1) represents the depreciation rate. The aggregate level of consumption is a fraction of the total output: Ct=(1)Yt