[Mankiw 10e, Chapter 8. Q1] Consider the Solow Growth model with constant pop- ulation and technology, as follows. Yt = F(Kt, Lt) = Kl/3 1213. (1) Yt = Ct + St (2 ) St = oYt ( 3 ) Kt+1 = (1 - 8) K+ + It (4 ) St = It (5) where Yt is output in period t, Kt is capital stock in period t, Lt is labor in period t, Ct is consumption in period t, St is savings in period t, and It is investment in period t. 1. Find output per worker in period t, denoted as yt, as a function of the capital per worker in period t, that is, yt = f(kt). 2. Write the equation (1) ~ (5) in per worker terms. Hints: Since we have assumed that population is constant (i.e. labor L is the same in every period), what does this tell you about capital per work in period t+ 1? 3. Write the fundamental equation of capital accumulation, that is, capital ac- cumulativequation as a function of kt and kt+1. (Hint. Use five equations from Q2, and you should start by subtracting current capital stock from both sides, and then do some algebra to get the same equation from class.). 4. Suppose that the savings rate in this economy is 0.35 and depreciation rate is 0.05, and initial capital per worker is 2. Find the steady state values of all of the variables in the equations. Is this consistent with the steady state pertaining to the golden rule of capital per worker? If not, what would the savings rate need to be to be consistent with it