Question 1 long run equilibrium and the golden rule Suppose that the production function is given by: Y = 10 KP 2NO.8 and the evolution of capital stock given by: Kt+1 = (1-o )K, + and in equilibrium It = St = SYt a. Derive the steady state levels of capital per worker k* = (K /Nt)" in terms of the saving rate (s) and the depreciation rate (6). Explain why and how s and & affect k*. b. Derive the equation for steady-state output per worker (y*) and steady-state consumption per worker (c*) in terms of s and 5. Explain why and how s and & affect y* and c*. C. Suppose that 6= 5% (=0.05) and s = 5% (=0.05). Calculate k*, y* and c*. Calculate saving per worker (s*=S*/N=sY*/N=sy*)) d. Show these solutions for k*, y*, c* and s* on the Solow-Swan diagram. e. Using 6 = 0.1, what is the saving rate that maximizes consumption per worker? What is the golden rule level of capital per worker, output per worker and consumption per worker? Why is this a useful concept