Question 1 long run equilibrium and the golden rule Suppose that the production function is given by: Y; = 150 K0:41:06 and the evolution of capital stock given by: Kt+1 = (1-8)K4 +17 and in equilibrium 1 = St = sy a. Derive the steady state levels of capital per worker k* = (K:/N+)* in terms of the saving rate (s) and the depreciation rate (8). Explain why and how s and 8 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 8. Explain why and how s and Saffect y* and c* C. Suppose that 8 = 5% (=0.05) and s = 6% (=0.06). 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 8 = 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