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' Question 1 long run equilibrium and the golden rule Suppose that the production function is given by: Yt = 150 KEANE-6 and the evolution of capital stock given by: Kt+1 = (1 6)Kt+1t and in equilibrium If = St = SYL- a. Derive the steady state levels of capital per worker k* = (Kc/NJ in terms of the saving rate (5) and the depreciation rate (:5). Explain why and how 5 and 6 aect k*. b. Derive the equation for steady-state output per worker (31*) and steady-state consumption per worker (c*) in terms of s and 5. Explain why and how 5 and (Soect y* and c*. c. Suppose that 6: 5% (=0.05) and s = 6% (=0. 06). Calculate k*, y* and c*. Calculate saving per worker (s *=$*/N=sY*/N=sy*)) d. Show these solutions for k*, y*, c* and 5* on the SolowSwan 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