The economy operates based on the assumptions of the Solow model. There is no population growth and technological progress. We know the following information: The production function: Y =zK&N-a The evolution of capital stock: Kt+1 = (1-8) Kt + It The equilibrium condition at the goods market: It = St= syt a) Derive the output per worker production function (y =). b) Derive the long-run steady-state equilibrium levels of capital per worker k* = (K)* in terms of the saving rate (s), the depreciation rate (6), and the other parameters (z, a). Explain why and how s and 8 affect k*. c) Derive the equation for steady-state output per worker (y* = ()*), the steady-state investment per worker (i* = ()*) and the steady-state consumption per worker (e* = ()*) and in terms of s, 6 and the other parameters (z, a). Explain why and how s and 6 affect y,c* and i*. d) Suppose that 8 = 10%, s = 6.5%, z = 10, a= 0.45 and the economy is in steady-state. Calculate the following steady-state values: k*,y*, c* and i*. e) Show these solutions for k", y,c* and i* on the Solow-Swan diagram. f) Suppose the saving rate, ceteris paribus increases from its initial level of 6.5% to 8%. Calculate the new steady-state value: k*, y,c* and i*. Show these change on your Solow-Swan diagram.