A closed economy has a constant return to scale production technology as following : Y = zF (K, N), where Y is the aggregate output of consumption goods, 2 is the level of productivity, K denotes aggregate capital stocks, and N is the labor size. The capital stock accumulation function is: K'=(15)K+I where K ' represents the aggregate capital stock of tomorrow, K denotes the aggregate capital stock of today, 6 is the depreciation rate of capital, and I is today's aggregate investment. The rate of growth in the population equals to n which is a constant over time. The government purchases G units of consumption goods in the current period, where G : 9N and g is a posi- tive constant. The government nances its purchases through lump-sum taxes on consumers, where T denotes total taxes, and the government balances its budget each period, so that G = T. consumers consume a constant fraction of disposable income. i.e. C = (1 s) (YT), where s is the saving rate and C is the aggregate consumption, with O 0. (a) Soppose T = 0. i. Derive the capital / labor ratio of tomorrow as a function capital / labor ratio of today. ii. Suppose that the population growth rate R increases. Analyze, using diagrams and equations, what will happen to the steady-state capital per worker k, the steady- state output per worker 31, and the steady-state consumption per worker c. (b) Suppose 0