Consider an economy inhabited by a continuum of identical house- holds and each household solves: :5 [u( ct) +2} (1ht)] {0: hr it mkt+1}'3_ 0 subject to ptbt-ll 'l' Ct + it = \"(1 Tk,t)lt 'l' (1 Tw,t)wtht + bt and kt\" = (1 (5)13: +7315. bt+1 is government debt which the government must pay back to the households in period t + 1. This asset is traded at period t at price pt. All other variables have the usual interpretation. In each period, tax revenues and government debt are used by the government to finance some exogenously given and constant government spending G. Perfectly competitive firms solve each period max [Akh El) rtkf wthf] , led hd where [Cd and hd denote capital and labour demand. A 2 0 is a productivity parameter. Preferences and production function f have the usual neoclassical assumptions. ,8 and 5 6 (0,1), and agents have rational expectations. (a) Find the first order conditions for the representative household and firm. (b) Write down the problem of a benevolent planner. (c) Find the first order conditions of a benevolent planner and ex plain whether there is a market equilibrium with the same allo cations. (d) Write down the implementability constraints that a Ramsey plan ner would take as given and explain why the solution to a Ramsey problem differs from that of a Planner problem. (e) Show the long run level of capital income taxes chosen by the Ramsey planner