Twoperiod Ramsey optimal taxation. Consider a twoperiod economy in which the government must collect taxes in order to nance government purchases EL and E's. Suppose that the government cannot levy lumpsum taxes; instead, all taxes are in the form of proportional consumption taxes (i_e.__ sales taxes}. When taxes are pro- portional, one general lesson we've seen is that the timing of taxes does matter (for consumption and national savings)_m 1'What it means that the timing of taxes \"matters\" is that consumption decisions of the economy are affected by the tax rates that the government levies. In order to raise the revenue needed to pay.r for 1 and Hz, the government does have to levy some taxes: an interesting question is what is the optimal tax rates for the government to set. Here we mean \"optimal" in the sense that the goverimient ultimately cares about the representa tive consumer's lifetime utility, which is known as a \"Ramsey government problem." The Ramsey government problem essentially tries to answer the following question: 1|What tax rates should the government set? Assume the following: a. b. E. f. The real interest rate between period 1 and period 2 is zero (i.e., r1 = U}. The representative agent has no control over his real income yl or yg. The consumption tax rates in the two periods are denoted IF and If. The representative consumer starts with zero initial assets [on = G}; thus the LBC of the consumer is (I + Efe] +{l Hack] = y] + y]. The government starts with zero initial assets (bu = D}, thus the LEC of the gov ernment is 31+ g] = tf'cl + tfcz. The lifetime utility function of the consumer is at cl, c2 } = In c] + l'g. There are three steps to computing the Ramsey-optimal tax rates. a. The rst step is to determine the consumer's optimal choices of CL and c: as func- tions of y]. yg, :l, and If. In setting up the appropriate Lagrangian, solve for the optimal choices of consumption in period 1 and consumption in period 2 as a function of these four objects. Next, for a moment, suppose that the government did have the ability to levy lump- sum taxes. If it could lety lump-sum taxes, then the government's LBC would be 3' + g: = TI +Tp {i.e., these are the some EL and H: as above} and the consumefs LEC would be cl +Tl + [72 + T3 2 ya + F3, where T1 and T3 denote lump-sum taxes in periods 1 and 2. b. In the case of lump-sum taxes, what would he the consumer's optimal choices of consumption in period 1 and period 2? (S et up a Lagrangian here if you need, but if you are able to logically determine the optimal quantities of consumption here, you may do so.) Compare your solutions for optimal period-l consumption and optimal period-2 consumption in parts a and h above. Solve for the tax rates {F and if that equate these two different sets of choices. These tax rates you nd, which are the optimal tax rates, should he mctions of .'FI, J's, 1, and 3 and no other variables. How do the two tax rates compare to each other\