2. (70 points) Suppose (just as in Chapter 14) that a representative consumer has a lifetime utility function starting from period t Ml+1 Pt+1 Mt+2 + . . . Pt+2 ) 1n(c:)+1n(AI;It1)+ 61n(c.+1)+ 51n( )+ 621n(6=+2) + 521n( and her period-t budget constraint is given by Pic; + FEB? + Pfo + Mz + Stag = Y} + M._1 + 83. + Big + (St + D)a_1 where Bag and B{' denotes short and longterm period bond which pays back its face value one and two periods after purchase, respectively. a. (20 points) Based on the utility function and budget constraint given above, set up an appropriate Lagrangian in order to derive the representative consumer's first-order conditions with respect to both Big and B? (as usual, the analysis is being conducted from the perspective of the very beginning of period t). Define any auxiliary notation that you need in order to conduct your analysis. b. (20 points) Using the two rstorder conditions you obtained in part a, construct a relationship between the price of a twoperiod bond and the price of a oneperiod bond. Your nal relationship should be of the form Pf' = . . . , and on the righthand side of this expression should appear (potentially among other things), HS. c. (30 points) Suppose that the optimal nominal expenditure on consumption (Ptct) is equal to 1 in every period. Using this fact, is the price of a two-period bond greater than, smaller than, or equal to the price of a oneyear bond? If it is impossible to tell, explain why; if you can tell, be as precise as you can be about the relationship between the prices of the two bonds