Problem 3. MI Money and M2 Money (35 points). Consider an extended version of the money- in-the-utility (MIU) function framework. In addition to stocks and nominal bonds, suppose there are two types of money in the utility function: MI money and M2 money. MI money is denoted as M : and M2 money is denoted as M : The representative consumer's period-t utility function is which, note, has three arguments. = In c, + In In The exogenous parameter K (the lowercase Greek letter "kappa") in the utility function is between zero and one (i.e., O < K < l). The period-t budget constraint is in which i, denotes the nominal interest rate on bonds B, held between period t and t+l (thus denotes the nominal interest rate on bonds B, _1 held between period t-l and t) and denotes the nominal interest rate on M2 money held between period t and t+l (thus iy_l denotes the nominal interest rate on M2 money held between period t-l and t). Note that M2 money potentially pays positive interest, in contrast to MI money, which pays zero interest. The rest of the notation is standard: a, denotes real stock holdings at the end of period t, S, denotes the period-t nominal price of a unit of stock, D, denotes the period-t nominal dividend, P, denotes the period-t nominal price of consumption goods, and Y, (which is strictly positive) denotes period-t exogenous nominal income.