Can someone show me how and what the optimality condition between M_1_t and M_2_t is - based on the 3 first order conditions I have already derived?

Attached is the original Lagrange, but I already derived the 3 first-order-conditions needed to construct the optimality condition.

+ a FOC for By 6 For for MY u MI M busmt wed C ) FOC for MZ . M' + BA (1 + M = 0Letting B stand for the one-period-ahead "impatience" parameter and 2, as the Lagrange multiplier on the period-t budget constraint, the sequential Lagrange function starting from period t is M2 1+ + K . In Inc, + In + K . In Mi + B. Inc + In P P M2 1+2 + K . In 1+ 2 + .... + 32. Inc,, + In P+ +2 P+ +2 +2 Y, + M' , + ( 1tim ) M2 ,+(1+i , ) B, + (S, + D,)a,_-P,c, -M; -M, -B, -S,a, +....Consider an extended version of the money- in-theutility (MIU) function framework. In addition to stocks and nominal bonds, suppose there are two types of money in the utility function: M1 money and M2 money. M1 money is denoted as M ,1 and M2 money is denoted as M ,2 . The representative consumer's period-t utility function is l 2 1 2 u 6,,M' ,M' =lnct+lnM' +K-hiM' , I: I: P P t t which, note, has three arguments. The exogenous parameter K' (the lowercase Greek letter \"kappa\") in the utility function is between zero and one (i.e., 0