Let's assume a simple model of consumption and demand in real balances described by

 

max s.t. Eo t=0 3 u (Cr Ft) PC + B + M = (1 + r) B-1 + (1+1) Mt-11 where C, is real consumption at time t; M/P, is real money balances (M, is money holdings and P, is the price level); B, is bond holdings, which earn a gross rate of return (1+r); money holdings earn a gross rate of return (1+r). The representative household also enjoys utility from holding real money balances. In this economy, the household chooses sequences for consumption, {C}, and real money balances, {M/Po a. Obtain the first-order conditions for the maximization of the household problem (hint: divide the period-t budget constraint by P, before maximizing). b. Assume now that the utility function is Cobb-Douglas in consumption and real money balances, i.e., 1-a u(C)C(M) where 0