If the representative consumer’s period –t utility function is u(c _t M ^D _t /P _t ) = lnc _t + ln (M ^D _t /P _t ), then the (real) money-demand function in period –t is

M ^D _t /P _t = c _t .((1 + i _t ) /i _t )

In which the left-hand side is m ^D _t = M ^D _t /P _t (recall that uppercase M denotes nominal money whereas lowercase m denotes money in purchasing power terms).

In “conventional times,” the nominal interest rate I can never fall below zero, which, for the analysis below, is a maintained assumption.

(a) Based on the real money-demand function, compute the point elasticity of m ^D _t (i.e., of the optimal choice m ^D _t ) with respect to i _t .

(b) Is the elasticity computed in part a strictly positive strictly negative, exactly zero, or impossible to determine?