f.o.c. for Ct: U'(Ct) 0 t (1+r)t= – so using the similar condition for t+1 the following holds between t an t+1: (1+r)t U'(Ct) = t t+1(1+r)t+1U'(Ct+1) U'(Ct) = (1+r) U'(Ct+1)  define: = 1/(1+) where = rate of time preference   U'(Ct) = (1+r) U'(Ct+1) (1) (1+) - this implies: Ct<Ct+1 if r> (assuming U''<0). Ct>Ct+1 if r< (assuming U''<0). Ct=Ct+1 if i.e. trend in consumption over time depends on size of the rate of time preference vs. rate of interest. - height of the consumption-time profile depends on available financial resources. Romer considers a special case (Constant-relative-risk-aversion utility): which gives: (see equation (1) above) where slope of C profile over time depends on r vs. and the  preference parameter . - Empirical studies often suggest that consumption growth is not very
f.o.c. for Ct: t U'(Ct) – (1+r)t= 0 so using the similar condition for t+1 the following holds between t an t+1: t (1+r)t U'(Ct) = t+1(1+r)t+1U'(Ct+1) U'(Ct) =  (1+r) U'(Ct+1) define:  = 1/(1+) where  = rate of time preference U'(Ct) = (1+r) U'(Ct+1) (1) (1+) - this implies: Ct<Ct+1 if r> (assuming U''<0). Ct>Ct+1 if r< (assuming U''<0). Ct=Ct+1 if i.e. trend in consumption over time depends on size of the rate of time preference vs. rate of interest. - height of the consumption-time profile depends on available financial resources. Romer considers a special case (Constant-relative-risk-aversion utility): which gives: (see equation (1) above) where slope of C profile over time depends on r vs.  and the preference parameter . - Empirical studies often suggest that consumption growth is not very