Consider a representative consumer who lives 2 periods and has the following utility function
V= √c ​+ β √c′ ​
where c and ′ c ′ represent consumption in the current and future periods, respectively. β is the discount factor where β = 1/(1) β=1/(1 + rho) with rho > 0 rho>0 being the rate of time preference. The current-period budget constraint is given by
c + 8 = y
and the future-period budget constraint is given by
c′ = y′ (1 + r)s
where y and y' are exogenous income in the current and future periods, respectively, and s is asset savings.