Dynamic Lecture 5: Discrete Time Intertemporal Optimization

at+1 = (1 + r)(at + yt − ct), t = 0, 1, . . . , T r > 0, a0 given Where at denotes assets (or wealth) held at the beginning of period t, yt is labor income in period t, ct denotes consumption expenditure incurred in period t, β is the discount factor, r is the interest rate, and u() represents the period-by-period utility function, assumed to be twice continuously differentiable, strictly increasing and strictly concave. We also assume that limct→0 u (ct) =∞.