ECON 20000 Lecture Notes - Lecture 9: Composite Good, Budget Constraint, Utility Maximization Problem

Consider an economy where each representative agent lives for two periods. In each period t, there are N_t young individuals and N_t-1 old individuals, where Nt/Nt 1 = 1. Each young individual obtains a quantity I_t of the unique good, which can be used for consumption in period 1 c_yt or saved s_t. In the second period, when the individual is old, h/she obtains a quantity I_t+1 of the good and obtains (1 + r_t) s_t. The old individual uses the proceeds for consumption c_ot+1. Assume the individual maximizes lifetime utility U = ln (c_yt) + I² ln (c_ot+1), where 0 < I² < 1.

a) State mathematically the individual's optimization problem.

b) Solve for the individual's utility-maximizing path of consumption c_yt and c_ot+1 and of saving st.

c) Will intergenerational transactions take place? Why/why not?