Consider a two-period model of intertemporal choice. Bob has wealth $10 at the beginning and will receive
Question:
Consider a two-period model of intertemporal choice. Bob has wealth $10 at the beginning and will receive $11 in earnings at the end of the first year. Bob can either borrow or save at 10% interest per year. Bob’s utility over consumption c1 in the first year and consumption c2 in the second year is given by
U (c1, c2) = √ c1 + δ √ c2
where δ ∈ [0, 1] is his discount rate. All consumptions occur at the beginning of the year.
(1) What is Bob’s budget constraint?
(2) Solve for the optimal c1 and c2 as functions of the discount rate δ
(3) As δ increases, how does c1 and c2 change? Provide some economic intuition.
(4) For what values of δ will Bob save? For what values of δ will he borrow? Provide some economic intuition.
