In class, we solved a two-period savings model where a consumer allocates income across two periods. We assumed the consumer’s intertemporal utility function was given by: U(c₁,c₂) = log(c₁) + δlog(c₂) and that their intertemporal budget constraint was M₁ + M₂ = c₁ + c₂ . 1+r 1+r

Along the way to solving that problem, we found that consumers should select their consumption in each period so that:
u′(c₁) = δ(1 + r)u′(c₂),
where δ is the exponential discount rate and r is the interest rate.

a. Assume the consumer’s "flow" utility is given by log(ct) in each period and that the consumer has an exponential discount rate δ. What is the intertemporal utility function with three periods (instead of two)?