Suppose you 3 days to spread out the unpleasant task of eating a cauliflower of size 1. Let c1 and c2 denote the amounts you eat on Day 1 and Day 2, respectively, leaving the amount 1 c1 c2 for you to eat on Day 3. You are time-consistent with = 1/2. Your utility on Day 1 is given by U1 = (c1)^2 (1/2)(c2)^2 (1/2)^2 (1 c1 c2)^2

On Day 1, what values of c1 and c2 should you choose to maximize U1? You do not need to show that you have indeed found a maximum (and not a minimum).