Problem 4. (35 points total) There are three consumption periods. Emma has wealth $10 at the beginning and she cannot borrow. She can save at 100% annual interest (i.e. any money left at the bank doubles every year). Emma is a quasi-hyperbolic discounter: given consumption c, in year t, "Year 1" Emma has utility UI (CI, C2, (3) = CI + Boc2 + Boc3 and "Year 2" Emma has utility U2 (C2, (3) = C2 + Boc3 Suppose 8 = = and 6 = 1. All consumptions occur at the beginning of the year. (1) Write down the budget constraint for "Year 1" Emma. (5 pts) (2) Show that a naive Emma will consume all her wealth in Year 2. (Hint: you don't need calculus) (10 pts) (3) Write down the budget constraint for "Year 2" Emma assuming she consumed c in Year 1. (5 pts) (4) Show that a sophisticated Emma will consume all her wealth in Year 1. (10 pts) (5) Why does a sophisticated Emma consume earlier than a naive Emma? (5 pts)