Bob lives two periods: today and tomorrow. His preference is represented by the following utility function: U(C1, C2) = C1 C₂⁰⁹
where cı is today's consumption level and C2 is tomorrow's consumption level. Suppose Bob's income today is yi $100 and his income tomorrow is $y2 190. Interest rate is denoted by r. = = 1. Write down Bob's utility maximization problem (including the budget set). 2. Determine Bob's optimal consumption bundle (c1, c) as a function of r. Draw the inverse demand curve for consumption tomorrow (i.e., con X axis and p2 Y axis). on 1+r 3. (10 points bonus) Suppose today Bob can borrow at most $40 (i.e., C1 < 140). Then determine Bob's optimal consumption bundle (ci, cm) as a function of r.