Need help with this economics question please! Thank you!

Problem 1. Bob lives two periods: today and tomorrow. His preference is represented by the following utility function: U(c1,cg) = .5 + awe2 where .21 is today's consumption level and (:2 is tomorrow's consumption level. Suppose Bob's income today is m = $100 and his income tomorrow is ya = $100. Interest rate is denoted by r. 1. (5 points) Write down Bob's utility maximization problem [including the budget set). 2. (5 points) Determine Bob's MRS. 3. (15 points) Determine Bob's optimal consumption bundle (oi, oi) as a flmction of r. 4. (5 points) Draw the inverse demand curve for consumption tomorrow (i.e., c5 on X axis and p2=F1ronYaxisl 5. (10 points) For which values of r does Bob save money today (i.e., of