Shelly is a talented researcher who has just received a large (two-year) research grant. The universityallows Shelly to borrow and save (research) money at the interest rater= 0.2, and her utility fromconsumption (of grant money) in years 1 and 2 is given byu(c1,c2) =c31c2[whereMU1= 3c21c2andMU2=c31]. For this question, please use thefuturevalue form for Shelly’s budget and/orvaluations (e.g. supposep1= 1 +randp2= 1). (a)If Shelly’s research grant pays $8,000 this year and $8,000 next year, how should she allocateher consumption of grant money between the two years? (b)If Shelly could choose between the grant in part (a), and a different grant that would pay her$3,700 in the first year and $12,500 in the second, which would she prefer? (c)How would your answer to part (b) change if we allowed Shelly to borrow or save with nointerest (i.e. withr= 0%)?
Shelly is a talented researcher who has just received a large (two-year) research grant. The universityallows Shelly to borrow and save (research) money at the interest rater= 0.2, and her utility fromconsumption (of grant money) in years 1 and 2 is given byu(c1,c2) =c31c2[whereMU1= 3c21c2andMU2=c31]. For this question, please use thefuturevalue form for Shelly’s budget and/orvaluations (e.g. supposep1= 1 +randp2= 1).
(a)If Shelly’s research grant pays $8,000 this year and $8,000 next year, how should she allocateher consumption of grant money between the two years?
(b)If Shelly could choose between the grant in part (a), and a different grant that would pay her$3,700 in the first year and $12,500 in the second, which would she prefer?
(c)How would your answer to part (b) change if we allowed Shelly to borrow or save with nointerest (i.e. withr= 0%)?
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