This problem uses calculus to compare two menarios of consumer optiimzation. 3. Nina has the following utility function: U = 111(C1) + ln(C2) + 111(C3). She starts with wealth of $120,000, earns no additional income, and faces a zem interest rate. How much does she consume in each of the three periods? a. David is just like Nina, except he always get: em utility from present consumption. From the perspective of period 1, his utility function is U = 21n(C1) + ln(C2) + m(c3). In period 1, how much does David decide to consume in each of the three periods? How much wealth does he have left aer period 1? c. When David enters period 2., his utility function is U = ln(C1) + 2111(C2) + 1:403). How much does he consume in periods 2 and 3? How does your answer here compare to David's decision in part (b)? d. If, in period 1, David were able to constrain the choices he can make in period 2, what would he do? Relate this example to one of the theories of consumption discussed in the chapuer