1. This problem requires the use of calculus to solve some consumer optimization problems 1) Nina has the following utility function U = ln (C₁) + ln (C₂)+In (C3) She starts with wealth of $120,000 earns no additional income, and faces a zero interest rate. How much does she consume in each of the three periods (Hint: The marginal rate of substitution between consumption in any two periods is the ratio of marginal utilities). 2) David is just like Nina, except he always gets extra utility from present consumption. From the perspective of period one, his utility function is U= 2ln (C₁)+In (C₂)+In (C₂) In period one, how much does David decide to consume in each of the three periods? How much wealth does he have left after period one?