Problem 4- [23 TOTAL POINTS] Consider a consumer faced with a 'vice' good such as vodka which he is tempted to consume rapidly. In period 0, the consumer can buy a large 2serving bottle or a small 1serving bottle of vodka and plan consumption over the next periods. There are 3 options: a Plan A: Buy the small bottle in period 0 and consume 1 serving in period 1. 0 Plan B: Buy the large bottle in period 0, consume 1 serving in period 1, and consume 1 serving in period 2. 0 Plan C: Buy the large bottle in period 0 and consume 2 servings in period 1. Vodka gives immediate utility when consumed but reduces utility next period. The large bottle has a lower perserving price so consuming from it gives more utility. The table below shows the utility of each of the consumption plans: 2 Plan | Period 1 Utility Period 2 Utility Period 3 Utility I 1 1 1 A i 5 1 4 i B 1 6 1 2 4 ' 1 C I 12 1 13 ' Assume that consumers have quasihyperbolic preferences and 5 = 0.9. Analyze the optimal consumption plan of an exponential agent with B = 1 and a quasihyperbolic agent with l3 = 0.5. a. Assuming it is Period 0, calculate the discounted utility of each plan for the exponen tial agent. What size of vodka bottle would he purchase? [3 POilltS] b. Assuming it is Period 0, calculate the discounted utility of each plan for the quasi hyperbolic agent. What size of vodka bottle does a naive quasihyperbolic agent purchase? [5 points] 0- Assume it is Period 1 and the large vodka bottle was purchased in Period 0. Calculate the discounted utility of plans B and C for the exponentially discounting agent. Will he consume one or both servings? [5 POintS] (1. Assume it is Period 1 and the large vodka bottle was purchased in Period 0. Calculate the discounted utility of plans B and C for the quasi-hyperbolically discounting agent. Will he consume one or both servings? [5 points] 6. Assume it is period 0 and there is a sophisticated quasihyperbolically discounting agent. The sophisticated quasihyperbolic agent can foresee that he won't be able to resist consuming two servings in period 1 if he buys the large bottle in Period 0. Therefore, based on this insight, he reasons that his choices in Period 0 are really Plan A and Plan C. Which size of bottle would he purchase? [5 points]