Suppose you observe a person's answer to two decision problems. Problem 1: You are offered $40 today. What is the minimum amount at you demand one month from today in order to be willing to give up the $40 now? Answer: x = 52. ' Problem 2: Your are offered $40 today. What is the minimum amount x you demand one year from today in order to be willing to give up the $40 now? Answer: $60. _ 1. Demonstrate that the rational model of time preferences is violated for this choice pattern. __ 2. Derive this individual's and i) for the hyperbolic time discounting model. 3. Suppose the utility you get from eating ice cream now is 10 utils. But you pay a r: cost of -4 utils per hour for the next 4 hours, because it gives you indigestion and makes you feel lethargic. Ifyour hourly 3 and 6 for this problem are 0 = .6 and 6 = .9, . 1. What is the total discounted utility of eating ice cream now? 2. What is your total discounted utility now of planning to eat ice cream after- lunch tomorrow? 3. Do you eat ice cream now? h 4\" Do you plan to eat ice cream tomorrow