Please answer the question provided in the image below.

Question 2: This question asks you to reconsider the model of optimal sin taxes that we studied in class when there is heterogeneity in people's tastes for potato-chip consumption (in addition to heterogeneity in self-control problems). Suppose that everyone has Y 40 (everyone has the same susceptibility to health consequences). Suppose that 1/2 of the population has [3 I while 1/2 of the population has [3 0.85. Suppose further that 2/3 of the population has p 75 and the other 1/3 of the population has p 45, where the distributions of [3 and p are independent. Note that there are four types: (i) people with [3 I and p 75; (ii) people with [3 I and p 45; (iii) people with [3 0.85 and p 75; and (iv) people with [3 0.85 and p 45. (a) As a function of t, how many potato chips will each type consume? (b) As a function of t, what is the uniform lump-sum transfer? (c) For each type, compare people's utility for t 0% vs. t 10%. (d) Are all types better off when t 10%? Provide some intuition for this answer. (e) Are the two types with [3 I on average better off? Are the two types with [3 average better off? Provide some intuition for this answer. 0.85 on