3. Consider a consumer faced with chocolate which she is tempted to consume rapidly. The consumer can buy a large (2-serving) or small (1-serving) pack at period 0. In period 1, she must decide how much to consume. If she bought only the small pack, she consumes one serving. If she bought the large pack, she can consume two servings right away, or one sewing and save another serving for the future (which is automatically consumed in period 2). Instantaneous utility ows from various are displayed in the table below. Purchase Decision Instantaneous Utility Instantaneous Utility in Consumption Decision in Period 1 Small 1 serving Large 1 serving 2 servings Consider a [5-6 quasi-hyperbolic framework. For simplicity assume 5:1. Analyze the optimal consumption decisions of three types of agents: Exponential (B=1, B'=1); na'I've hyperbolic (B=D.5, B'=1); and sophisticated hyperbolic (B'=B=O.5). (40 points) For each agent, gure out: (i) What will they expect to do, at time 0, if they buy either the large and small packages? (ii) Given your answer in (i), which package will the period-0 \"self" purchase, for each of the three types? (iii) After they buy their optimal package, how much will they consume in period 1? (iv) Which of the type's (if any) plans embedded in (i) are actually violated in (iii) (v) Suppose agents could purchase external commitment, in which they could only consume 1 of the 2 servings in the large pack in period 1, at a price of P>O (think of this as buying pre-packaged dietary portions of food). Which agents would commit at time zero to pay P, and how much would they pay