2 Which is right/wrong and Why? 1. There is a country with a population of 100 mln. All these people care only about their personal wealth. Suppose that some of them get wealthier and none becomes poorer. Which of the following is possible and why? (a) Maximin welfare goes down. (b) Gini coeffcient goes down. (c) Maximin welfare goes up. ((1) Gini coeffcient goes up. 2. There is a country with a population of 100 mln. Consider two possible wealth distributions Inequality? One citizen has half of the country's wealth. The remaining 99,999,999 10% citizens all share the remaining half equally. Half of the population has 60% nothing. The remaining half of the population share the entire wealth of the country. Figure 1: Which represents a greater inequality? Survey results. (a) One citizen has half of the country's wealth. The remaining 99,999,999 citizens all share the remaining half equally (b) Half of the population has nothing. The remaining half of the population share the entire wealth of the country. Is this claim true or false and why: "These two distribution are very different in terms of equality, therefore, the Gini coefficients must be different." (To simplify the calculations, you may assume that the population is "continuous" rather than "discrete") 3. 10 portions of pizza and 10 portions of chips are available, quantities of which are denoted x and y, respectively. These two goods can be split in any way between Robinson and Friday. Suppose that Robinson's utility depends on how much pizza, ER, and chips, yR, he consumes. In particular, his utility is equal to the summation of the two quantities, CR+ yR. Friday's utility also depends on the consumption of these two goods, (XF, UF), and it is equal to XF + 2yF. (a) Consider equal split: 5 pizzas and 5 chips for Robinson, the rest for Friday. Is this Pareto efficient and why? (b) All pizza and all chips for Robinson, none for Friday. Is this Pareto efficient and why? (c) 7 pizzas and 7 chips for Robinson, the rest for Friday. Is this Pareto efficient and why? (d) All chips for Robinson, all pizza for Friday. Is this Pareto efficient and why?4. The same pizza & chips situation as above. (a) Equal split: 5 pizzas and 5 chips for Robinson. The rest for Fri- day. Is this outcome envy-free and why? (b) 4 pizzas and 6 chips for Robinson. Remaining 6 pizzas and 4 chips for Friday. Is this outcome envy-free and why? (c) 6 pizzas and 4 chips for Robinson. Remaining 4 pizzas and 6 chips for Friday. Is this outcome envy-free and why? (d) Neither Robinson nor Friday gets any good. All pizzas and chips are discarded. Is this outcome envy-free and why