Question 5: Suppose the following world: There are two members of society: Erica and Kelly. There are two goods in the world: Eclairs (E) and Kit Kats (K). There are 100 Eclairs and 100 Kit Kats. Erica's preferences over these goods can be represented by UE(E, K) = E and Kelly's preferences over these goods can be represented by UK(E, K) = K. Using this information, answer the following questions. Part (a) On separate graphs, illustrate Erica's and Kelly's preference map over Eclairs and Kit Kats putting Eclairs on the y-axis and Kit Kats on the x-axis. [By preference map, I mean illus- trate several indifference curves for each person.] Note: When referencing these graphs below, I'll refer to Erica's preference map as Al and Kelly's preference map as A2. Part (b) On a different graph, illustrate the set of utility possibilities for Erica and Kelly when all Eclairs and Kit Kats are distributed, putting Erica's utility on the y-axis and Kelly's utility on the x-axis. Note: When referencing this graph below, I'll refer to it as B. Part (c) Suppose Erica and Kelly are given 50 Eclairs and 50 Kit Kats each. On graph B, illus- trate the utility pairs associated with this initial allocation. Label this point X. Is this allocation Pareto optimal? Is it efficient? Why or why not? Part (d) On graphs Al and A2, illustrate the initial allocation (label it X) and indicate the set of allocations that are preferred by each to this initial allocation. Part (e) Combine graphs Al and A2 to create an Edgeworth Box of Erica's and Kelly's pref- erences and possible trades. Put Erica's origin (0 Eclair and 0 Kit Kats) at the bottom left corner and put Kelly's origin (0 Eclair and 0 Kit Kats) at the top right corner. Label the initial allocation X and indicate the set of possible mutually beneficial trades. Part (f) On graph B, identify and label the utility pairs associated with allocations that are Pareto preferred to X. Part (g) On graph B, identify the set of allocations that are Pareto optimal (i.e. utility pairs for which there are no Pareto preferred pairs). Label this "PF" for the Pareto Frontier