Accounting Ralph and Piggy are alone on an Island. Ralph has 5 X and 15 Y. Piggy has 20 X and 5 Y.

a. (6) Graph their endowments below labeling each endowment and total X and Y on the graph, labeling origins with Ralph's origin on the left and X on the x-axis.

 

b. (6) At this endowment, Ralph has an MRS of 1 X for 5 Y; Piggy has an MRS of 4 X for 1 Y. Can Ralph and Piggy be made better off by a trade? If no, explain why not, If yes, give an example trade that both would accept showing that they would accept. Is such a trade a Pareto efficient exchange? Explain why or why not including the definition of a PEA.

c) Define Pareto efficiency allocation (distribution of goods). Explain why if all consumers face the same price for all goods, then we have efficiency (this takes a few steps of logic). Include a graph of a consumer maximizing their utility given their budget constraint.