6. Allison is chronically homeless, has been diagnosed with schizophrenia, and prefers to live in Uptown (sleeping in the park and spending her days in the public library). Bill also lives in Uptown, but he prefers not to have to see Allison. Allison's preferences over money, X., and hours per day she spends in Uptown, xz, are represented by the utility function . (X, ) = x2 + VX Bill's preferences over money. Y, and hours per day Allison spends outside of Uptown, Y, are represented by the utility function us (Yu, ya) y1 + vy2. Current Uptown law gives Allison the right to spend as much time in Uptown as she wants per 24 hour day. Allison has a daily income of So and Bill has a daily income of $100. (a) Draw an Edgeworth Box which represents this economy. Label the graph with each consumer, all four axes, the endowment allocation and the indifference curves for each consumer containing their endowment bundle. (b) Is it Pareto efficient for Allison to spend all of her time in Uptown? Lightly shade the region on your Edgeworth Box which includes all allocations which would make both Allison and Bill better o than the endowment allocation. (c) An economist suggests creating a market so that Bill doesn't have to face Allison in person when paying her off to not have to see her. What is the equilibrium price per hour for Bill not having to see Allison? How many hours does Allison spend in Uptown? How much money does Allison end up with? Draw the budget line and equilibrium allocation on your Edgeworth Box from part (a). (d) While Bill appreciates not having to face Allison to pay her off, paying a daily price still makes him feel a bit uneasy. The economist proposes a solution - just pass a law that forbids Allison to be in Uptown unless she pays an hourly fee to spend time there. How much money should Bill donate to Allison per day that would lead to the same allocation under the equilibrium you found above? What will the hourly fee be? (e) Indicate the Pareto set on your Edgeworth Box from part (a). Should society always strive to move to Pareto efficient allocations? 6. Allison is chronically homeless, has been diagnosed with schizophrenia, and prefers to live in Uptown (sleeping in the park and spending her days in the public library). Bill also lives in Uptown, but he prefers not to have to see Allison. Allison's preferences over money, X., and hours per day she spends in Uptown, xz, are represented by the utility function . (X, ) = x2 + VX Bill's preferences over money. Y, and hours per day Allison spends outside of Uptown, Y, are represented by the utility function us (Yu, ya) y1 + vy2. Current Uptown law gives Allison the right to spend as much time in Uptown as she wants per 24 hour day. Allison has a daily income of So and Bill has a daily income of $100. (a) Draw an Edgeworth Box which represents this economy. Label the graph with each consumer, all four axes, the endowment allocation and the indifference curves for each consumer containing their endowment bundle. (b) Is it Pareto efficient for Allison to spend all of her time in Uptown? Lightly shade the region on your Edgeworth Box which includes all allocations which would make both Allison and Bill better o than the endowment allocation. (c) An economist suggests creating a market so that Bill doesn't have to face Allison in person when paying her off to not have to see her. What is the equilibrium price per hour for Bill not having to see Allison? How many hours does Allison spend in Uptown? How much money does Allison end up with? Draw the budget line and equilibrium allocation on your Edgeworth Box from part (a). (d) While Bill appreciates not having to face Allison to pay her off, paying a daily price still makes him feel a bit uneasy. The economist proposes a solution - just pass a law that forbids Allison to be in Uptown unless she pays an hourly fee to spend time there. How much money should Bill donate to Allison per day that would lead to the same allocation under the equilibrium you found above? What will the hourly fee be? (e) Indicate the Pareto set on your Edgeworth Box from part (a). Should society always strive to move to Pareto efficient allocations
