Question

Please look at the utility functions, they have changed.

Consider the Isle of lost 60’s sitcom stars. Adam once played a campy version of Batman and Eve played a daughter in a large family. Both left Hollywood to live on an island. Since they are the only two on the island they form a very small exchange economy where there are only two goods: food (F) and housing (H). Eve who has the utility ??(??,??)=?_??_?² and Adam who has the utility ??(??,??)=?_?²?_?. Let ??denote the food and ?? denote the housing that Eve consumes. ?? and ?? are analogously defined.
a) Suppose that Eve has an endowment of 20 units of housing and 20 units of food; and, Adam has and endowment of 20 units of housing and 20 units of food. Find an equation for Eve’s MRS (MRSe) and her MRSe at her endowment. Find an equation for Adam’s MRS (MRSa) and his MRSa at his endowment.
b) Using an Edgeworth Box with Eve’s origin in the lower left corner and her consumption of food on the horizontal axis, illustrate Adam’s and Eve’s endowments and roughly draw their indifference curves that go through their endowments.
c) Explain why both Adam and Eve could be better off by trading with each other versus simply consuming their own endowments. Give an example of a trade that would lead to each being better off than if they just consumed their endowments of the two goods. Support your answer with a comparison of utility levels for each before and after the trade.
d) Set up and solve Eve’s utility maximization problem where her income is denoted by ??. Do the same for Adam where his income is ??. Let ?? and ?ℎdenote the prices of food and housing. Solve for the utility maximizing quantities of food and housing for both.
e) Let ??=2 and ?ℎ=4. Imagine that Adam and Eve sell their endowments at the market prices togenerate income and then use that money to purchase the amount of food and housing that makes them happiest. Using you answers from part d) determine who much each would like to purchase at these prices. Given you answers, can you determine whether these prices are equilibrium prices? Support your answer in no more than two sentences.

Answer 1