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Let Ella’s preferences for goods x and y are represented by the utility function ?(E) (?,...

Let Ella’s preferences for goods x and y are represented by the utility function ?(E) (?, ?) = 2? + ?,
whereas Louis’ utility function is ?(L) (?, ?) = ? + ?
The initial endowments of Ella and Louis include 8 units of x and 4 units of y each (i.e., there are
a total of 16 units of x and 8 units of y in this economy).
a. (2 points) What are the marginal rates of substitution for Ella and Louis?
b. (5 points) Draw the Edgeworth box to show the initial endowments and the utility functions for Ella and Louis. Calculate their utility levels from their initial endowments.
c. (2 points) Do the initial endowments represent a Pareto efficient allocation? Please discuss.
d. (3 points) If Ella convinces Louis to exchange at terms which would leave Louis at his initial utility level (i.e., without making him worse-off), what is the set of (?, ?) that would make Ella better off. Just show this on the Edgeworth box that you drew in part (b).
e. (3 points) What will be the final allocation of goods x and y, if Ella convinces Louis to exchange at terms which would leave Louis at his initial utility level. What will be Ella’s utility after the exchange? What is the exchange rate (x per y)?
f. (2 points) Show, on the Edgeworth box, the set of exchange possibilities for Ella and Louis which would make at least one of them better-off without making the other worse-off.
g. (3 points) Based on your response to part (f), show the contract curve on the Edgeworth box. What is the range of exchange rate?
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It's Mandatory to solve only first 4 parts

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