Calculate the reservation utility levels of Robinson and Friday.

Robinson Crusoe and Friday are the two only person on a small island. Suppose there are only two goods available for consumption, good and good . Robinson has initial endowment of 1 unit of and 2 units of , while Friday has 2 units of and 1 unit of . Robinson and Friday have the same utility function being , where and are the amount of good and the amount of good that individual consumes.
(a) Calculate the reservation utility levels of Robinson and Friday.
(b) If Robinson proposes a new allocation: for Robinson, and for Friday, where the first number in the parentheses represents amount of good and the second number represents the amount of good . Should Friday accept the offer?
(c) Based on (b), is the initial endowment allocation “pareto efficient”?
(d) Derive the formula for pareto efficient locus in this two-person exchange economy.
(e) Graph initial endowment allocation, pareto efficient locus, contract curve, and all allocations that are pareto superior to the initial endowment.
(f) Calculate the competitive equilibrium allocation, and the equilibrium price ratio of good to good .

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