Robinson Crusoe and Friday are the two only person on a small island. Suppose th

Question

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 "paretoefficient"?

(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 .

Explanation / Answer

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