Eve (consumer A) and June (consumer B) growing old together on a remote island on which only fish (good 1) and coconut (good 2) are available for consumption. Eve's preferences are described by the utility function u(xA1 , xA2 ) = (xA1 )(xA2 ), where xAj is Eve's good j consumption with j = 1, 2. Similarly, June's utility function is u(xB1 , xB2 ) = (xB1 )3(xB2 ), where xBj is June's good j consumption with j = 1, 2. Also, Eve's initial endowment is A = (1A, 2A) = (2, 1) while June's initial endowment is B = (1B , 2B ) = (3, 3).

1. a)Draw the Edgeworth box for this economy. Mark the point indicating the initial endowment of each consumer.
2. b)Explain if it is Pareto efficient for Eve and June to consume their endowments.
3. c)What is the set of allocations that could be the outcome under barter in this economy?
4. d)Let the price of fish be p1 while the price of coconut be normalized to 1 without loss
5. of generality. For each consumer, solve the utility maximization problem, i.e., derive
6. xi forj=1,2andi=A,Basafunctionofthepricep. j1
7. e)Calculate the equilibrium prices and demands for the economy.
8. f)Explain if the equilibrium you find in part e) is Pareto Optimal.
9. g)Suppose now that Eve discovered a new territory of coconut trees. As a result, Eve's endowment of coconuts (i.e., 2A) has increased slightly. Explain how this alters the equilibrium price of fish.