Consider an economy with two periods (interpreted as “when young” and “when old” periods)and two consumers, Gillian Davis and Joana Wolinsky. Gillian is a star ballet dancer with a lifetime income given by ωG= (400,0). Joana is an Econ Ph.D. student with incomeωJ= (0,400). Gillian and Joana have identical utility functions given by Ui(x1,x2) = 6 lnx1+ 3 lnx2 for i=G, J a) Plot an Edgeworth box and mark the initial endowment point. b) Write the general definition of Pareto efficient allocation (one sentence) and give the equivalent condition in terms of MRS (give formula). Check if this condition is satisfied for initial endowments. c) Derive the contract curve (write down the appropriate conditions and solve for the curve) and depict it in the Edgeworth box.
Consider an economy with two periods (interpreted as “when young” and “when old” periods)and two consumers, Gillian Davis and Joana Wolinsky. Gillian is a star ballet dancer with a lifetime income given by ωG= (400,0). Joana is an Econ Ph.D. student with incomeωJ= (0,400). Gillian and Joana have identical utility functions given by Ui(x1,x2) = 6 lnx1+ 3 lnx2 for i=G, J
a) Plot an Edgeworth box and mark the initial endowment point.
b) Write the general definition of Pareto efficient allocation (one sentence) and give the equivalent condition in terms of MRS (give formula). Check if this condition is satisfied for initial endowments.
c) Derive the contract curve (write down the appropriate conditions and solve for the curve) and depict it in the Edgeworth box.
d) Suppose Gillian and Joana can “trade” consumption in both periods at pricesp1,p2. Find the competitive equilibrium (6 numbers) and depict the equilibrium allocation in the Edgeworth box.
e) Using the MRS condition from part b), verify that the equilibrium allocation obtained in part d) is Pareto efficient.
f) Find the equilibrium interest rate r using competitive prices from part d) (one number).
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