Question 1. Consider an exchange economy with two goods, ale and bread. There are two individuals, Ann and Bob, whose initial endowments are as follows: Ann has 40 units of ale and 20 units of bread, and Bob has 20 units of ale and 40 units of bread. The utility from consuming a1 ale and b1 bread is 13 u1(a1,b1) = (a1)4 (b1)4 for Ann, and the utility from consuming a2 ale and b2 11 bread is u2(a2,b2) = (a2)2 (b2)2 for Bob.
(1) If we normalize the price of bread to 1, for an arbitrary ale price p (relative to bread), given Ann's endowments, what is the demand for ale and bread for Ann?
(2) If we normalize the price of bread to 1, for an arbitrary ale price p (relative to bread), given Bob's endowments, what is the demand for ale and bread for Bob?
(3) What is the price that will clear both markets?
(4) What is the competitive equilibrium allocation for this exchange economy? Is it Pareto efficient?
Question 2. (Adapted from Leach textbook, Ch.2 Q1)
Consider an exchange economy with two goods, ale and bread, and two individ- uals, George and Harriet. For each of the situations below, draw an Edgeworth box containing an endowment point and a budget line. Use ale as the horizontal axis, bread the vertical axis, put George's origin point in the bottom-left corner of the box and Harriet's origin point in the top-right corner of the box.
(1) Draw an indifference curve for George and an indifference curve for Harriet, both tangent to the budget line, such that George wants to buy ale, Harriet wants to sell ale, and George wants to buy less ale than Harriet wants to sell. (2) Draw two indifference curves, both tangent to the budget line, such that George and Harriet both want to buy ale.
(3) Draw two indifference curves, both tangent to the budget line, such that the current price is market-clearing but no goods are traded.