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HW07 - Economics 11 Winter 2006 Homework#07 Due Thursday...

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Economics 11, Winter 2006: Homework #07 Due : Thursday March 2, 3PM For each of the following two-person, two-good economies, find the equilib- rium and (an equation for) the Pareto set, and sketch an Edgeworth box showing the endowments, the Pareto set and the equilibrium price line and consumption choices. (You do not need to show preferences or the individu- ally rational set or the contract curve.) Your sketch does not need to be very precise, but make sure straight lines look straight, curved lines look curved, and curves intersect the boundaries of the box at the right points. 1. e A = (100 , 200); u A ( x, y ) = x 1 / 3 y 2 / 3 e B = (300 , 200); u B ( x, y ) = x 1 / 2 y 1 / 2 2. e A = (100 , 700); u A ( x, y ) = x 1 / 2 y 1 / 2 e B = (300 , 100); u B ( x, y ) = log x + 1 2 log y The purpose of the next set of problems is to see how the relative wealth of agents and their preferences affect the interest rate. In each of these problems consider an economy in two dates: today and one year from today; write x for consumption (money) today and y for consumption (money) one year from today. There are two types of agents. Agents of type A have no endowment today but are wealthy tomorrow: e A = (0 , 1). Agents of type B are wealthy in both dates e B = ( W, W ). ( W is a parameter of the problem. In class we did the case W = 1.) 3. First assume both types of agent have utility function
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