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_Lecture_14

# _Lecture_14 - Lecture 14 1-minute review exchange...

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Lecture 14 1-minute review exchange competitive equilibrium 1

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Exchange Economy An exchange economy consists of goods/commodities x, y, z . . . consumers A, B, C . . . : endowments e , utility functions u Competitive Equilibrium A competitive equilibrium consists of prices for all commodities choices for all consumers such that choices are optimal in budget sets defined by endowments markets clear: sum of choices = sum of endowments Caution Only relative prices matter. Nothing would change if we multiplied all prices by c > 0 measured prices in yuan instead of dollars normalized so that sum of all prices = 1 normalized so that price of first good = 1 ( numeraire ) 2
Example three goods x, y, z three consumers u A ( x, y, z ) = xyz , e A = (300 , 0 , 0) u B ( x, y, z ) = xyz 2 , e B = (0 , 200 , 200) u C ( x, y, z ) = x 2 yz , e C = (100 , 0 , 200) To solve for equilibrium: variable prices p x , p y , p z find demands for each good at these prices set demand = supply for each good solve Consumer A : income = 300 p x demands x A = (1 / 3)(300 p x ) p x y A = (1 / 3)(300 p x ) p y z A = (1 / 3)(300 p x ) p z Consumer B :

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_Lecture_14 - Lecture 14 1-minute review exchange...

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