Section-11-Competitive-Equilibrium-slides

Section-11-Competitive-Equilibrium-slides - Competitive...

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Unformatted text preview: Competitive Equilibrium Todd Sarver Northwestern University Econ 310-2 Fall 2011 Todd Sarver (Northwestern University) Competitive Equilibrium Econ 310-2 Fall 2011 1 / 27 Setting: An Exchange Economy Suppose there are n consumers and two goods, x and y . (For simplicity, we will often focus on the case of 2 consumers.) Todd Sarver (Northwestern University) Competitive Equilibrium Econ 310-2 Fall 2011 2 / 27 Setting: An Exchange Economy Suppose there are n consumers and two goods, x and y . (For simplicity, we will often focus on the case of 2 consumers.) Use ( x i ,y i ) to denote an allocation for consumer i . Each consumer has a utility function u i ( x i ,y i ) . Todd Sarver (Northwestern University) Competitive Equilibrium Econ 310-2 Fall 2011 2 / 27 Setting: An Exchange Economy Suppose there are n consumers and two goods, x and y . (For simplicity, we will often focus on the case of 2 consumers.) Use ( x i ,y i ) to denote an allocation for consumer i . Each consumer has a utility function u i ( x i ,y i ) . Endowment economy (i.e., no production): Each consumer has an initial endowment of each good and can buy and sell the goods at the going market prices p x and p y . Let ( e x i ,e y i ) denote consumer i s initial endowments of x and y . Todd Sarver (Northwestern University) Competitive Equilibrium Econ 310-2 Fall 2011 2 / 27 Budget Constraints in an Exchange Economy Suppose the prices of the two goods are p x and p y . What is budget constraint for a consumer? Lets use consumer 1 to illustrate: Todd Sarver (Northwestern University) Competitive Equilibrium Econ 310-2 Fall 2011 3 / 27 Budget Constraints in an Exchange Economy Suppose the prices of the two goods are p x and p y . What is budget constraint for a consumer? Lets use consumer 1 to illustrate: In 310-1, we would have specified an income (or wealth) I 1 for consumer 1, and the budget constraint would be: p x x 1 + p y y 1 = I 1 Todd Sarver (Northwestern University) Competitive Equilibrium Econ 310-2 Fall 2011 3 / 27 Budget Constraints in an Exchange Economy Suppose the prices of the two goods are p x and p y . What is budget constraint for a consumer? Lets use consumer 1 to illustrate: In 310-1, we would have specified an income (or wealth) I 1 for consumer 1, and the budget constraint would be: p x x 1 + p y y 1 = I 1 Things are basically the same now, except that income comes from her endowment ( e x 1 ,e y 1 ) : I 1 = p x e x 1 + p y e y 1 In other words, the consumer does not come to the market with money. She only has her endowment of goods, which she can then sell to get money to buy other goods. Todd Sarver (Northwestern University) Competitive Equilibrium Econ 310-2 Fall 2011 3 / 27 Budget Constraints in an Exchange Economy Suppose the prices of the two goods are p x and p y . What is budget constraint for a consumer? Lets use consumer 1 to illustrate: In 310-1, we would have specified an income (or wealth) I 1 for consumer 1, and the budget constraint would be:...
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Section-11-Competitive-Equilibrium-slides - Competitive...

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