Demand could be less than supply for a good with zero

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Unformatted text preview: ice set is closed, convex, and bounded. • Use the excess demand functions to define a mapping on the normalized price set. F i (P ) = Pi + EDi (P ) ∀i • To be rigorous, we need to worry about what happens to demand when some price is zero. – Demand could be less than supply for a good with zero price. – We will ignore this case here. • By Brouwer’s FP Theorem, a fixed point must exist. Lecture 17 Lecture 17 16 Lecture 17 Econ 11--Spring 2001 17 () () F i P* = Pi* + EDi P * = P* ∀i • At the fixed point P*, all n of the excess demand functions equal zero. () () EDi P* = Di P* − S i = 0 ∀i • All markets clear, so a competitive equilibrium must exist. Econ 11--Spring 2001 18 3 Prof. Jay Bhattacharya Econ 11--Spring 2001 Two-Good Two-Input Economy • Now, an economy that includes production. • Two types of firms, each producing one of two goods X and Y, which are sold to consumers. • The firms buy inputs K and L from consumers to produce the outputs using production technologies X=F(K, L) and Y=G(K,L). • Consumers own the firms--they collect any profits made by the firms. Consumer and Producer Goals • Consumers (i = 1…n) maximize utility subject to their budget constraint. – Income from labor and capital: r Li + w Ki – Income from profits: αi πX + β i πY • Producers maximize profits πX and πY. n n • Profit shares sum to one: ∑ α i = 1 ∑ β i = 1 i =1 i =1 • Labor and capital constraint...
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This note was uploaded on 02/11/2012 for the course ECON 51 at Stanford.

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