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Unformatted text preview: ice set is closed, convex,
• 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
– 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.
• Profit shares sum to one: ∑ α i = 1 ∑ β 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.
- Perfect Competition