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Unformatted text preview: f this were a linear system, this would mean there are
infinitely many solutions. • This happens because demand is homogenous of
– Suppose we have found the equilibrium.
– Doubling all prices would also double income
– We have seen that doubling prices and income at the
same time does not change demand. Lecture 17 i =1 Econ 11--Spring 2001 Only Relative Prices Are
Identified • Now there are n + 1 equations in P, and only n
unknowns. Econ 11--Spring 2001 n Total value of demand = ∑ Pi Di (P ) = ∑ Pi Si = Total value of supply Zero Degree Homogeneity of
Demand Lecture 17 i =1 – Summing all the budget constraints yields:
i =1 Lecture 17 8 – We’re back to where we were--no guarantee of
a solution, since the system is non-linear.
11 Lecture 17 Econ 11--Spring 2001 12 2 Prof. Jay Bhattacharya Econ 11--Spring 2001 Mathematical Digression-Brouwer’s Fixed Point Theorem • Intuition: Consider a continuous function f(x)
with domain and range [0,1]. • Any continuous mapping F(X) of a closed,
bounded, convex set into itself has at least one
fixed point (X*) such that F(X*)=X*
– Mapping: A rule a...
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This note was uploaded on 02/11/2012 for the course ECON 51 at Stanford.
- Perfect Competition