Föreläsningsunderlag för Gravelle-Rees. Del 3. Thomas Sonesson
General equilibrium Existence • Counting equations and unknowns (Walras) o n markets → n excess demand equations z j ( p) but at the same time only n -1 unknown relative prices However if n-1 of the equations are satisfied the last one will be satisfied as well (Walras’ law) Walras’ law: ∑ p j z j = 0 . The total value of excess demands is exactly zero • Fixed Point Theorem (a Walrasian equilibrium where agents are passive price takers) o Define a mapping from a price vector p to a new price vector by the following rules If excess demand is positive add to the initial price some multiple of the excess demand (increase price) If excess demand is zero let the new price equal the old price If excess demand is negative add to the initial price some multiple of the excess demand (decrease price), unless doing so would make the new price negative, in which case set it instead at zero Normalize, making ∑ p j = 1 o Fixed Point Theorem: There exists a price vector p that maps into itself, the equilibrium vector p*
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