Consider the mapping Q : P P, where the ith coordinate mapping of Qis max[0,...

 

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Consider the mapping Q : P → P, where the ith coordinate mapping of Qis max[0, pi + piZi (p)] Qi (p) := := N Σ max[0, p; + pjZ;(p)]* Assume that Walras' Law holds as an equality, p · Ž (p) = 0. . A. Show that every competitive equilibrium price vector pº is a fixed point of Q. B. Show that every vertex of the price simplex P is also a fixed point of Q. C. Suppose p*= Q(p*) is a fixed point of Q(.). Does this prove that the economy has a competitive equilibrium? Consider the mapping Q : P → P, where the ith coordinate mapping of Qis max[0, pi + piZi (p)] Qi (p) := := N Σ max[0, p; + pjZ;(p)]* Assume that Walras' Law holds as an equality, p · Ž (p) = 0. . A. Show that every competitive equilibrium price vector pº is a fixed point of Q. B. Show that every vertex of the price simplex P is also a fixed point of Q. C. Suppose p*= Q(p*) is a fixed point of Q(.). Does this prove that the economy has a competitive equilibrium?

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A Since the Walras Law holds as an equality p Zp 0 we know that at a competitive equilibrium the pri... View the full answer