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Consider a pure exchange economy, ({Xi, Zi}}=1> {Y; = -R} }}=1> {0;}}}]). Consumer i is said to envy consumer j at allocation x if consumer
Consider a pure exchange economy, ({Xi, Zi}}=1> {Y; = -R} }}=1> {0;}}}]). Consumer i is said to envy consumer j at allocation x if consumer i strictly prefers consumer j's consumption vector, i.e., X; >; X;. An allocation is said to be envy-free if no consumer envies any other consumer. Given a Walrasian equilibrium price vector p*, we say that wi = p* 0; is the equilibrium wealth of consumer i and w* (w1, ... , w*) the equilibrium wealth profile. Characterize an equilibrium wealth profile under which the associated equilibrium allocation is envy-free. (You do not need to show that the Walrasian equilibrium exists under such a wealth profile. You can assume that it does but need to show that, given the definition of Walrasian equilibrium, the allocation is envy- free.) Consider a pure exchange economy, ({Xi, Zi}}=1> {Y; = -R} }}=1> {0;}}}]). Consumer i is said to envy consumer j at allocation x if consumer i strictly prefers consumer j's consumption vector, i.e., X; >; X;. An allocation is said to be envy-free if no consumer envies any other consumer. Given a Walrasian equilibrium price vector p*, we say that wi = p* 0; is the equilibrium wealth of consumer i and w* (w1, ... , w*) the equilibrium wealth profile. Characterize an equilibrium wealth profile under which the associated equilibrium allocation is envy-free. (You do not need to show that the Walrasian equilibrium exists under such a wealth profile. You can assume that it does but need to show that, given the definition of Walrasian equilibrium, the allocation is envy- free.)
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