Uniqueness and Stability Consider a pure exchange economy with two goods. (a) Show that the gross...

 

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Uniqueness and Stability Consider a pure exchange economy with two goods. (a) Show that the gross substitute property implies z(p) = 0 and z(p') #0 implies p.z(p') > 0, so that a unique Walrasian equilibrium is globally stable. (b) Prove that if (1) holds, the set of equilibrium price vectors {p = R²: z(p) = 0} is a convex set. (1) (c) Suppose that all the consumers in the economy have quasilinear utility functions of the form u² (x1, x2) = v(x1) + x2, where v(.) is strictly concave. Show that the gross substitute property is then satisfied, so that a Walrasian equilibrium is unique and (globally) stable. Uniqueness and Stability Consider a pure exchange economy with two goods. (a) Show that the gross substitute property implies z(p) = 0 and z(p') #0 implies p.z(p') > 0, so that a unique Walrasian equilibrium is globally stable. (b) Prove that if (1) holds, the set of equilibrium price vectors {p = R²: z(p) = 0} is a convex set. (1) (c) Suppose that all the consumers in the economy have quasilinear utility functions of the form u² (x1, x2) = v(x1) + x2, where v(.) is strictly concave. Show that the gross substitute property is then satisfied, so that a Walrasian equilibrium is unique and (globally) stable.

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a Show that the gross substitute property implies zp 0 and zp 0 implies p zp 0 1 so that a unique Wa... View the full answer