Suppose that both of Carl and David have a same Cobb-Douglas utility function as U(x1, x2) = In x1 + ln x2 Carl obtains an endowment of (w₁, w) = (20,40), while David has an endowment of (w, w2) = (40,20). Denote the prices of x₁ and x2 as p₁ and p₂, respectively. (a) Write down their utility maximization problems. (b) Please derive their individual demand functions for both x₁ and x2 (in terms of p₁ and p₂). (c) Please derive the aggregate excess demands for the two goods (in terms of p₁ and p₂). (d) Solve for the equilibrium relative price P1. P2

Suppose that both of Carl and David have a same Cobb-Douglas utility function as U(x1, x2) = In x1 + ln x2 Carl obtains an endowment of (w₁, w) = (20,40), while David has an endowment of (w, w2) = (40,20). Denote the prices of x₁ and x2 as p₁ and p₂, respectively. (a) Write down their utility maximization problems. (b) Please derive their individual demand functions for both x₁ and x2 (in terms of p₁ and p₂). (c) Please derive the aggregate excess demands for the two goods (in terms of p₁ and p₂). (d) Solve for the equilibrium relative price P1. P2

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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