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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AutoSave File Document! Word Chris Navo Home Insert Draw Design Layout References Mailings Review View MathType Help Acrobat Graphs Format Cobb and Douglas used economic data published by the government to obtain Table 2. Year P Year 1899 100 100 DOL 1911 148 216 1900 101 105 107 1912 155 1901 112 110 114 1912 1902 122 117 122 1014 169 152 244 1903 124 122 131 1915 109 156 266 1904 122 121 138 1916 225 183 1905 143 125 149 1917 227 1905 152 124 163 1915 223 201 1907 151 140 170 1919 218 19.08 126 123 485 1920 231 104 407 19.09 155 143 198 1921 179 146 417 1910 159 208 1922 240 161 431 Table 2 Swords et Predictions. The Cobb Douglass formula is P(L, K) = bLa K¹-a Determine monetary value of all the goods produced in 1 year or simply the production level in 1920 for a=.20 and b=1.01. Round to one decimal place.
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Q TFC TVC TC MC AFC AVC ATC $20 $0 1 $20 $15 2 $20 $25 3 $30 4 $6 $8.80