Consider a consumer with the Cobb-Douglas utility function U(q₁,q₂)=
,where q₁ and q₂ are the quantities of goods 1 and 2 consumed,respectively.This consumer derives a level of utility denoted by U₀.The prices of goods 1 and 2 are denoted p₁ and p₂.
a.Write out the Lagrangian for the consumer's expenditure minimization problem.
b.Using the Lagrangian method,derive the consumer's (expenditure-minimizing)quantity of good 1 as functions of the variables p₁,p₂,and U₀.
c.Derive the consumer's expenditure function,E(p₁,p₂,U₀).

Question

Consider a consumer with the Cobb-Douglas utility function U(q₁,q₂)=

Consider a consumer with the Cobb-Douglas utility function U(q<sub>1</sub>,q<sub>2</sub>)= ,where q<sub>1</sub> and q<sub>2</sub> are the quantities of goods 1 and 2 consumed,respectively.This consumer derives a level of utility denoted by U<sub>0</sub>.The prices of goods 1 and 2 are denoted p<sub>1</sub> and p<sub>2</sub>. a.Write out the Lagrangian for the consumer's expenditure minimization problem. b.Using the Lagrangian method,derive the consumer's (expenditure-minimizing)quantity of good 1 as functions of the variables p<sub>1</sub>,p<sub>2</sub>,and U<sub>0</sub>. c.Derive the consumer's expenditure function,E(p<sub>1</sub>,p<sub>2</sub>,U<sub>0</sub>).

,where q₁ and q₂ are the quantities of goods 1 and 2 consumed,respectively.This consumer derives a level of utility denoted by U₀.The prices of goods 1 and 2 are denoted p₁ and p₂.
a.Write out the Lagrangian for the consumer's expenditure minimization problem.
b.Using the Lagrangian method,derive the consumer's (expenditure-minimizing)quantity of good 1 as functions of the variables p₁,p₂,and U₀.
c.Derive the consumer's expenditure function,E(p₁,p₂,U₀).

Quizplus · Accepted Answer

The Answer of Consider a consumer with the Cobb-Douglas utility function U(q₁,q₂)= ,where q₁ and q₂ are the quantities of goods 1 and 2 consumed,respectively.This consumer derives a level of utility denoted by U₀.The prices of goods 1 and 2 are denoted p₁ and p₂. a.Write out the Lagrangian for the consumer's expenditure minimization problem. b.Using the Lagrangian method,derive the consumer's (expenditure-minimizing)quantity of good 1 as functions of the variables p₁,p₂,and U₀. c.Derive the consumer's expenditure function,E(p₁,p₂,U₀).

Consider a Consumer with the Cobb-Douglas Utility Function U(q1,q2)=

Consider a Consumer with the Cobb-Douglas Utility Function U(q₁,q₂)=