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)=  ,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)=