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 has an income denoted by Y which is devoted to goods 1 and 2.The prices of goods 1 and 2 are denoted p₁ and p₂.
a.What is this consumer's MRS as functions of q₁ and q₂?
b.Write out the Lagrangian for the consumer's utility maximization problem.
c.Using the Lagrangian method,derive the consumer's demand equations for both goods as functions of the variables p₁,p₂,and Y.

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 has an income denoted by Y which is devoted to goods 1 and 2.The prices of goods 1 and 2 are denoted p₁ and p₂.
a.What is this consumer's MRS as functions of q₁ and q₂?
b.Write out the Lagrangian for the consumer's utility maximization problem.
c.Using the Lagrangian method,derive the consumer's demand equations for both goods as functions of the variables p₁,p₂,and Y.

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 has an income denoted by Y which is devoted to goods 1 and 2.The prices of goods 1 and 2 are denoted p₁ and p₂.
a.What is this consumer's MRS as functions of q₁ and q₂?
b.Write out the Lagrangian for the consumer's utility maximization problem.
c.Using the Lagrangian method,derive the consumer's demand equations for both goods as functions of the variables p₁,p₂,and Y.

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