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

question 55

Essay

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.

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Definitions:

Producers

Entities or individuals that create or supply goods and services.

Minimum Imposed Price

A price floor set by the government, preventing prices from falling below a certain level.

Deadweight Loss

An economic inefficiency that occurs when market equilibrium is not achieved or is distorted, typically due to a price floor, ceiling, or tax.

Price Control

A government-imposed limit on the price charged for a product.