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

question 72

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 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).

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Definitions:

Optimum Credit Policy

A business strategy that seeks to balance the benefits of extending credit to customers with the costs, aiming to maximize profitability.

Incremental Profits

Additional earnings that result from a specific business decision or action, compared to what would have happened without that decision.

Extending Credit

The practice of lending money or goods with the expectation of repayment in the future, often with interest.

Current Ratio

The current ratio is a liquidity ratio that measures a company's ability to pay short-term obligations using its current assets.