Suppose that there are three goods, good X, good Y, and good Z, and suppose that the consumer has the utility function denoted by U(X, Y, Z) where X, Y, Z denote the quantities of goods. The prices of the goods are denoted by px, px, and pz, respectively, and the income of the consumer is denoted by I. a. Write down the consumer's optimization problem (formally, as we wrote in the lectures). b. Apply the Lagrangian method. Find the necessary conditions (NC) for the consumer's optimization problem of allocating budget between consumption of three goods (good X, good Y, good Z). c. Provide at least two interpretations of the NC (explain what these conditions mean in words). d. What if there were n goods listed as {X₁, X2, ..., Xn}? What would be the necessary condition for the optimal quantities of any pair of goods X₁ and X₁?

Suppose that there are three goods, good X, good Y, and good Z, and suppose that the consumer has the utility function denoted by U(X, Y, Z) where X, Y, Z denote the quantities of goods. The prices of the goods are denoted by px, px, and pz, respectively, and the income of the consumer is denoted by I. a. Write down the consumer's optimization problem (formally, as we wrote in the lectures). b. Apply the Lagrangian method. Find the necessary conditions (NC) for the consumer's optimization problem of allocating budget between consumption of three goods (good X, good Y, good Z). c. Provide at least two interpretations of the NC (explain what these conditions mean in words). d. What if there were n goods listed as {X₁, X2, ..., Xn}? What would be the necessary condition for the optimal quantities of any pair of goods X₁ and X₁?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter6: Demand Relationships Among Goods

Section: Chapter Questions

Problem 6.9P

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