A consumer’s preferences over two goods x and y are given by the utility function U(x, y) = x^αy^β with α, β > 0. The prices of the goods are px = 2 and py = 4. The consumer has an income of I > 0. • For what values of α and β are these utility functions strictly monotone? • For what values of α and β will the consumer demand (i.e., Walrasian demand) be more x than y? • For what values of α and β are these goods gross substitutes? For what values of α and β are these goods gross complements? Provide a justification for your answer.
A consumer’s preferences over two goods x and y are given by the utility function U(x, y) = x^αy^β with α, β > 0. The prices of the goods are px = 2 and py = 4. The consumer has an income of I > 0. • For what values of α and β are these utility functions strictly monotone? • For what values of α and β will the consumer demand (i.e., Walrasian demand) be more x than y? • For what values of α and β are these goods gross substitutes? For what values of α and β are these goods gross complements? Provide a justification for your answer.
Chapter5: Income And Substitution Effects
Section: Chapter Questions
Problem 5.1P
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A consumer’s preferences over two goods x and y are given by
the utility function U(x, y) = x^αy^β with α, β > 0. The prices of the goods are px = 2 and py = 4.
The consumer has an income of I > 0.
• For what values of α and β are these utility functions strictly monotone?
• For what values of α and β will the consumer
• For what values of α and β are these goods gross substitutes? For what values of α and β are these goods gross complements? Provide a justification for your answer.
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