Math Problem Statement
Solution
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Math Problem Analysis
Mathematical Concepts
Macroeconomics
Utility Functions
Optimization
Leisure-Consumption Tradeoff
Formulas
CRRA Utility Function: u(x) = (x^(1 - σ) - 1) / (1 - σ)
Utility over consumption and leisure: u(c) = (c^(1 - σ) - 1) / (1 - σ) + (l^(1 - σ) - 1) / (1 - σ)
Budget constraint: PC = Wn
Theorems
L'Hopital's Rule
First-Order Condition (FOC) for Utility Maximization
Suitable Grade Level
College-level Macroeconomics or Graduate Economics
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