Math Problem Statement
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Solution
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Math Problem Analysis
Mathematical Concepts
Optimal Consumption Path
Utility Function
Consumption Growth Over Time
Dynamic Optimization
Formulas
U(c) = log(c)
H'(a,g,u,c) = log(c) + C[(r-p)n + w - c]
Euler equation: U'(c) = c'(t)/r(t) - ρ
Consumption growth: c'(t)/c(t) = r(t) - ρ
Theorems
Euler’s Theorem on Consumption
Optimal Consumption and Growth Conditions
Suitable Grade Level
University Level
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