Math Problem Statement
Find the optimal point given utility function u(x 1 , x 2 ) = x 2 1 x 3 2 and budget constraint M = 4x 1 + 3x 2 find mrs
Solution
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Math Problem Analysis
Mathematical Concepts
Utility Function
Budget Constraint
Marginal Utility
Marginal Rate of Substitution (MRS)
Optimization
Formulas
u(x1, x2) = x1^2 x2^3
M = 4x1 + 3x2
MU1 = 2x1 x2^3
MU2 = 3x1^2 x2^2
MRS = (MU1 / MU2) = (2/3) * (x2 / x1)
Theorems
Optimization of Utility Subject to Budget Constraint
Suitable Grade Level
Undergraduate Economics or Mathematics
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