consumer_summary

consumer_summary - x,p y,I = x c p x,p y,V p x,p y,I y p...

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Consumer Theory Summary “Dual” Expenditure Utility Maximization Minimization max U ( x,y ) min p x x + p y y subject to p x x + p y y I subject to U ( x,y ) U Lagrangian Lagrangian U ( x,y ) + λ ( I - p x x - p y y ) p x x + p y y + μ ( U - U ( x,y )) FONCs FONCs ∂U ∂x - λp x = ∂U ∂y - λp y = 0 μ = 1 ←----→ p x - μ ∂U ∂x = p y - μ ∂U ∂y = 0 Common SOSC - diminishing MRS Marshallian Demands Hicksian Demands x = x ( p x ,p y ,I ) x = x c ( p x ,p y ,U ) y = y ( p x ,p y ,I ) y = y c ( p x ,p y ,U ) Indirect Utility Function Expenditure Function U = V ( p x ,p y ,I ) Inverses ←----→ I = E ( p x ,p y ,U ) Roy’s Identities Shepherd’s Lemma x = - ∂V/∂p x ∂V/∂I , y = - ∂V/∂p y ∂V/∂I x c = ∂E ∂p x , y c = ∂E ∂p y | {z } x ( p
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Unformatted text preview: x ,p y ,I ) = x c ( p x ,p y ,V ( p x ,p y ,I )) y ( p x ,p y ,I ) = y c ( p x ,p y ,V ( p x ,p y ,I )) x c ( p x ,p y ,U ) = x ( p x ,p y ,E ( p x ,p y ,U )) y c ( p x ,p y ,U ) = y ( p x ,p y ,E ( p x ,p y ,U )) ⇓ Slutsky Equations ∂x c ∂p x = ∂x ∂p x + x ∂x ∂I , ∂x c ∂p y = ∂x ∂p y + y ∂x ∂I ∂y c ∂p x = ∂y ∂p x + x ∂y ∂I , ∂y c ∂p y = ∂y ∂p y + y ∂y ∂I...
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