Lecture_Notes_Demand

Lecture_Notes_Demand - Demand Theory. Derivation of Demand...

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Demand Theory. Derivation of Demand Functions. Optimality conditions : MRS 1 n ( * X )= MU 1 ( * X ) MU n ( * X ) = p 1 p n MRS 2 n ( * X )= MU 2 ( * X ) MU n ( * X ) = p 2 p n . . . MRS n - 1 ,n ( * X )= MU n - 1 ( * X ) MU n ( * X ) = p n - 1 p n n ± i =1 P i * X i = I Solution : * X i = D i ( P 1 , . . . , P n ,I ) = D i ( P, I ) ,i =1 , . . . , n. D i is the demand function for commodity i .
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Example : U ( X 1 ,X 2 )=( X 1 - 2) X 2 . MU 1 ( X 1 ,X 2 )= X 2 MU 2 ( X 1 ,X 2 )= X 1 - 2 . Optimality conditions: * X 2 * X 1 - 2 = P 1 P 2 P 1 * X 1 + P 2 * X 2 = I Solution: * X 1 = I +2 P 1 2 P 1 = D 1 ( P 1 ,P 2 ,I ) * X 2 = I - 2 P 1 2 P 2 = D 2 ( P 1 ,P 2 ,I ) . Properties of Demand Functions. Homogeneity of degree zero (absence of money illusion): For any positive scalar λ , D i ( λP 1 , . . . , λP n , λI ) = D i ( P 1 , . . . , P n ,I ) i =1 , . . . , n. E.g. , doubling all prices and income leaves demands unchanged.
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Lecture_Notes_Demand - Demand Theory. Derivation of Demand...

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