Mermaid asked in 教育與參考考試 · 1 decade ago

個體經濟學-間接效用函數 20點

Consider the following indirect utility function v(p1,p2,y) = y/(p1 + p2),where p1 is the price of good 1,p2 is the price of good 2 and y is the income level.

(a) What is the demand functions?

(b) What is the direct utility function?

(c) What is the expenditure function?

請附上計算過程,謝謝

1 Answer

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  • 1 decade ago
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    Ans:

    間接效用函數為 V(P1,P2,Y) = Y/(P1+P2)

    令Y/(P1+P2)=U --> expenditure function為Y=(P1+P2)U

    利用Shephard's Lemma 可求出Hickian demand (Xh)

    Xh1=dY/dP1=U

    Xh2=dY/dP2=U

    利用Roy's Identity 可求出Marshllian demand (X)

    X1= -(dV/dP1)/(dV/dY)=Y/(P1+P2)

    X2= -(dV/dP2)/(dV/dY)=Y/(P1+P2)

    Source(s): myself
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