個體經濟學-間接效用函數 20點

Question

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

Answer 1

最佳解答

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)

參考資料： myself