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1、2007 FallZhang Yan-GDUF12007 FallZhang Yan-GDUF2Consumer Surplus消费者剩余2007 FallZhang Yan-GDUF3几个消费者剩余度量尺度n价格变动的补偿CVn等值变动EVn马歇尔的消费者剩余Consumer Surplusn补偿剩余CSn等值剩余ESn价格变化的Laspeyre成本差nPaasche成本差2007 FallZhang Yan-GDUF4价格变动的补偿CV0( ; , )( , ( , )( , ( , )( , )CV p pye pv pye pv pyy e pu 2007 FallZhang Yan-

2、GDUF5nPertaining to Price ReductionnThe Compensating income variation (shown as CV in the followed figure) equals the amout of a lump-sum tax which the consumer, after a reduction in the price of X has caused him to purchase a larger quantity of X at the lower price, would have to pay in order to be

3、 pushed back the same indifference level that he had attained when he purchased a smaller quantity of X at the higher pricen-Fritz Machlup”Professor Hicks revision of Demand Theory” P1222007 FallZhang Yan-GDUF6nPertaining to Price IncreasesnThe Compensating income variation equals the amout of a lum

4、p-sum subsidy which the consumer, after an increase in the price of X has caused him to purchase a smaller quantity of X at the higher price, would have to pay would have to receive in order to be lifted back to the same indifference level that he had attained when he purchased a larger quantity of

5、X at the lower pricen-Fritz Machlup”Professor Hicks revision of Demand Theory”P1222007 FallZhang Yan-GDUF7n它可以设想为计划者为使消费者同意价格发生变化而必须向消费者支付的金额的负数。补偿变化与可以表述为：0( ,)v p yCVu0( ; , )( , ( , )( , ( , )( ,)CV p p ye p v p ye p v p yy e p u 价格变动的补偿CV2007 FallZhang Yan-GDUF81uC VXy0uX 价 格 降 低价格变动的补偿CVXy0uXy0

6、u2007 FallZhang Yan-GDUF901000001( , )( ,)(,)( ,)( , ,)phpCVe p ue p ue p ue p ux p p u dp1(,)hxpp u价格变动的补偿CV1p 1p1x0(,)hxpp u01p希克斯需求函数希克斯需求函数(,)x p py马歇尔需求函数马歇尔需求函数2007 FallZhang Yan-GDUF101( ; , )( , ( , )( , ( , )( ,)EV p p ye p v p ye p v p ye p uy等值变动EV2007 FallZhang Yan-GDUF11等值变动EVnPertainin

7、g to Price ReductionsnThe equivalent income variation(shown as EV in the followed figure) equals the amount of a lump-sum subsidy which the consumer, after purchasing a certain quantity of X at a given price, would have to receive in order to be lifted up to the same indifference level that he would

8、 attain if a reduction in the price of X at the lower pricen-Fritz Machlup”Professor Hicks revision of Demand Theory”P1232007 FallZhang Yan-GDUF12等值变动EVnPertaining to Price IncreasesnThe equivalent income variation equals the amount of a lump-sum tax which the consumer, after purchasing a certain qu

9、antity of X at a given price, would have to pay in order to be pushed down to the same indifference level that he would attain if an increase in the price of X caused him to purchase a smaller quantity of X at the higher pricen-Fritz Machlup”Professor Hicks revision of Demand Theory”P1232007 FallZha

10、ng Yan-GDUF131( ; , )( , ( , )( , ( , )( ,)EV p p ye p v p ye p v p ye p uy等值变动EV2007 FallZhang Yan-GDUF14EV0uXy1p 价格下降等值变动EV1u2007 FallZhang Yan-GDUF15011111(,)(,)(,)(,)(,)phpE Vppyep uyep uep uxpp udp1(, ,)hxpp u希克斯需求函数( , , )xp p y马歇尔需求函数等值变动EVX0( , ,)hxp p u希克斯需求函数XPpp 2007 FallZhang Yan-GDUF16马

11、歇尔的消费者剩余Consumer Surplus0uXy1uAB2007 FallZhang Yan-GDUF17补偿剩余CS2007 FallZhang Yan-GDUF18补偿剩余CSnPertaining to Price ReductionsnThe compensating consumers surplus (shown as CS in the followed figure) equals the amout of a lump-sum tax which the consumer, after a reduction in the price of X has caused

12、him to purchase a larger quantity of X at the lower price, would have to pay in order to be pushed back to the same indifference level that he had attained when he purchased a smaller quantity of X at the higher pricen-Fritz Machlup”Professor Hicks revision of Demand Theory”P1232007 FallZhang Yan-GD

13、UF19补偿剩余CSnPertaining to Price IncreasesnThe compensating consumers surplus equals the amout of a lump-sum subsidy which the consumer, after an increase in the price of X has caused him to purchase a smaller quantity of X at the higher price, would have to receive in order to be lifted back to the s

14、ame indifference level that he had attained when he purchased a larger quantity of X at the lower pricen-Fritz Machlup”Professor Hicks revision of Demand Theory”P1232007 FallZhang Yan-GDUF20补偿剩余CS1uXy0uX 价 格 降 低2007 FallZhang Yan-GDUF211111( , )hx p p u补偿剩余CS1p 1p1x0111(,)hxp pu01p希克斯需求函数希克斯需求函数111(

15、 , )x p py马歇尔需求函数马歇尔需求函数2007 FallZhang Yan-GDUF222007 FallZhang Yan-GDUF23补偿剩余ESnPertaining to Price ReductionsnThe equibalent consumers surplus (shown as ES in the following figure) equals the amout of a lump-sum subsidy which the consumer, after purchasing a certain quantity of X at a given price,

16、 would have to receive in order to be lifted up to the same indifference level that he would attain if a reduction in the price of X cause him to purchase a larger quantity of X at the lower pricen-Fritz Machlup”Professor Hicks revision of Demand Theory”P1242007 FallZhang Yan-GDUF24补偿剩余ESnPertaining

17、 to Price IncreasesnThe equibalent consumers surplus equals the amout of a lump-sum tax which the consumer, after purchasing a certain quantity of X at a given price, would have to pay in order to be pushed down to the same indifference level that he would attain if an increase in the price of X cau

18、se him to purchase a smaller quantity of X at the higher pricen-Fritz Machlup”Professor Hicks revision of Demand Theory”P1242007 FallZhang Yan-GDUF25补偿剩余ES1uXy0uX 价 格 降 低2007 FallZhang Yan-GDUF26等值补偿ES1p1( , , )hx p pu希 克 斯 需 求 函 数( , , )x ppy 马 歇 尔 需 求 函 数X0( , , )hx p pu希 克 斯 需 求 函 数XPpp 2007 Fall

19、Zhang Yan-GDUF27价格变化的Laspeyre成本差n价格变化的Laspeyre成本差：为使消费者刚好能够购买变化前他所能购买的物品量而从他那里取走的补偿金的数额。n变化后的价格n价格变化前的商品量2007 FallZhang Yan-GDUF28价格变化的Laspeyre成本差nPertaining to Price ReductionsnThe cost difference Lfor Laspeyre equals the amout of a lump-sum tax which the consumer, following a reduction in the pric

20、e of X, would have to pay in order to be able to purchase just the same quantities, and no more of X and of all other goods that he purchased before the price reductionn-Fritz Machlup”Professor Hicks revision of Demand Theory”P1222007 FallZhang Yan-GDUF29价格变化的Laspeyre成本差1111( , )hx p p u1p 1p1x0111(

21、,)hxp pu01p希克斯需求函数希克斯需求函数111( , )x p py马歇尔需求函数马歇尔需求函数2007 FallZhang Yan-GDUF30价格变化的Laspeyre成本差1uXy0uX 价 格 降 低Laspeyre成本差成本差2007 FallZhang Yan-GDUF31Paasche成本差2007 FallZhang Yan-GDUF32Paasche成本差nPertaining to Price IncreasesnThe cost difference Pfor Paasche equals the amount of a lump-sum subsidy whi

22、ch the consumer, following an increase in the price of X, would have to receive in order to be able to purchase just the same quantities, and no less, of X and of all other goods that he purchased before the price increase.n-Fritz Machlup”Professor Hicks revision of Demand Theory”P1222007 FallZhang

23、Yan-GDUF33Paasche成本差1111( , )hx p p u1p 1p1x0111(,)hxp pu01p希克斯需求函数希克斯需求函数111( , )x p py马歇尔需求函数马歇尔需求函数2007 FallZhang Yan-GDUF34Paasche成本差1uXy0uX 价 格 降 低Paasche成本差成本差2007 FallZhang Yan-GDUF35参考文献nFritz Machlup, 1957, “Professor Hicks Recision of Demand Theory”, The American Economic Review, Vol. 47, 119-135nFritz Machlup, 1940, “Professor Hicks Statics”, The Quarterly Journal of Economics, Vol.54, 277-297