第四章 经济剩余分析
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❖ ---Fritz Machlup”Professor Hicks’ revision of Demand Theory” P122
4
价格变动的补偿CV
❖ Pertaining to Price Increases
❖ The Compensating income variation 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 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 X at the lower price…
❖ ---Fritz Machlup”Professor Hicks’ revision of Demand Theory”P122
5
价格变动的补偿CV
❖ 补偿变化衡量的是一个计划者的净收 入。这个计划者必须在价格变化发生之 后，对消费者进行补偿使消费者的效用 恢复到初始效用水平。
CV ( p; p%, y) e( p%,v( p%, y)) e( p%,v( p, y)) y e( p%,u0 ) ❖ 它可以设想为计划者为使消费者同
第四章 经济剩余分析
1
几个消费者剩余度量尺度
❖ 马歇尔的消费者剩余Consumer Surplus
❖ 价格变动的补偿CV ❖ 等值变动EV
❖ 补偿剩余CS ❖ 等值剩余ES
2
价格变动的补偿 CV
❖ 常被称为补偿变化compensating variation：为使某人保持变化以前的福利 水平，应该从他那里取走的补偿金的数额。
the followed figure) equals the amount of a lumpsum 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 attain if a reduction in the price of X at the lower price…
15
补偿剩余CS
❖ Pertaining to Price Reductions ❖ The compensating consumer’s 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 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 price…
❖ 回想卡尔多补偿 ❖ 对良种农产品的补贴，对农民养猪的补
贴
CV( p; p%, y) e(p%,v(p%, y)) e(p%,v(p, y)) y e(p%,u0)
3
价格变动的补偿CV
❖ Pertaining to Price Reduction
❖ The Compensating income variation (shown as CV in the followed figure) equals the amout of a lumpsum 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 pushed back the same indifference level that he had attained when he purchased a smaller quantity of X at the higher price…
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：
v( p%, y CV ) u0
6
价格变动的补偿CV
y
X 价格降低
CV
u0
u1
X
7
价格变动的补偿CV CV e( p%,u1) e( p%,u0) e( p0,u0) e( p%,u0)
p0 p%
x1h
❖ ---Fritz Machlup”Professor Hicks’ revision of Demand Theory”P123
11
等同变差EV
❖ 关于等同变差说明
➢
等同变差可想象为一笔金钱，消费者在接
受这一笔钱和接受价格变化间是无差异的，也
就是说，就对福利的影响而言，这笔钱和价格
百度文库
变化等价的。
(
p,
p%,u
0
)dp
xh ( p, p%, u 0 ) 希克斯需求函数
p1
xh ( p , p%,u1)
p10
p%1
x( p, p%, y)
马歇尔需求函数
8
x1
等同变差或等值变动（EV）
❖ 等同变差equivalent variation：在 没有变化发生的情况下，为了使某人达 到变化发生后他可能达到的福祉水平而 应给予他的补偿金的数额。
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 same indifference level that he had attained when he purchased a larger quantity of X at the lower price…
❖ ---Fritz Machlup”Professor Hicks’ revision of Demand Theory”P123
10
等同变差EV
❖ Pertaining to Price Increases ❖ The equivalent income variation equals the
❖ ---Fritz Machlup”Professor Hicks’ revision of Demand Theory”P123
17
补偿剩余CS
y X 价格降低
u1
X
u0
18
补偿剩余CS
x1h ( p1, p1,u0 ) 希克斯需求函数
p1
x1h ( p1, p1,u1)
p10
p%1
x1( p1, p1, y)
❖ ---Fritz Machlup”Professor Hicks’ revision of Demand Theory”P123
16
补偿剩余CS
❖ Pertaining to Price Increases ❖ The compensating consumer’s surplus equals the
净收入变化。用间接效用函数可将等价变化表示如下：
v( p, y EV ) u1
12
y
EV
等同变差EV
u0 u1
p1价格下降
X13
等同变差EV
EV ( p, p%, y) e( p, u1) y
e( p, u1 ) e( p%, u 1 )
p0 xh ( p
p%
, p%, u1)dp1
等值剩余ES
❖ Pertaining to Price Reductions ❖ The equibalent consumer’s 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, 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 price…
马歇尔需求函数
19
x1
等值剩余ES
❖ 等值剩余Equivalent Surplus：在没 有发生变化的情况下，如果某人被限制以 旧的价格来购买如果没有补偿金他可能购 买的物品的量，为使他能够达到变化发生 后他可能达到的福祉水平而应该给予他的 补偿金数额。
❖ 与EV的区别？ ❖ 变化前的价格 ❖ 没有补偿的数量（－－－变化前的数量） 20
EV ( p; p%, y) e( p,v( p%, y)) e( p,v( p, y)) e( p,u1) y
特别地，由于e( p,u1)正是使消费者在价格 p 上获得效用水平u1的
收入水平，而u1又正是价格变化后的效用水平，因此，等价的变 化e( p,u1) y就是使消费者在价格 p 上获得效用水平u1所需的
xh ( p , p%,u1)希克斯需求函数
x ( p, p%, y)马歇尔需求函数
14
补偿剩余CS
❖ 补偿剩余Compensating Surplus：当 某人被限制以变化后的新价格购买如果没 有补偿他所购买的物品的量时，为使他保 持变化以前的福利水平，而应该从他那里 取走的补偿金的数额。
❖ 与补偿变化CV的区别？ ❖ 变化后的价格 ❖ 没有补偿的数量－－－变化后的数量
amount 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 caused him to purchase a smaller quantity of X at the higher price…
❖ ---Fritz Machlup”Professor Hicks’ revision of Demand Theory”P124
❖ 与补偿变动的区别？ ❖ 回想希克斯补偿标准 ❖ 向农民征地前政府承诺的补偿
EV ( p; p%, y) e( p,v( p%, y)) e( p,v( p, y)) e( p,u1) y
9
等同变差EV
❖ Pertaining to Price Reductions ❖ The equivalent income variation(shown as EV in
4
价格变动的补偿CV
❖ Pertaining to Price Increases
❖ The Compensating income variation 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 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 X at the lower price…
❖ ---Fritz Machlup”Professor Hicks’ revision of Demand Theory”P122
5
价格变动的补偿CV
❖ 补偿变化衡量的是一个计划者的净收 入。这个计划者必须在价格变化发生之 后，对消费者进行补偿使消费者的效用 恢复到初始效用水平。
CV ( p; p%, y) e( p%,v( p%, y)) e( p%,v( p, y)) y e( p%,u0 ) ❖ 它可以设想为计划者为使消费者同
第四章 经济剩余分析
1
几个消费者剩余度量尺度
❖ 马歇尔的消费者剩余Consumer Surplus
❖ 价格变动的补偿CV ❖ 等值变动EV
❖ 补偿剩余CS ❖ 等值剩余ES
2
价格变动的补偿 CV
❖ 常被称为补偿变化compensating variation：为使某人保持变化以前的福利 水平，应该从他那里取走的补偿金的数额。
the followed figure) equals the amount of a lumpsum 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 attain if a reduction in the price of X at the lower price…
15
补偿剩余CS
❖ Pertaining to Price Reductions ❖ The compensating consumer’s 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 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 price…
❖ 回想卡尔多补偿 ❖ 对良种农产品的补贴，对农民养猪的补
贴
CV( p; p%, y) e(p%,v(p%, y)) e(p%,v(p, y)) y e(p%,u0)
3
价格变动的补偿CV
❖ Pertaining to Price Reduction
❖ The Compensating income variation (shown as CV in the followed figure) equals the amout of a lumpsum 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 pushed back the same indifference level that he had attained when he purchased a smaller quantity of X at the higher price…
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：
v( p%, y CV ) u0
6
价格变动的补偿CV
y
X 价格降低
CV
u0
u1
X
7
价格变动的补偿CV CV e( p%,u1) e( p%,u0) e( p0,u0) e( p%,u0)
p0 p%
x1h
❖ ---Fritz Machlup”Professor Hicks’ revision of Demand Theory”P123
11
等同变差EV
❖ 关于等同变差说明
➢
等同变差可想象为一笔金钱，消费者在接
受这一笔钱和接受价格变化间是无差异的，也
就是说，就对福利的影响而言，这笔钱和价格
百度文库
变化等价的。
(
p,
p%,u
0
)dp
xh ( p, p%, u 0 ) 希克斯需求函数
p1
xh ( p , p%,u1)
p10
p%1
x( p, p%, y)
马歇尔需求函数
8
x1
等同变差或等值变动（EV）
❖ 等同变差equivalent variation：在 没有变化发生的情况下，为了使某人达 到变化发生后他可能达到的福祉水平而 应给予他的补偿金的数额。
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 same indifference level that he had attained when he purchased a larger quantity of X at the lower price…
❖ ---Fritz Machlup”Professor Hicks’ revision of Demand Theory”P123
10
等同变差EV
❖ Pertaining to Price Increases ❖ The equivalent income variation equals the
❖ ---Fritz Machlup”Professor Hicks’ revision of Demand Theory”P123
17
补偿剩余CS
y X 价格降低
u1
X
u0
18
补偿剩余CS
x1h ( p1, p1,u0 ) 希克斯需求函数
p1
x1h ( p1, p1,u1)
p10
p%1
x1( p1, p1, y)
❖ ---Fritz Machlup”Professor Hicks’ revision of Demand Theory”P123
16
补偿剩余CS
❖ Pertaining to Price Increases ❖ The compensating consumer’s surplus equals the
净收入变化。用间接效用函数可将等价变化表示如下：
v( p, y EV ) u1
12
y
EV
等同变差EV
u0 u1
p1价格下降
X13
等同变差EV
EV ( p, p%, y) e( p, u1) y
e( p, u1 ) e( p%, u 1 )
p0 xh ( p
p%
, p%, u1)dp1
等值剩余ES
❖ Pertaining to Price Reductions ❖ The equibalent consumer’s 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, 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 price…
马歇尔需求函数
19
x1
等值剩余ES
❖ 等值剩余Equivalent Surplus：在没 有发生变化的情况下，如果某人被限制以 旧的价格来购买如果没有补偿金他可能购 买的物品的量，为使他能够达到变化发生 后他可能达到的福祉水平而应该给予他的 补偿金数额。
❖ 与EV的区别？ ❖ 变化前的价格 ❖ 没有补偿的数量（－－－变化前的数量） 20
EV ( p; p%, y) e( p,v( p%, y)) e( p,v( p, y)) e( p,u1) y
特别地，由于e( p,u1)正是使消费者在价格 p 上获得效用水平u1的
收入水平，而u1又正是价格变化后的效用水平，因此，等价的变 化e( p,u1) y就是使消费者在价格 p 上获得效用水平u1所需的
xh ( p , p%,u1)希克斯需求函数
x ( p, p%, y)马歇尔需求函数
14
补偿剩余CS
❖ 补偿剩余Compensating Surplus：当 某人被限制以变化后的新价格购买如果没 有补偿他所购买的物品的量时，为使他保 持变化以前的福利水平，而应该从他那里 取走的补偿金的数额。
❖ 与补偿变化CV的区别？ ❖ 变化后的价格 ❖ 没有补偿的数量－－－变化后的数量
amount 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 caused him to purchase a smaller quantity of X at the higher price…
❖ ---Fritz Machlup”Professor Hicks’ revision of Demand Theory”P124
❖ 与补偿变动的区别？ ❖ 回想希克斯补偿标准 ❖ 向农民征地前政府承诺的补偿
EV ( p; p%, y) e( p,v( p%, y)) e( p,v( p, y)) e( p,u1) y
9
等同变差EV
❖ Pertaining to Price Reductions ❖ The equivalent income variation(shown as EV in