ECO204-2022/23-Week 6
Welfare Summary
In this lecture we develop ways to measure the impact of a change in the price of a good
on consumer welfare. This is important to know because many public policies and
corporate decisions change prices.
Consumer Surplus: The “surplus” in consumer surplus is motivated by viewing points
along a demand curve as reservation prices. For an individual’s demand curve the
reservation price is the highest price s/he would pay for a particular unit of a good. For a
market demand curve the reservation price is the highest price someone would pay for a
particular unit of a good.
Suppose we are at a point on a demand curve where 7 units are sold at a price of $10. We
call units 1-6 of the 7 units sold the inframarginal units (the 7th unit is called the marginal
unit). Since demand curves usually have a negative slope, each of these inframarginal
units will be sold at less than their reservation price generating a surplus. Summing up
the surplus across the inframarginal units we get the consumer surplus (CS) at the
outcome 7 units and $10.
With a linear demand curve this sum can be represented as the area of the triangle formed
by the demand curve, the price line and the horizontal axis. This area is ½*b*h.
A more general way of calculating the area that can handle non linear demand curves is
to use integration. Let 𝑝!" (𝑥# , 𝑥$ , … ) = 𝑝!" (𝑥! ) be the inverse demand curve for the good.
Then the consumer surplus can be calculated as
%
𝐶𝑆 = * +𝑝!" (𝑥! ) − 10/𝑑𝑥!
&
Or more generally
(!"
𝐶𝑆 = * +𝑝!" (𝑥! ) − 𝑝' /𝑑𝑥!
&
Where the e superscript denotes the equilibrium or starting price or quantity.
We can use changes in CS between one price and another to measure the welfare
consequences of the change in price. (Note in general this is an approximation, because
the amount a consumer is willing to purchase of a good will depend on how much money
they have to purchase other goods. However, when there are no income effects (e.g.,
quasilinear utility) this definition is exact.)
Welfare Summary
In this lecture we develop ways to measure the impact of a change in the price of a good
on consumer welfare. This is important to know because many public policies and
corporate decisions change prices.
Consumer Surplus: The “surplus” in consumer surplus is motivated by viewing points
along a demand curve as reservation prices. For an individual’s demand curve the
reservation price is the highest price s/he would pay for a particular unit of a good. For a
market demand curve the reservation price is the highest price someone would pay for a
particular unit of a good.
Suppose we are at a point on a demand curve where 7 units are sold at a price of $10. We
call units 1-6 of the 7 units sold the inframarginal units (the 7th unit is called the marginal
unit). Since demand curves usually have a negative slope, each of these inframarginal
units will be sold at less than their reservation price generating a surplus. Summing up
the surplus across the inframarginal units we get the consumer surplus (CS) at the
outcome 7 units and $10.
With a linear demand curve this sum can be represented as the area of the triangle formed
by the demand curve, the price line and the horizontal axis. This area is ½*b*h.
A more general way of calculating the area that can handle non linear demand curves is
to use integration. Let 𝑝!" (𝑥# , 𝑥$ , … ) = 𝑝!" (𝑥! ) be the inverse demand curve for the good.
Then the consumer surplus can be calculated as
%
𝐶𝑆 = * +𝑝!" (𝑥! ) − 10/𝑑𝑥!
&
Or more generally
(!"
𝐶𝑆 = * +𝑝!" (𝑥! ) − 𝑝' /𝑑𝑥!
&
Where the e superscript denotes the equilibrium or starting price or quantity.
We can use changes in CS between one price and another to measure the welfare
consequences of the change in price. (Note in general this is an approximation, because
the amount a consumer is willing to purchase of a good will depend on how much money
they have to purchase other goods. However, when there are no income effects (e.g.,
quasilinear utility) this definition is exact.)
