### Consumer`s and Producer`s Surpluses

```Consumer’s and Producer’s
Surpluses
Consumer Welfare
• How much are consumers helped or harmed by shocks that
affect the equilibrium price and quantity?
• Shocks may come from new inventions that reduce firm
costs, natural disasters, or government-imposed taxes,
subsidies, or quotas.
• You might think utility is a natural measure of consumer
welfare. Utility is problematic because:
• we rarely know a consumer’s utility function
• utility doesn’t allow for easy comparisons across
consumers
• A better measure of consumer welfare is in terms of dollars.
Consumer’s Surplus
• Consumer’s surplus
(CS) is the monetary
difference between
the maximum
amount that a
consumer is willing
to pay for the
quantity purchased
and what the good
actually costs.
• Step function
Marginal Value and Demand
• Marginal Value: The maximum amount a consumer would
be willing to pay to acquire an additional unit of a good
– Marginal value curve and demand curve convey similar
information
• Application of equi-marginal principle
– Buy the good as long as marginal value exceeds the price
– The consumer is in equilibrium where marginal value
equals the price
• Total Value: The maximum amount a consumer would be
willing to pay to acquire a given quantity of a good.
A Numerical Example
Quantity
Price
Willing to
Pay
Actual
Payment
Consumer
Surplus
1
15
15
15
0
2
13
28
26
2
3
10
38
30
8
4
7
45
28
17
5
5
50
25
25
6
2
52
12
40
7
1
53
7
46
Marginal and Total Value
The Consumer’s Surplus
Consumer’s Surplus
• Consumer’s surplus (CS)
is the area under the
inverse demand curve
and above the market
price up to the quantity
purchased by the
consumer.
• Smooth inverse
demand function
Effect of a Price Change on Consumer’s Surplus
• If the price of a good rises
(e.g. £0.50 to £1),
purchasers of that good
lose consumer’s surplus
(falls by A + B)
• This is the amount of
income we would
have to give the
consumer to offset
the harm of an
increase in price.
Consumer’s Surplus: A Mathematical Application
• Suppose that the demand function of a consumer is given by QD = 40 – 2P. If
the market price P = 10, what is the consumer’s surplus?
• Given the market price P = 10, a consumer’s quantity demanded
QD = 40 – 2P = 40 – 2*10 = 20
• The consumer’s surplus is the area of the triangle between the price line and
the inverse demand curve
• The inverse demand function is P = 20 – (1/2)QD; the height of the triangle is
the intercept of the inverse demand curve minus P, that is 20 – 10 = 10.
CS = ½ (20*10) = 100
• If the market price falls to P = 5, how the consumer’s surplus would change?
• Given the market price P = 5, a consumer’s quantity demanded
QD = 40 – 2P = 40 – 2*5 = 30
• So the consumer’s surplus (the area of the triangle between the price line
and the inverse demand curve) is
CS = ½ (30*15) = 225 (because the height of the triangle is 20 – 5 = 15)
• The change in consumer’s surplus, ∆CS = 225 – 100 = 125
Market Consumer Surplus
• Market demand is the
(horizontal) sum of individual
demand curves; market CS is
the sum of each individual
consumer’s surplus.
• CS losses following a price
increase are larger:
• the greater the initial
revenue (p∙Q) spent on
the good
• the less elastic the
demand curve at
equilibrium
Effect of a 10% Price Increase on Consumer Surplus
• Revenue and Consumer Surplus in Billions of 2008 Dollars
Deriving Demand Curves Graphically
• Allowing the price of the
good on the x-axis to fall,
the budget constraint
rotates out and shows how
the optimal quantity of the
x-axis good purchased
increases.
• This traces out points
along the demand curve.
Expenditure Function and Consumer Welfare
• One measure of the harm to a consumer of a price increase is an increase
in the consumer’s income needed to maintain the consumer’s utility.
• Cannot use an uncompensated demand curve because utility varies along
the curve
•
Can use compensated demand and the expenditure function because both
hold utility constant
• Recall that the minimal expenditure necessary to achieve a specific utility
level and given a set of prices is:
• Welfare change associated with price increase to p1*:
Expenditure Function and Consumer Welfare
• Which level of utility should be used in this calculation?
• Two options:
• Compensating variation is the amount of money we would
have to give a consumer after a price increase to keep the
consumer on their original indifference curve.
• Equivalent variation is the amount of money we would have
to take away from a consumer to harm the consumer as
much as the price increase did.
Compensating Variation and Equivalent Variation
• Indifference curves
can be used to
determine
compensating
variation (CV) and
equivalent variation
(EV).
Three Measures: CS, CV, and EV
• Relationship between these
measures for normal goods:
• |CV| > |∆CS| > |EV|
• For small changes in price, all
three measures are very
similar for most goods.
Effects of Government Policies
on Consumer Welfare
• Government programs can alter consumers’ budget
constraints and thereby affect consumer welfare.
• Examples
• Quota: reduces the number of units that a consumer buys
• Subsidy: causes a rotation or parallel shift of the budget
constraint
• Welfare programs: may produce kinks in budget
constraint
Effects of Government Policies: Quotas
• Quotas limit how much of a
good consumers can
purchase.
• Quota of 12 units
generates kink in budget
triangle region from
individual’s choice set.
• Because of this quota,
the consumer’s
equilibrium will be at the
kink of the budget line,
that is tangent to a lower
indifference curve
indicating lower level of
utility.
Effects of Government Policies: Welfare Programs
• Welfare programs provide
either in-kind transfers or a
comparable amount of cash to
low-income individuals.
• Example: food stamps
• \$100 in food stamps (inkind) generates kinked
budget line.
• \$100 cash transfer
increases opportunity set
further.
Effects of Government Policies: Welfare Programs
• Because food stamps can only be used on food, consumers
are potentially worse off if they would find it optimal to
consume less food and more other goods than allowed by the
program.
• Despite this, food stamps are used rather than comparable
cash transfers in order to:
• reduce expenditures on drugs and alcohol
• encourage appropriate expenditure on food from a
nutrition standpoint
• maintain program support from taxpayers, who feel more
comfortable providing in-kind rather than cash benefits
Effects of Government Policies: Subsidies
• Subsidies either lower prices or
provide lump-sum payments to
low-income individuals.
• Example: child care subsidy
• Reducing price of child care
rotates budget line out
• Unrestricted lump-sum
payment (equal to
taxpayers’ cost of the
subsidy) shifts budget line
out in a parallel fashion and
increases opportunity set
Challenge Question: Child-Care Subsidies
• Background:
• Government child-care subsidies are common throughout the
world.
• Rather than subsidizing the price of child care, the government
could provide an unrestricted lump-sum payment that could be
spent on child care or on all other goods, such as food and
housing.
• Questions:
• For a given government expenditure, does a price subsidy or a
lump-sum subsidy provide greater benefit to recipients?
• Which option increases the demand for child-care services
more?
• Which one inflicts less cost on other consumers of child care?
Challenge Solution
• Child-care subsidy or lumpsum subsidy?
• Original budget constraint is
LO
• If child-care subsidy, budget
constraint is LPS . Family
chooses e2 and utility is I2.
• If lump-sum subsidy so that
e2 is affordable, budget
constraint is LLS . Family
chooses e3 and utility is I3.
• Taxpayer costs for the two
programs are the same, but
family is better off with the
lump-sum subsidy.
The Producer’s Surplus
The Producer’s Surplus is defined as the dollar
amount by which a firm benefits by producing
its profit maximizing level of output.
In other words, a Producer’s Surplus is the
amount by which the producer’s revenue
exceeds her variable production costs
The Producer’s Surplus
Producer Surplus
• Producer surplus
(PS) is the difference
between the
amount for which a
good sells (market
price) and the
minimum amount
necessary for sellers
to be willing to
produce it (marginal
cost).
• Step function
Producer Surplus
• Producer surplus
(PS) is the area
above the inverse
supply curve and
below the market
price up to the
quantity purchased
by the consumer.
• Smooth inverse
supply function
Producer’s Surplus: A Mathematical Application
• Suppose that the supply function is given by QS = 2P. If the market
price P = 10, what is the producer’s surplus?
• Given the market price P = 10, a producer’s quantity supplied
QS = 2P = 2*10 = 20
• So the producer’s surplus (the area of the triangle between the
price line and the inverse supply curve) is
•
PS = ½ (20*10) = 100
• If the market price falls to P = 5, how the producer’s surplus would
change?
• Given the market price P = 5, a producer’s quantity supplied
QS = 2P = 2*5 = 10
• So the producer’s surplus (the area of the triangle between the
price line and the inverse supply curve) is
•
PS = ½ (5*10) = 25
• The change in producer’s surplus, ∆PS = 25 – 100 = – 75
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