Lecture 4
What is an externality?
James Sallee
EEP 101/ECON 125
January 27, 2021
James Sallee (EEP 101/ECON 125)
Externalities
January 27, 2021
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Recap of Lecture 3
1
When should governments intervene in markets?
- Three reasons: efficiency (market failure), equity (market
distribution is unfair), or stability (market is volatile)
2
What is the social welfare function (SWF)?
- The SWF is a hypothetical function that aggregates utility to
describe society’s preferences over allocations. The social
planner is a hypothetical actor who is supposed to maximize
the SWF.
- Today we will start our discussion of externalities, which are
one potential cause of market failure and thus rationalize policy
intervention for the sake of efficiency
James Sallee (EEP 101/ECON 125)
Externalities
January 27, 2021
2 / 25
Lecture 4 Outline
1
What is an externality?
- One agent’s production/consumption directly (not through
prices) influences the utility/production of another agent
2
Why do externalities cause market failure (inefficiency)?
- Because market transactions do not reflect full costs and
benefits to society
James Sallee (EEP 101/ECON 125)
Externalities
January 27, 2021
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What are some examples of externalities?
•
•
•
•
•
Air pollution from burning coal
Groundwater pollution from fertilizer use
Loud music in a dorm room
Aesthetic benefits from neighbor’s beautiful landscaping
Knowledge spillovers
- Many examples seem obvious and intuitive, but there are tricky
cases, and we need a precise definition to help us
James Sallee (EEP 101/ECON 125)
Externalities
January 27, 2021
4 / 25
What is our definition of an externality?
Definition: externalities
A good causes an externality if the consumption (or production) of
that good directly (not through prices or markets) affects the
well-being of other people (or the costs of other firms)
• An externality shifts utility function or production function
- E.g., the same inputs produce less output because of a negative
externality
• Approximate rule for identifying an externality: if the effects on
welfare or profit of the third party do not operate through a
market/price, then it is probably an externality. Otherwise not.
James Sallee (EEP 101/ECON 125)
Externalities
January 27, 2021
5 / 25
Useful taxonomy of externalities
Production
Positive
Bees and orchard
Consumption Home improvement
(spillovers)
Negative
Factory pollutes
nearby river
Cigarettes
(second-hand smoke)
• Externalities can be positive (good) or negative
• Externalities can be associated with the production or
consumption of a good
(All of these have the same implication that market outcomes
are not efficient)
James Sallee (EEP 101/ECON 125)
Externalities
January 27, 2021
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Externality shifting production function
Workers (x1)
Chemicals (x2)
Machines (x3)
Laundry
Production
Function
f(.)
Output,
Clean clothes
(y)
Building (x4)
Smoke from Factory (z)
• A production function specifies how a vector of inputs
determines the quantity of output: y = f (x1 , x2 , ...xk ; z)
• An externality exists when the actions of a third party shift the
output, for a constant set of inputs. E.g.,
f (10, 7, ..., 100; 10) < f (10, 7, ..., 100; 0)
James Sallee (EEP 101/ECON 125)
Externalities
January 27, 2021
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Externality shifting utility function
• A utility function specifies how a vector of goods determines
someone’s happiness
U i = U(x1i , x2i , ..., xki )
• An externality exists when the consumption of person j changes
the utility of person i, even when person i holds constant the
amount they are consuming
U i = U(x1i , x2i , ..., xki ; x1j , x2j , ..., xkj )
James Sallee (EEP 101/ECON 125)
Externalities
January 27, 2021
8 / 25
Are these things externalities?
a.
You have always loved Chia seeds. Suddenly, everyone starts
loving Chia seeds, and the price goes up so you have to pay
more now. (Or, same, but with N95 masks.)
b.
You manage a Peet’s coffee. Starbucks opens a branch directly
across the street, which lowers your profits.
c.
You run a factory in a small town. Another factory opens nearby
and tries to hire some of your workers. Wages rise, which
increases your cost.
James Sallee (EEP 101/ECON 125)
Externalities
January 27, 2021
9 / 25
Are these things externalities?
a.
Chia seed:
b.
Starbucks:
c.
Local labor market:
- Our definition of an externality is designed so that any
externality will create a market failure (market not Pareto
efficient). There is no market failure in these examples.
James Sallee (EEP 101/ECON 125)
Externalities
January 27, 2021
10 / 25
Lecture 4 Outline
1
What is an externality?
- One agent’s production/consumption directly (not through
prices) influences the utility/production of another agent
2
Why do externalities cause market failure (inefficiency)?
- Because market transactions do not reflect full costs and
benefits to society
James Sallee (EEP 101/ECON 125)
Externalities
January 27, 2021
11 / 25
Externalities cause market failure
Markets for an externality-generating good that is uncorrected by
policy will generally not be efficient.
• Specifically, we mean that markets are not Pareto efficient. A
reallocation exists that could make everyone better off.
• But, we might not be able to achieve a Pareto improvement via
policy. Often we will only produce a Kaldor-Hicks improvement.
• We will illustrate how externalities impact efficiency in three
ways:
- Voluntary exchange intuition
- Mathematical optimization
- Graphical representation
James Sallee (EEP 101/ECON 125)
Externalities
January 27, 2021
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1. Voluntary exchange intuition
• How many cigarettes will this smoker buy in a free market?
• Value creation through exchange:
- She buys until marginal benefit (MB) equals the price (=
cigarette maker’s marginal cost (MC) in competitive
equilibrium)
- This maximizes value creation if there is no externality
James Sallee (EEP 101/ECON 125)
Externalities
January 27, 2021
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1. Voluntary exchange intuition
• Second-hand smoke externality ⇒ MB=MC does not maximize
value creation for society because smoker and cigarette maker
are ignoring some costs
• A Pareto improvement could occur if people harmed paid smoker
to reduce smoke
• Why doesn’t this happen? Market for clean air is missing
James Sallee (EEP 101/ECON 125)
Externalities
January 27, 2021
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2. Mathematical optimization (spherical cow)
• Consider the market for a good Q that creates a negative
production externality (e.g., cigarettes)
• For illustration, suppose total externality = φQ, with φ > 0
• Assume constant returns to scale, perfectly competitive supply
⇒ P = MC ≡ marginal cost
• Representative consumer has fixed income Y
• Assume there is a quasi-linear numeraire good, X, so utility is:
Ũ(Q, X ) = U(Q) + X
(quasi-linear numeraire means X has price of 1 and consumer
spends remaining income on X , after choosing Q)
• Consumer maximizes utility, subject to budget constraint by
solving:
max Ũ(Q, X ) = U(Q) + (Y − PQ)
Q
• The consumer is ignoring the externality
James Sallee (EEP 101/ECON 125)
Externalities
January 27, 2021
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2. Mathematical optimization
• Social planner wants to maximize total social welfare, including
the externality (by subtracting externality from utility)
- (Under our assumptions, there is no producer surplus and no
revenue, which we introduce later)
• So, the planner solves
max SWF = U(Q) + (Y − PQ) − φQ
Q
FOC: UQ0 = P + φ
• This differs from consumer’s behavior:
max Ũ(Q, X ) = U(Q) + (Y − PQ)
q
FOC: UQ0 = P
• The planner and representative consumer act differently ⇒
inefficiency
James Sallee (EEP 101/ECON 125)
Externalities
January 27, 2021
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3. Graphical version: market with no externality
Market for Apples
Price
Consumer
Surplus
Pm=P*
S=MC
Producer
Surplus
D=MB
Qm=Q*
Quantity
• Market equilibrium for a good with no externality will maximize
consumer plus producer surplus
• Market price (Pm ) and ideal price (P ∗ ) are the same
James Sallee (EEP 101/ECON 125)
Externalities
January 27, 2021
17 / 25
3. Graphical version: market with externality
Market for Cigarettes
Price
marginal externality=Hq
MSC
P*
S=MC
Pm
D=MB
Q*
•
•
•
•
•
Qm
Quantity
Negative production externality (second-hand smoke)
Market supply is MC; ignores pollution
Marginal social cost (MSC ) is MC + (marginal) externality
Ideal allocation is where MSC = MB
Market price (Pm ) and ideal price (P ∗ ) are NOT the same
James Sallee (EEP 101/ECON 125)
Externalities
January 27, 2021
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3. Graphical version: the SWF in a graph
• We introduced the Social Welfare Function last lecture thinking
only about consumers
• But we will also have producers, and sometimes government
revenue, and we have decide how to incorporate externalities
• Our typical solution, especially for graphs, is to assume
Consumer Surplus is independent of the externality
• We then will put equal weight on Producer Surplus (PS) and
Consumer Surplus (CS), and also equal weight on Government
Revenue (which can be given to someone)
• In sum, we will use a graphical interpretation that the Social
Welfare Function is:
SWF = CS + PS - Externality + Government Revenue
James Sallee (EEP 101/ECON 125)
Externalities
January 27, 2021
19 / 25
3. Graphical version: market with externality
Market for Cigarettes
Price
DWL
MSC
P*
S=MC
Pm
D=MB
Q*
Qm
Quantity
• Oversupply of good leads to deadweight loss (DWL)
• For each unit between Q ∗ and Qm , true marginal cost exceeds
benefit; each unit sold here destroys value; an allocation with
lower Q could make everyone better off
• Total welfare (=CS+PS-Externality) is lower at Qm than at Q ∗
• The difference in total welfare is DWL
James Sallee (EEP 101/ECON 125)
Externalities
January 27, 2021
20 / 25
Summary
• The (1) voluntary exchange intuition, (2) mathematical
optimization, and (3) graphical version are three different
methods of conveying the same point, which is that the market
outcome of a good with an externality is not efficient
• In these examples, the market will choose an amount of the good
that creates deadweight loss and is therefore not Pareto efficient
• (Note however that it may prove tricky to actually achieve a
Pareto improvement in practice via policy. More on this later in
the course.)
• Supplemental video after class: the slides next discuss a
numerical example. You will do related numerical examples in
problem set 1
James Sallee (EEP 101/ECON 125)
Externalities
January 27, 2021
21 / 25
Numerical example: Negative consumption
externality
• Total benefit: TB
= 12Q − Q 2
• Total cost: TC = 12 Q 2
• Total externality: TEC = 3Q
• D=MB =12 − 2Q
• S=MC = Q
• Marginal externality costs=
MEC = 3
• What is the social loss that
results from the market
equilibrium?
• Often call marginal
externality marginal
damages or marginal
external damages (or
benefits)
• Will use MED or MEC, or
for benefits, MEB
James Sallee (EEP 101/ECON 125)
Externalities
January 27, 2021
22 / 25
Numerical example: Results
• Social optimum: MB = MSC → 12 − 2Q = Q + 3 → Q ∗ = 3.
(MSC is marginal social cost = private MC + MEC)
• Competitive equilibrium:
MB = MC → 12 − 2Q = Q → Qm = 4.
• Too much is being consumed under free market!
• How do we calculate DWL?
- It is a triangle: area = 1/2 base × height
- DWL =
(7−4)(4−3)
2
James Sallee (EEP 101/ECON 125)
= 1.5. (the shaded area)
Externalities
January 27, 2021
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Numerical example: Graph
• DWL is shaded area
• DWL= (7−4)(4−3)
= 1.5
2
MED×∆Q
• DWL=
= 1.5
2
P
MB
MSC
=MC+MEC
DWL
=1.5
MC
6
4
3
MEC
3
James Sallee (EEP 101/ECON 125)
Externalities
4
6
Q
January 27, 2021
24 / 25
Lecture 4 Outline
1
What is an externality?
- One agent’s production/consumption directly (not through
prices) influences the utility/production of another agent
2
Why do externalities cause market failure (inefficiency)?
- Because market transactions do not reflect full costs and
benefits to society
James Sallee (EEP 101/ECON 125)
Externalities
January 27, 2021
25 / 25