Supply function
Aggregation
Equilibrium
Example: Tax
Partial equilibrium
or, a review of micro principles
Intermediate Micro
Lecture 10
Chapter 16 of Varian
Pareto efficiency
Supply function
Aggregation
Equilibrium
Example: Tax
Equilibrium
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Up until now: taking prices as given, find demand
Today: how are prices determined?
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Supply and demand story
Taxes
Efficiency
Pareto efficiency
Supply function
Aggregation
The supply function
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Consumption must be
produced
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Supplied by firms
When p low
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Low effort in
production
Few firms enter
market
Quantity supplied
is low
Equilibrium
Example: Tax
Pareto efficiency
Supply function
Aggregation
The supply function
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When p high
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High effort in
production
Many firms enter
market
Quantity supplied
is high
Standard story - there
are exceptions!
Equilibrium
Example: Tax
Pareto efficiency
Supply function
Aggregation
Equilibrium
Example: Tax
Pareto efficiency
Market demand function
4 identical consumers
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Market demand: The
total quantity demanded
by all consumers for a
given price
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Market demand function:
D(p) A function that
gives the market demand
for any price
Supply function
Aggregation
Equilibrium
Example: Tax
Pareto efficiency
Market demand function
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Finding the market
demand function
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4 identical consumers
P
D(p) = x(p)
On graph: sum
demands horizontally
Supply function
Aggregation
Equilibrium
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Competitive market:
Firms and consumers
are price-takers
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Look at price on
market, decide
quantity
supply/demand, q
Equilibrium price:
Price where market
demand = market
supply
Equilibrium
Example: Tax
Pareto efficiency
Supply function
Aggregation
Equilibrium
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What if p > p ∗ ?
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S(p) > D(p)
Firms with unsold
goods lower price
or drop out of
market
Competition forces
p↓
Equilibrium
Example: Tax
Pareto efficiency
Supply function
Aggregation
Equilibrium
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What if p < p ∗ ?
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D(p) > S(p)
Firms can charge
more and still find
customers
Consumers can
resell to highest
bidder
Competition forces
p↑
Equilibrium
Example: Tax
Pareto efficiency
Supply function
Aggregation
Demand shifts
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Say x is quinoa
Quinoa becomes
trendy in US
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p↑
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x↑
D(p) ↑ at any p
Demand curve
shifts up/right
Equilibrium
Example: Tax
Pareto efficiency
Supply function
Aggregation
Supply shifts
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Say x is oil
Oil well catches fire in
Gulf of Mexico
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p↑
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x↓
S(p) ↓ at any p
Supply curve shifts
up/left
Equilibrium
Example: Tax
Pareto efficiency
Supply function
Aggregation
A per-unit tax
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Government imposes
a per-unit tax t
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On graph: t-sized
gap between supply,
demand curves
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Demanders pay pD
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Suppliers receive pS
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pD − pS = t
Equilibrium
Example: Tax
Pareto efficiency
Supply function
Aggregation
A per-unit tax
Effect of t
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CS ↓ by a,b
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PS ↓ by c,d
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Gov’t collects a,c
b,d =
deadweight loss:
surplus that is lost
under an inefficient
policy
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Efficiency to be
defined in a few
slides
Equilibrium
Example: Tax
Pareto efficiency
Supply function
Aggregation
Inelastic supply
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What if supply is
fixed at x ∗
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Supply is inelastic:
quantity supplied
does not change with
price
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Suppliers pay entire
tax
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Demanders
unaffected
Equilibrium
Example: Tax
Pareto efficiency
Supply function
Aggregation
Inelastic demand
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What if demand is
fixed at x ∗
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Demand is inelastic:
quantity demanded
does not change with
price
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Demanders pay entire
tax
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Suppliers unaffected
Equilibrium
Example: Tax
Pareto efficiency
Supply function
Aggregation
Equilibrium
Example: Tax
Elasticity and DWL
dD(p) p
dp D(p)
dS(p) p
=
dp S(p)
D,p = −
S,p
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Price changes more for inelastic participant
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Notice that DWL = 0 when D or S inelastic
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DWL is smaller when D or S is highly inelastic
If you must tax something
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tax goods with inelastic supply/demand
Pareto efficiency
Supply function
Aggregation
Equilibrium
Inelastic Supply/Demand - Short run
Response to ↑ t
I Gasoline
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Supply inelastic wells are already
drilled...
Demand inelastic hard to drive much
less
Labor
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Supply inelastic People like to work
40 hours a week
Demand inelastic hiring and firing
are slow
Example: Tax
Pareto efficiency
Supply function
Aggregation
Equilibrium
Inelastic Supply/Demand - Long run
Response to ↑ t
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Supply - stop
drilling oil wells
Demand - buy a
Prius
Labor
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Supply - retire
earlier, invest less
in education
Demand - replace
workers with
machines
Example: Tax
Pareto efficiency
Supply function
Aggregation
Equilibrium
Example: Tax
Pareto efficiency
Pareto efficiency
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An outcome is Pareto efficient if the only way to make
someone better off is to make someone else worse off
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Pareto inefficient: Adi has 2 left shoes, and Rudi has 2 right
shoes
Pareto efficient: Imelda has 1,000 pairs of shoes, and Francis
has none
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Pareto efficiency means all gains from trade are realized
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Pareto efficiency need not mean the outcome is fair
Supply function
Aggregation
Equilibrium
Market equilibrium and PE
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Competitive market
outcome is efficient
At equilibrium price
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All trades
($-for-good) are
made willingly
No trades left
undone are worth
doing
Example: Tax
Pareto efficiency
Supply function
Aggregation
Equilibrium
Example: Tax
Pareto efficiency
Pareto improvement
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Pareto improvement: a trade that makes at least one person
better off, and no one worse off
Example: StubHub trades
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Washington Nationals have 81 home games
Season-ticket holder not very interested in next game, willing
to sell for $100
Visiting fan willing to pay up to $120
Sell ticket for $110
Both $10 better off