Download Equilibrium Market Equilibrium Excess Supply

Market Equilibrium
D(p*) = S(p*); market is in equilibrium
Equilibrium
p
Market
demand
Market
supply
q=S(p)
ECON 370: Microeconomic Theory
Summer 2004 – Rice University
p*
Stanley Gilbert
q=D(p)
q*
D(p), S(p)
Econ 370 - Equilibrium
2
Excess Supply
Excess Demand
D(p’) < S(p’); Market price must fall towards p*
D(p”) > S(p”); Market price must rise towards p*
p
Market
demand
Market
supply
q=S(p)
p
Market
demand
Market
supply
q=S(p)
p’
p*
p*
q*
Econ 370 - Equilibrium
p’’
q=D(p)
q=D(p)
q*
D(p), S(p)
3
Econ 370 - Equilibrium
D(p), S(p)
4
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Quantity Taxes: Introduction
Quantity Taxes
• Quantity tax - a tax of $t paid on each unit traded
• A tax rate t makes price paid by buyers, pb higher
by t from the price received by sellers, ps
• What is the effect of quantity tax on equilibrium?
• Consumers make their decisions based on what
they actually pay (pb)
• How are prices affected?
• How is the quantity traded affected?
• Who pays the tax?
• Producers make their decisions based on what
they actually receive (ps)
• How are gains-to-trade altered?
• But ps ≠ pb,
Rather: ps + t = pb
• Even with tax (different consumer and producer
prices) the market must clear
– That is: D(pb) = S(ps)
Econ 370 - Equilibrium
5
Econ 370 - Equilibrium
Mathematically
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Quantity Taxes on Producers
No tax
• Market equilibrium is described by:
– pb – ps = t and
– D(pb) = S(ps)
p
• So, we can solve for either
Mkt S
– D(ps + t) = S(ps) or
– D(pb) = S(pb + t)
p*
• Note that it doesn’t matter whether you tax
producers or consumers
• Prices, quantities, and tax collected are the same
Econ 370 - Equilibrium
Mkt D
q*
7
Econ 370 - Equilibrium
D(p), S(p)
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2
Quantity Taxes on Producers
Quantity Taxes on Producers
A producer tax raises market supply curve by $t
A producer tax raises the buyers’ price, lowers q
p
p
Mkt D
Mkt D
Mkt S
Mkt S
$t
pb
p*
p*
q*
$t
qt q*
D(p), S(p)
Econ 370 - Equilibrium
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D(p), S(p)
Econ 370 - Equilibrium
10
Quantity Taxes on Producers
Quantity Taxes on Consumers
And sellers receive only ps = pb - t
No tax
p
p
Mkt D
Mkt D
Mkt S
$t
pb
p*
ps
p*
qt q*
Econ 370 - Equilibrium
Mkt S
q*
D(p), S(p)
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Econ 370 - Equilibrium
D(p), S(p)
12
3
Quantity Taxes on Consumers
Quantity Taxes on Consumers
A consumer tax lowers market demand by $t
Consumer tax lowers sellers’ price, reduces q
p
p
Mkt D
Mkt D
Mkt S
Mkt S
p*
p*
ps
$t
q*
$t
qt q*
D(p), S(p)
Econ 370 - Equilibrium
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D(p), S(p)
Econ 370 - Equilibrium
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Quantity Taxes on Consumers
Quantity Taxes on Consumers
And buyers pay pb = ps + t
Identical effects, whether quantity tax levied on
sellers or producers
p
p
Mkt D
Mkt D
Mkt S
Mkt S
pb
pb
ps
ps
p*
p*
$t
qt q*
Econ 370 - Equilibrium
$t
qt q*
D(p), S(p)
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Econ 370 - Equilibrium
D(p), S(p)
16
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Tax Incidence
Tax Incidence Graph
• Who pays the tax of $t per unit traded?
Buyer’s Share
• Economic incidence (of a tax)
p
– division of tax burden between buyers and sellers after
all market adjustments
– Not statutory incidence
Mkt D
Mkt S
pb
p*
ps
Seller’s Share
qt q*
Econ 370 - Equilibrium
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Quantity Tax Example
D(p), S(p)
Econ 370 - Equilibrium
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Tax Incidence and Own-Price Elasticities
• Linear market demand and supply curves:
• The incidence of a quantity tax can be expressed
in terms of own-price elasticities of demand and
supply
• D(pb) = a – bpb
• S(ps) = a – bps
• We seek
– Pretax equilibrium
– Post-tax equilibrium
– Tax Share
• Where Tax shares are
– Seller’s Share = p* – ps
– Buyer’s Share = pb – p*
Econ 370 - Equilibrium
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Econ 370 - Equilibrium
20
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Tax Incidence and Own-Price Elasticities
Tax Incidence and Own-Price Elasticities
Around p = p* the own-price elasticity
of demand is approximately
Around p = p* the own-price elasticity
of supply is approximately
εD
∆q
q*
≈
pb − p *
p*
∆q
q*
εS ≈
ps − p*
p*
∆q × p *
⇒ pb − p * ≈
ε D × q*
Econ 370 - Equilibrium
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Tax Incidence and Own-Price Elasticities
pb − p * ≈
∆q × p *
ε D × q*
ps − p* ≈
Econ 370 - Equilibrium
Tax incidence ratio is:
∆q × p *
ε S × q*
Consumer Share is:
Producer Share is:
pb − p*
ε
≈− S
*
εD
p − ps
Econ 370 - Equilibrium
∆q × p *
ε S × q*
22
Tax Incidence and Own-Price Elasticities
pb − p*
p* − ps
Tax incidence ratio =
⇒ ps − p* ≈
23
Econ 370 - Equilibrium
pb − p*
ε
≈− S
*
εD
p − ps
− εS
εD − εS
εD
εD − εS
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Tax Incidence and Own-Price Elasticities
DWL and Own-Price Elasticities
• Fraction of quantity tax paid by buyers rises as
• A quantity tax imposed on a competitive market
– supply becomes more own-price elastic
– as demand becomes less own-price elastic
– reduces quantity traded
– reduces gains-to-trade (i.e. the sum of Consumers’ and
Producers’ Surpluses)
• When εD = 0, buyers pay entire tax, even though it
is levied on the sellers
• Deadweight loss - lost total surplus
– Excess burden
– Welfare cost
– Efficiency cost
• The fraction of quantity tax paid by sellers rises as
– supply becomes less own-price elastic or
– as demand becomes more own-price elastic
• When εs = 0, sellers pay entire tax, even though it
is levied on the buyers
Econ 370 - Equilibrium
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Econ 370 - Equilibrium
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DWL and Own-Price Elasticities: Graph
DWL and Own-Price Elasticities: Graph
No tax
The tax reduces both CS and PS, transfers some
of this surplus to government as tax revenue
p
p*
Mkt D
Mkt D
Mkt S
pb CS
p* Tax
ps PS
CS
PS
q*
Econ 370 - Equilibrium
p
Mkt S
qt q*
D(p), S(p)
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Econ 370 - Equilibrium
D(p), S(p)
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DWL and Own-Price Elasticities: Graph
DWL and Own-Price Elasticities: Graph
Dead-weight Loss is surplus lost as a result of
the tax
p
Mkt D
pb CS
p* Tax
ps PS
When εD = 0, the tax causes no deadweight loss
p
Mkt S
pb
ps= p*
DWL
qt q*
Mkt S
$t
qt = q*
D(p), S(p)
Econ 370 - Equilibrium
Mkt D
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Econ 370 - Equilibrium
D(p), S(p)
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DWL and Own-Price Elasticities
• DWL due to a quantity tax rises as either market
demand/supply becomes more own-price elastic
• If either εD = 0 or εs = 0 then the DWL is zero
Econ 370 - Equilibrium
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