1 equilibrium molly w. dahl georgetown university econ 101 – spring 2009

1

Equilibrium

Molly W. DahlGeorgetown UniversityEcon 101 – Spring 2009

2

Market Equilibrium

A market is in equilibrium when total quantity demanded by buyers equals total quantity supplied by sellers.

3

Market Equilibrium

p

D(p), S(p)

q=D(p)

Marketdemand

Marketsupply

q=S(p)

p*

q*

D(p*) = S(p*): the marketis in equilibrium.

4

Market Equilibrium

p

D(p), S(p)

q=D(p)

Marketdemand

Marketsupply

q=S(p)

p*

S(p’)

D(p’) < S(p’): an excessof quantity supplied overquantity demanded.

p’

D(p’)

Market price must fall towards p*.

5

Market Equilibrium

p

D(p), S(p)

q=D(p)

Marketdemand

Marketsupply

q=S(p)

p*

D(p”)

D(p”) > S(p”): an excessof quantity demandedover quantity supplied.

p”

S(p”)

Market price must rise towards p*.

6

Market Equilibrium

In class: Calculating the market equilibrium when the

market demand and supply curves are linear.Calculating the market equilibrium using the

inverse market demand and supply curves.

7

Quantity Taxes

A quantity tax levied at a rate of $t is a tax of $t paid on each unit traded.Excise Tax: tax is levied on sellers.Sales Tax: tax is levied on buyers.

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Quantity Taxes

What is the effect of a quantity tax on a market’s equilibrium?

How are prices affected? How is the quantity traded affected? Who pays the tax? How are gains-to-trade altered?

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Quantity Taxes

A tax rate t makes the price paid by buyers, pb, higher by t from the price received by sellers, ps.

p p tb s

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Quantity Taxes

Even with a tax the market must clear. That is, the quantity demanded by buyers

at price pb must equal quantity supplied by sellers at price ps.

D p S pb s( ) ( )

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Quantity Taxes

p p tb s D p S pb s( ) ( )and

describe the market’s equilibrium.

Notice that these two conditions apply nomatter if the tax is levied on sellers or onbuyers.

Hence, a sales tax rate $t has thesame effect as an excise tax rate $t.

12

Quantity Taxes & Market Equilibrium

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

No tax

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Quantity Taxes & Market Equilibrium

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

An excise taxraises the marketsupply curve by $t,raises the buyers’price and lowers thequantity traded.

$tpb

qt

And sellers receive only ps = pb - t.

ps

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Quantity Taxes & Market Equilibrium

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

No tax

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Quantity Taxes & Market Equilibrium

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

An sales tax lowersthe market demandcurve by $t, lowersthe sellers’ price andreduces the quantitytraded.$t

pbpb

qt

pb

And buyers pay pb = ps + t.

ps

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Quantity Taxes & Market Equilibrium

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

A sales tax levied atrate $t has the sameeffects on themarket’s equilibriumas does an excise taxlevied at rate $t.$t

pbpb

qt

pb

ps

$t

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Tax Incidence

Who pays the tax of $t per unit traded? The division of the $t between buyers and

sellers is the tax incidence.

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Tax Incidence

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

pbpb

qt

pb

ps

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Tax Incidence

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

pbpb

qt

pb

ps

Tax paid by buyers

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Tax Incidence

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

pbpb

qt

pb

psTax paid by sellers

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Tax Incidence

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

pbpb

qt

pb

ps

Tax paid by buyers

Tax paid by sellers

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Tax Incidence and Own-Price Elasticities

The incidence of a quantity tax depends upon the own-price elasticities of demand and supply.The incidence of a tax is usually shared,

though not always.

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Tax Incidence and Own-Price Elasticities

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

$tpb

qt

ps

As market demandbecomes less own-price elastic, taxincidence shifts moreto the buyers.

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Tax Incidence and Own-Price Elasticities

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

$tpb

qt

ps

As market demandbecomes less own-price elastic, taxincidence shifts moreto the buyers.

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Tax Incidence and Own-Price Elasticities

p

D(p), S(p)

Marketdemand

Marketsupply

ps= p*

$tpb

qt = q*

As market demandbecomes less own-price elastic, taxincidence shifts moreto the buyers.

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Tax Incidence and Own-Price Elasticities

Perfectly Inelastic Demand Demander pays all tax

Perfectly Elastic Demand Supplier pays all tax

Perfectly Inelastic Supply Supplier pays all tax

Perfectly Elastic Supply Demander pays all tax

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DWL and Own-Price Elasticities

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

$tpb

qt

ps

CS

PS

The tax reducesboth CS and PS,transfers surplusto government,and lowers total surplus.

Tax

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DWL and Own-Price Elasticities

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

$tpb

qt

ps

CS

PSTax

Deadweight loss

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DWL and Own-Price Elasticities

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

$tpb

qt

ps

Deadweight loss fallsas market demandbecomes less own-price elastic.

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DWL and Own-Price Elasticities

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

$tpb

qt

ps

Deadweight loss fallsas market demandbecomes less own-price elastic.

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DWL and Own-Price Elasticities

p

D(p), S(p)

Marketdemand

Marketsupply

ps= p*

$tpb

qt = q*

Deadweight loss fallsas market demandbecomes less own-price elastic.

When demand is perfectly inelastic, the tax causes no deadweight loss.

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DWL and Own-Price Elasticities

Deadweight loss due to a quantity tax rises as either market demand or market supply becomes more own-price elastic.

If either demand or supply are perfectly inelastic, then the deadweight loss is zero.