Chapter 16 Equilibrium. Market Equilibrium A market is in equilibrium when total quantity demanded...
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Transcript of Chapter 16 Equilibrium. Market Equilibrium A market is in equilibrium when total quantity demanded...
![Page 1: Chapter 16 Equilibrium. Market Equilibrium A market is in equilibrium when total quantity demanded by buyers equals total quantity supplied by sellers.](https://reader036.fdocuments.net/reader036/viewer/2022062313/56649c895503460f94941f11/html5/thumbnails/1.jpg)
Chapter 16Equilibrium
![Page 2: Chapter 16 Equilibrium. Market Equilibrium A market is in equilibrium when total quantity demanded by buyers equals total quantity supplied by sellers.](https://reader036.fdocuments.net/reader036/viewer/2022062313/56649c895503460f94941f11/html5/thumbnails/2.jpg)
Market Equilibrium
A market is in equilibrium when total quantity demanded by buyers equals total quantity supplied by sellers.
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Market Equilibriump
D(p), S(p)
q=D(p)
Marketdemand
Marketsupply
q=S(p)
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Market Equilibriump
D(p), S(p)
q=D(p)
Marketdemand
Marketsupply
q=S(p)
p*
q*
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Market Equilibriump
D(p), S(p)
q=D(p)
Marketdemand
Marketsupply
q=S(p)
p*
q*
D(p*) = S(p*): the marketis in equilibrium.
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Market Equilibriump
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’)
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Market Equilibriump
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 will fall towards p*.
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Market Equilibriump
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”)
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Market Equilibriump
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 will rise towards p*.
9
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Market Equilibrium
An example of calculating a market equilibrium when the market demand and supply curves are both linear. D p a bp( )
S p c dp( )
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Market Equilibriump
D(p), S(p)
D(p) = a-bp
Marketdemand
Marketsupply
S(p) = c+dp
p*
q*
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Market Equilibriump
D(p), S(p)
D(p) = a-bp
Marketdemand
Marketsupply
S(p) = c+dp
p*
q*
What are the valuesof p* and q*?
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Market EquilibriumD p a bp( ) S p c dp( )
At the equilibrium price p*, D(p*) = S(p*).That is,
a bp c dp * *
which givesp
a cb d
*
and q D p S pad bcb d
* * *( ) ( ) .
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Market Equilibriump
D(p), S(p)
D(p) = a-bp
Marketdemand
Marketsupply
S(p) = c+dpp
a cb d
*
dbbcad
q*
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Market Equilibrium
Can we calculate the market equilibrium using the inverse market demand and supply curves?
Yes, it is the same calculation.
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Market Equilibriumq D p a bp p
a qb
D q ( ) ( ),1
q S p c dp pc qd
S q ( ) ( ),1
the equation of the inverse marketdemand curve. And
the equation of the inverse marketsupply curve.
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Market Equilibrium
q
D-1(q),S-1(q)
D-1(q) = (a-q)/b
Marketinversedemand
Market inverse supplyS-1(q) = (-c+q)/d
p*
q*
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Market Equilibrium
q
D-1(q),S-1(q)
D-1(q) = (a-q)/b
Marketdemand
S-1(q) = (-c+q)/d
p*
q*
At equilibrium,D-1(q*) = S-1(q*).
Market inverse supply
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Market Equilibriump D q
a qb
1( ) p S qc qd
1( ) .and
At the equilibrium quantity q*, D-1(p*) = S-1(p*).That is,
d
qc
b
qa **
which gives qad bcb d
*
and p D q S qa cb d
* * *( ) ( ) .
1 1
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Market Equilibrium
q
D-1(q),S-1(q)
D-1(q) = (a-q)/b
Marketdemand
Marketsupply
S-1(q) = (-c+q)/dp
a cb d
*
dbbcad
q*
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Market Equilibrium
Two special cases:quantity supplied is fixed, independent
of the market price, andquantity supplied is extremely sensitive
to the market price.
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Market Equilibrium
S(p) = c+dp, so d=0and S(p) c.
p
qq* = c
Market quantity supplied isfixed, independent of price.
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Market Equilibrium
S(p) = c+dp, so d=0and S(p) c.
p
q
p*
D-1(q) = (a-q)/b
Marketdemand
q* = c
Market quantity supplied isfixed, independent of price.
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Market Equilibrium
S(p) = c+dp, so d=0and S(p) c.
p
q
p* =(a-c)/b
D-1(q) = (a-q)/b
Marketdemand
q* = c
p* = D-1(q*); that is,p* = (a-c)/b.
Market quantity supplied isfixed, independent of price.
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Market Equilibrium
S(p) = c+dp, so d=0and S(p) c.
p
q
D-1(q) = (a-q)/b
Marketdemand
q* = c
p* = D-1(q*); that is,p* = (a-c)/b.
db
cap
*
db
bcadq
*with d = 0 give
b
cap
*
.* cq
p* =(a-c)/b
Market quantity supplied isfixed, independent of price.
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Market Equilibrium
Two special cases arewhen quantity supplied is fixed,
independent of the market price, andwhen quantity supplied is extremely
sensitive to the market price.
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Market EquilibriumMarket quantity supplied isextremely sensitive to price.
S-1(q) = p*.
p
q
p*
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Market EquilibriumMarket quantity supplied isextremely sensitive to price.
S-1(q) = p*.
p
q
p*
D-1(q) = (a-q)/b
Marketdemand
q*
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Market EquilibriumMarket quantity supplied isextremely sensitive to price.
S-1(q) = p*.
p
q
p*
D-1(q) = (a-q)/b
Marketdemand
q* =a-bp*
p* = D-1(q*) = (a-q*)/b soq* = a-bp*
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Quantity Taxes
A quantity tax levied at a rate of $t is a tax of $t paid on each unit traded.
Quantity taxes might be levied on sellers or 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.
i.e. 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 the same effect as an excise tax rate $t.
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Quantity Taxes & Market Eqmp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
No tax
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Quantity Taxes & Market Eqmp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
$t
A quantity tax levied on sellers raises the market supply curve by $t.
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Quantity Taxes & Market Eqmp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
A quantity tax levied on sellers raises the market supply curve by $t, raises the buyers’price and lowers thequantity traded.
$tpb
qt
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Quantity Taxes & Market Eqmp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
A quantity tax levied on sellers raises the market supply 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 Eqmp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
No tax
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Quantity Taxes & Market Eqmp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
A quantity tax levied on buyers lowersthe market demandcurve by $t.
$t
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Quantity Taxes & Market Eqmp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
A quantity tax levied on buyers lowersthe market demandcurve by $t, lowersthe sellers’ price andreduces the quantitytraded.
$t
qt
ps
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Quantity Taxes & Market Eqmp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
A quantity tax levied on buyers 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 Eqmp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
A quantity tax levied on sellers at rate $t has the same effects on themarket’s equilibriumas does a quantity taxlevied on buyers at rate $t.
$t
pbpb
qt
pb
ps
$t
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Quantity Taxes & Market Eqm Who pays the tax of $t per unit
traded? The division of the $t between
buyers and sellers is the incidence of the tax.
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Quantity Taxes & Market Eqmp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
pbpb
qt
pb
ps
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Quantity Taxes & Market Eqmp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
pbpb
qt
pb
ps
Tax paid by buyers
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Quantity Taxes & Market Eqmp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
pbpb
qt
pb
ps
Tax paid by buyers
Tax paid by sellers
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Quantity Taxes & Market Eqm E.g. suppose the market demand and
supply curves are linear.
D p a bpb b( )
S p c dps s( )
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Quantity Taxes & Market EqmD p a bpb b( ) S p c dps s( ) . and
With the tax, the market equilibrium satisfiesp p tb s D p S pb s( ) ( )and so
p p tb s a bp c dpb s .and
49
pa c btb ds
p
a c dtb db
qad bc bdt
b dt
Solving these two equations gives
Therefore,
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Quantity Taxes & Market Eqmp
a c btb ds
pa c dtb db
qad bc bdt
b dt
As t 0, ps and pb theequilibrium price ifthere is no tax (t = 0) and qt the quantity traded at equilibrium when there is no tax.
*,pdb
ca
50
*qdb
bcad
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Quantity Taxes & Market Eqmp
a c btb ds
pa c dtb db
qad bc bdt
b dt
As t increases, ps falls,
pb rises,
and qt falls.
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Quantity Taxes & Market Eqmp
a c btb ds
pa c dtb db
qad bc bdt
b dt
The tax paid per unit by the buyer isp p
a c dtb d
a cb d
dtb db
* .
The tax paid per unit by the seller isp p
a cb d
a c btb d
btb ds
* .
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Quantity Taxes & Market Eqump
a c btb ds
pa c dtb db
qad bc bdt
b dt
The total tax paid (by buyers and sellers combined) is
T tq tad bc bdt
b dt
.
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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.
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Tax Incidence and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
$tpb
qt
ps
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Tax Incidence and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
$tpb
qt
ps
Change to buyers’price is pb - p*.Change to quantitydemanded is q.
q56
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Tax Incidence and Own-Price Elasticities
Around p = p* the own-price elasticityof demand is approximately
Db
bD
q
q
p p
p
p pq p
q
*
*
*
**
*.
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Tax Incidence and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
$tpb
qt
ps
58
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Tax Incidence and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
$tpb
qt
ps
Change to sellers’price is ps - p*.Change to quantitydemanded is q.
q59
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Tax Incidence and Own-Price Elasticities
Around p = p* the own-price elasticityof supply is approximately
Ss
sS
q
q
p p
p
p pq p
q
*
*
*
**
*.
60
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Tax Incidence and Own-Price Elasticitiesp
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 Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
pbpb
qt
pb
ps
Tax paid by buyers
Tax paid by sellers
Tax incidence = p p
p pb
s
*
*.
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Tax Incidence and Own-Price ElasticitiesTax incidence =
p p
p pb
s
*
*.
p pq p
qb
D
*
*
*.
p p
q p
qs
S
*
*
*.
So p p
p pb
s
S
D
*
*.
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Tax Incidence and Own-Price Elasticities
p p
p pb
s
S
D
*
*.
Tax incidence is
The fraction of a $t quantity tax paid by buyers rises as supply becomes more own-price elastic or as demand becomes less own-price elastic.
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Tax Incidence and Own-Price Elasticitiesp
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 Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
$tpb
qt
ps
As market demandbecomes less own-price elastic, taxincidence shifts moreto the buyers.
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Tax Incidence and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
ps= p*$tpb
qt = q*
As market demandbecomes less own-price elastic, taxincidence shifts moreto the buyers.
67
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Tax Incidence and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
ps= p*$tpb
qt = q*
As market demandbecomes less own-price elastic, taxincidence shifts moreto the buyers.
When D = 0, buyers pay the entire tax, even though it is levied on the sellers. 68
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Tax Incidence and Own-Price Elasticities
p p
p pb
s
S
D
*
*.
Tax incidence is
Similarly, the fraction of a $t quantity tax paid by sellers rises as supply becomes less own-price elastic or as demand becomes more own-price elastic.
69
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Deadweight Loss and Own-Price Elasticities
A quantity tax imposed on a competitive market reduces the quantity traded and so reduces gains-to-trade (i.e. the sum of Consumers’ and Producers’ Surpluses).
The lost total surplus is the tax’s deadweight loss, or excess burden.
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Deadweight Loss and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
No tax
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Deadweight Loss and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
No taxCS
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Deadweight Loss and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
No taxCS
PS
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Deadweight Loss and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
No taxCS
PS
74
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Deadweight Loss and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
$tpb
qt
ps
CS
PS
The tax reducesboth CS and PS
75
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Deadweight Loss and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
$tpb
qt
ps
CS
PS
The tax reducesboth CS and PS,transfers surplusto government
Tax
76
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Deadweight Loss and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
$tpb
qt
ps
CS
PS
The tax reducesboth CS and PS,transfers surplusto government
Tax
77
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Deadweight Loss and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
$tpb
qt
ps
CS
PS
The tax reducesboth CS and PS,transfers surplusto government
Tax
78
![Page 79: Chapter 16 Equilibrium. Market Equilibrium A market is in equilibrium when total quantity demanded by buyers equals total quantity supplied by sellers.](https://reader036.fdocuments.net/reader036/viewer/2022062313/56649c895503460f94941f11/html5/thumbnails/79.jpg)
Deadweight Loss and Own-Price Elasticitiesp
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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Deadweight Loss and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
$tpb
qt
ps Deadweight loss
80
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Deadweight Loss and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
$tpb
qt
ps
Deadweight loss fallsas market demandbecomes less own-price elastic.
81
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Deadweight Loss and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
$tpb
qt
ps
Deadweight loss fallsas market demandbecomes less own-price elastic.
82
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Deadweight Loss and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
ps= p*$tpb
qt = q*
Deadweight loss fallsas market demandbecomes less own-price elastic.
When D = 0, the tax causes no deadweight loss.
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Deadweight Loss 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 D = 0 or S = 0 then the deadweight loss is zero.
84