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Chapter 16Equilibrium
Market Equilibrium
A market is in equilibrium when total quantity demanded by buyers equals total quantity supplied by sellers.
2
Market Equilibriump
D(p), S(p)
q=D(p)
Marketdemand
Marketsupply
q=S(p)
3
Market Equilibriump
D(p), S(p)
q=D(p)
Marketdemand
Marketsupply
q=S(p)
p*
q*
4
Market Equilibriump
D(p), S(p)
q=D(p)
Marketdemand
Marketsupply
q=S(p)
p*
q*
D(p*) = S(p*): the marketis in equilibrium.
5
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’)
6
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*.
7
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”)
8
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
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( )
10
Market Equilibriump
D(p), S(p)
D(p) = a-bp
Marketdemand
Marketsupply
S(p) = c+dp
p*
q*
11
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*?
12
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
* * *( ) ( ) .
13
Market Equilibriump
D(p), S(p)
D(p) = a-bp
Marketdemand
Marketsupply
S(p) = c+dpp
a cb d
*
dbbcad
q*
14
Market Equilibrium
Can we calculate the market equilibrium using the inverse market demand and supply curves?
Yes, it is the same calculation.
15
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.
16
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*
17
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
19
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*
20
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.
23
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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25
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.
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.
26
Market EquilibriumMarket quantity supplied isextremely sensitive to price.
S-1(q) = p*.
p
q
p*
27
Market EquilibriumMarket quantity supplied isextremely sensitive to price.
S-1(q) = p*.
p
q
p*
D-1(q) = (a-q)/b
Marketdemand
q*
28
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*
29
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.
30
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?
31
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
32
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( ) ( )
33
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.
34
Quantity Taxes & Market Eqmp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
No tax
35
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.
36
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
37
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
38
Quantity Taxes & Market Eqmp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
No tax
39
Quantity Taxes & Market Eqmp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
A quantity tax levied on buyers lowersthe market demandcurve by $t.
$t
40
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
41
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
42
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
43
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.
44
Quantity Taxes & Market Eqmp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
pbpb
qt
pb
ps
45
Quantity Taxes & Market Eqmp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
pbpb
qt
pb
ps
Tax paid by buyers
46
Quantity Taxes & Market Eqmp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
pbpb
qt
pb
ps
Tax paid by buyers
Tax paid by sellers
47
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( )
48
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,
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
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.
51
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
* .
52
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
.
53
Tax Incidence and Own-Price Elasticities The incidence of a quantity tax
depends upon the own-price elasticities of demand and supply.
54
Tax Incidence and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
$tpb
qt
ps
55
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
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
*
*
*
**
*.
57
Tax Incidence and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
$tpb
qt
ps
58
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
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
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
61
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
*
*.
62
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
*
*.
63
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.
64
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.
65
Tax Incidence and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
$tpb
qt
ps
As market demandbecomes less own-price elastic, taxincidence shifts moreto the buyers.
66
Tax Incidence and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
ps= p*$tpb
qt = q*
As market demandbecomes less own-price elastic, taxincidence shifts moreto the buyers.
67
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
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
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.
70
Deadweight Loss and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
No tax
71
Deadweight Loss and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
No taxCS
72
Deadweight Loss and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
No taxCS
PS
73
Deadweight Loss and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
No taxCS
PS
74
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
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
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
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
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
79
Deadweight Loss and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
$tpb
qt
ps Deadweight loss
80
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
Deadweight Loss and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
$tpb
qt
ps
Deadweight loss fallsas market demandbecomes less own-price elastic.
82
Deadweight Loss and Own-Price Elasticitiesp
D(p), S(p)
Marketdemand
Marketsupply
ps= p*$tpb
qt = q*
Deadweight loss fallsas market demandbecomes less own-price elastic.
When D = 0, the tax causes no deadweight loss.
83
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
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