Chapter Sixteen

1
Chapter Sixteen

• Equilibrium

2
Market Equilibrium

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

3
Market Equilibrium
Marketdemand
p
qD(p)
D(p)
4
Market Equilibrium
Marketsupply
p
qS(p)
S(p)
5
Market Equilibrium
Marketdemand
Marketsupply
p
qS(p)
qD(p)
D(p), S(p)
6
Market Equilibrium
Marketdemand
Marketsupply
p
qS(p)
p
qD(p)
D(p), S(p)
q
7
Market Equilibrium
Marketdemand
Marketsupply
p
qS(p)
D(p) S(p) the marketis in equilibrium.
p
qD(p)
D(p), S(p)
q
8
Market Equilibrium
Marketdemand
Marketsupply
p
qS(p)
D(p) lt S(p) an excessof quantity supplied
overquantity demanded.
p
p
qD(p)
D(p)
D(p), S(p)
S(p)
9
Market Equilibrium
Marketdemand
Marketsupply
p
qS(p)
D(p) lt S(p) an excessof quantity supplied
overquantity demanded.
p
p
qD(p)
D(p)
D(p), S(p)
S(p)
Market price must fall towards p.
10
Market Equilibrium
Marketdemand
Marketsupply
p
qS(p)
D(p) gt S(p) an excessof quantity
demandedover quantity supplied.
p
p
qD(p)
D(p), S(p)
D(p)
S(p)
11
Market Equilibrium
Marketdemand
Marketsupply
p
qS(p)
D(p) gt S(p) an excessof quantity
demandedover quantity supplied.
p
p
qD(p)
D(p), S(p)
D(p)
S(p)
Market price must rise towards p.
12
Market Equilibrium

• An example of calculating a market equilibrium
  when the market demand and supply curves are
  linear.

13
Market Equilibrium
Marketdemand
Marketsupply
p
S(p) cdp
p
D(p) a-bp
D(p), S(p)
q
14
Market Equilibrium
Marketdemand
Marketsupply
p
S(p) cdp
What are the valuesof p and q?
p
D(p) a-bp
D(p), S(p)
q
15
Market Equilibrium
At the equilibrium price p, D(p) S(p).
16
Market Equilibrium
At the equilibrium price p, D(p) S(p).That
is,
17
Market Equilibrium
At the equilibrium price p, D(p) S(p).That
is,
which gives
18
Market Equilibrium
At the equilibrium price p, D(p) S(p).That
is,
which gives
and
19
Market Equilibrium
Marketdemand
Marketsupply
p
S(p) cdp
D(p) a-bp
D(p), S(p)
20
Market Equilibrium

• Can we calculate the market equilibrium using the
  inverse market demand and supply curves?

21
Market Equilibrium

• Can we calculate the market equilibrium using the
  inverse market demand and supply curves?
• Yes, it is the same calculation.

22
Market Equilibrium
the equation of the inverse marketdemand curve.
And
the equation of the inverse marketsupply curve.
23
Market Equilibrium
Marketinversedemand
D-1(q),S-1(q)
Market inverse supply
S-1(q) (-cq)/d
p
D-1(q) (a-q)/b
q
q
24
Market Equilibrium
Marketdemand
D-1(q),S-1(q)
Market inverse supply
S-1(q) (-cq)/d
At equilibrium,D-1(q) S-1(q).
p
D-1(q) (a-q)/b
q
q
25
Market Equilibrium
and
At the equilibrium quantity q, D-1(p) S-1(p).
26
Market Equilibrium
and
At the equilibrium quantity q, D-1(p)
S-1(p).That is,
27
Market Equilibrium
and
At the equilibrium quantity q, D-1(p)
S-1(p).That is,
which gives
28
Market Equilibrium
and
At the equilibrium quantity q, D-1(p)
S-1(p).That is,
which gives
and
29
Market Equilibrium
Marketdemand
Marketsupply
D-1(q),S-1(q)
S-1(q) (-cq)/d
D-1(q) (a-q)/b
q
30
Market Equilibrium

• Two special cases
• quantity supplied is fixed, independent of the
  market price, and
• quantity supplied is extremely sensitive to the
  market price.

31
Market Equilibrium
Market quantity supplied isfixed, independent of
price.
p
q
q
32
Market Equilibrium
Market quantity supplied isfixed, independent of
price.
p
S(p) cdp, so d0 and S(p) º c.
q
q c
33
Market Equilibrium
Marketdemand
Market quantity supplied isfixed, independent of
price.
p
S(p) cdp, so d0 and S(p) º c.
D-1(q) (a-q)/b
q
q c
34
Market Equilibrium
Marketdemand
Market quantity supplied isfixed, independent of
price.
p
S(p) cdp, so d0 and S(p) º c.
p
D-1(q) (a-q)/b
q
q c
35
Market Equilibrium
Marketdemand
Market quantity supplied isfixed, independent of
price.
p
S(p) cdp, so d0 and S(p) º c.
p (a-c)/b
p D-1(q) that is,p (a-c)/b.
D-1(q) (a-q)/b
q
q c
36
Market Equilibrium
Marketdemand
Market quantity supplied isfixed, independent of
price.
p
S(p) cdp, so d0 and S(p) º c.
p (a-c)/b
p D-1(q) that is,p (a-c)/b.
D-1(q) (a-q)/b
q
q c
37
Market Equilibrium
Marketdemand
Market quantity supplied isfixed, independent of
price.
p
S(p) cdp, so d0 and S(p) º c.
p (a-c)/b
p D-1(q) that is,p (a-c)/b.
D-1(q) (a-q)/b
q
q c
with d 0 give
38
Market Equilibrium

• Two special cases are
• when quantity supplied is fixed, independent of
  the market price, and
• when quantity supplied is extremely sensitive to
  the market price.

ü
39
Market Equilibrium
Market quantity supplied isextremely sensitive
to price.
p
q
40
Market Equilibrium
Market quantity supplied isextremely sensitive
to price.
p
S-1(q) p.
p
q
41
Market Equilibrium
Marketdemand
Market quantity supplied isextremely sensitive
to price.
p
S-1(q) p.
p
D-1(q) (a-q)/b
q
42
Market Equilibrium
Marketdemand
Market quantity supplied isextremely sensitive
to price.
p
S-1(q) p.
p
D-1(q) (a-q)/b
q
q
43
Market Equilibrium
Marketdemand
Market quantity supplied isextremely sensitive
to price.
p
S-1(q) p.
p D-1(q) (a-q)/b soq a-bp
p
D-1(q) (a-q)/b
q
q a-bp
44
Quantity Taxes

• A quantity tax levied at a rate of t is a tax of
  t paid on each unit traded.
• If the tax is levied on sellers then it is an
  excise tax.
• If the tax is levied on buyers then it is a sales
  tax.

45
Quantity Taxes

• What is the effect of a quantity tax on a
  markets equilibrium?
• How are prices affected?
• How is the quantity traded affected?
• Who pays the tax?
• How are gains-to-trade altered?

46
Quantity Taxes

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

47
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.

48
Quantity Taxes
and
describe the markets equilibrium.Notice these
conditions apply nomatter if the tax is levied
on sellers or onbuyers.
49
Quantity Taxes
and
describe the markets 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.
50
Quantity Taxes Market Equilibrium
Marketdemand
Marketsupply
p
No tax
p
q
D(p), S(p)
51
Quantity Taxes Market Equilibrium
Marketdemand
Marketsupply
p
An excise tax raises the marketsupply curve by t
t
p
q
D(p), S(p)
52
Quantity Taxes Market Equilibrium
Marketdemand
Marketsupply
p
An excise tax raises the marketsupply curve by
t,raises the buyersprice and lowers
thequantity traded.
t
pb
p
q
qt
D(p), S(p)
53
Quantity Taxes Market Equilibrium
Marketdemand
Marketsupply
p
An excise tax raises the marketsupply curve by
t,raises the buyersprice and lowers
thequantity traded.
t
pb
p
ps
q
qt
D(p), S(p)
And sellers receive only ps pb - t.
54
Quantity Taxes Market Equilibrium
Marketdemand
Marketsupply
p
No tax
p
q
D(p), S(p)
55
Quantity Taxes Market Equilibrium
Marketdemand
Marketsupply
p
An sales tax lowersthe market demandcurve by t
p
t
q
D(p), S(p)
56
Quantity Taxes Market Equilibrium
Marketdemand
Marketsupply
p
An sales tax lowersthe market demandcurve by
t, lowersthe sellers price andreduces the
quantitytraded.
p
ps
t
q
qt
D(p), S(p)
57
Quantity Taxes Market Equilibrium
Marketdemand
Marketsupply
p
An sales tax lowersthe market demandcurve by
t, lowersthe sellers price andreduces the
quantitytraded.
pb
pb
pb
p
ps
t
q
qt
D(p), S(p)
And buyers pay pb ps t.
58
Quantity Taxes Market Equilibrium
Marketdemand
Marketsupply
p
A sales tax levied atrate t has the
sameeffects on themarkets equilibriumas does
an excise taxlevied at rate t.
t
pb
pb
pb
p
ps
t
q
qt
D(p), S(p)
59
Quantity Taxes Market Equilibrium

• Who pays the tax of t per unit traded?
• The division of the t between buyers and sellers
  is the incidence of the tax.

60
Quantity Taxes Market Equilibrium
Marketdemand
Marketsupply
p
pb
pb
pb
p
ps
q
qt
D(p), S(p)
61
Quantity Taxes Market Equilibrium
Marketdemand
Marketsupply
p
Tax paid by buyers
pb
pb
pb
p
ps
q
qt
D(p), S(p)
62
Quantity Taxes Market Equilibrium
Marketdemand
Marketsupply
p
pb
pb
pb
p
Tax paid by sellers
ps
q
qt
D(p), S(p)
63
Quantity Taxes Market Equilibrium
Marketdemand
Marketsupply
p
Tax paid by buyers
pb
pb
pb
p
Tax paid by sellers
ps
q
qt
D(p), S(p)
64
Quantity Taxes Market Equilibrium

• E.g. suppose the market demand and supply curves
  are linear.

65
Quantity Taxes Market Equilibrium
and
66
Quantity Taxes Market Equilibrium
and
With the tax, the market equilibrium satisfies
and
so
and
67
Quantity Taxes Market Equilibrium
and
With the tax, the market equilibrium satisfies
and
so
and
Substituting for pb gives
68
Quantity Taxes Market Equilibrium
give
and
The quantity traded at equilibrium is
69
Quantity Taxes Market Equilibrium

theequilibrium price ifthere is no tax
(t 0) and qt the quantity traded at
equilibriumwhen there is no tax.
As t 0, ps and pb

70
Quantity Taxes Market Equilibrium
As t increases, ps falls, pb rises,
and qt falls.
71
Quantity Taxes Market Equilibrium
The tax paid per unit by the buyer is
72
Quantity Taxes Market Equilibrium
The tax paid per unit by the buyer is
The tax paid per unit by the seller is
73
Quantity Taxes Market Equilibrium
The total tax paid (by buyers and
sellerscombined) is
74
Tax Incidence and Own-Price Elasticities

• The incidence of a quantity tax depends upon the
  own-price elasticities of demand and supply.

75
Tax Incidence and Own-Price Elasticities
Marketdemand
Marketsupply
p
t
pb
p
ps
q
qt
D(p), S(p)
76
Tax Incidence and Own-Price Elasticities
Marketdemand
Marketsupply
p
Change to buyersprice is pb - p. Change to
quantitydemanded is Dq.
t
pb
p
ps
q
qt
D(p), S(p)
Dq
77
Tax Incidence and Own-Price Elasticities
Around p p the own-price elasticityof demand
is approximately
78
Tax Incidence and Own-Price Elasticities
Around p p the own-price elasticityof demand
is approximately
79
Tax Incidence and Own-Price Elasticities
Marketdemand
Marketsupply
p
t
pb
p
ps
q
qt
D(p), S(p)
80
Tax Incidence and Own-Price Elasticities
Marketdemand
Marketsupply
p
Change to sellersprice is ps - p. Change to
quantitydemanded is Dq.
t
pb
p
ps
q
qt
D(p), S(p)
Dq
81
Tax Incidence and Own-Price Elasticities
Around p p the own-price elasticityof supply
is approximately
82
Tax Incidence and Own-Price Elasticities
Around p p the own-price elasticityof supply
is approximately
83
Tax Incidence and Own-Price Elasticities
Marketdemand
Marketsupply
p
Tax paid by buyers
pb
pb
pb
p
Tax paid by sellers
ps
q
qt
D(p), S(p)
84
Tax Incidence and Own-Price Elasticities
Marketdemand
Marketsupply
p
Tax paid by buyers
pb
pb
pb
p
Tax paid by sellers
ps
q
qt
D(p), S(p)
Tax incidence
85
Tax Incidence and Own-Price Elasticities
Tax incidence
86
Tax Incidence and Own-Price Elasticities
Tax incidence
So
87
Tax Incidence and Own-Price Elasticities
Tax incidence is
The fraction of a t quantity tax paidby buyers
rises as supply becomes moreown-price elastic or
as demand becomesless own-price elastic.
88
Tax Incidence and Own-Price Elasticities
Marketdemand
Marketsupply
p
As market demandbecomes less own- price elastic,
tax incidence shifts moreto the buyers.
t
pb
p
ps
q
qt
D(p), S(p)
89
Tax Incidence and Own-Price Elasticities
Marketdemand
Marketsupply
p
As market demandbecomes less own- price elastic,
tax incidence shifts moreto the buyers.
t
pb
p
ps
q
qt
D(p), S(p)
90
Tax Incidence and Own-Price Elasticities
Marketdemand
Marketsupply
p
As market demandbecomes less own- price elastic,
tax incidence shifts moreto the buyers.
t
pb
ps p
qt q
D(p), S(p)
91
Tax Incidence and Own-Price Elasticities
Marketdemand
Marketsupply
p
As market demandbecomes less own- price elastic,
tax incidence shifts moreto the buyers.
t
pb
ps p
qt q
D(p), S(p)
When eD 0, buyers pay the entire tax, even
though it is levied on the sellers.
92
Tax Incidence and Own-Price Elasticities
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.
93
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 taxs deadweight
  loss, or excess burden.

94
Deadweight Loss and Own-Price Elasticities
Marketdemand
Marketsupply
p
No tax
p
q
D(p), S(p)
95
Deadweight Loss and Own-Price Elasticities
Marketdemand
Marketsupply
p
No tax
CS
p
q
D(p), S(p)
96
Deadweight Loss and Own-Price Elasticities
Marketdemand
Marketsupply
p
No tax
p
PS
q
D(p), S(p)
97
Deadweight Loss and Own-Price Elasticities
Marketdemand
Marketsupply
p
No tax
CS
p
PS
q
D(p), S(p)
98
Deadweight Loss and Own-Price Elasticities
Marketdemand
Marketsupply
p
No tax
CS
p
PS
q
D(p), S(p)
99
Deadweight Loss and Own-Price Elasticities
Marketdemand
Marketsupply
p
The tax reducesboth CS and PS
t
CS
pb
p
ps
PS
q
qt
D(p), S(p)
100
Deadweight Loss and Own-Price Elasticities
Marketdemand
Marketsupply
p
The tax reducesboth CS and PS,transfers
surplusto government
t
CS
pb
p
Tax
ps
PS
q
qt
D(p), S(p)
101
Deadweight Loss and Own-Price Elasticities
Marketdemand
Marketsupply
p
The tax reducesboth CS and PS,transfers
surplusto government
t
CS
pb
p
Tax
ps
PS
q
qt
D(p), S(p)
102
Deadweight Loss and Own-Price Elasticities
Marketdemand
Marketsupply
p
The tax reducesboth CS and PS,transfers
surplusto government
t
CS
pb
p
Tax
ps
PS
q
qt
D(p), S(p)
103
Deadweight Loss and Own-Price Elasticities
Marketdemand
Marketsupply
p
The tax reducesboth CS and PS,transfers
surplusto government,and lowers total
surplus.
t
CS
pb
p
Tax
ps
PS
q
qt
D(p), S(p)
104
Deadweight Loss and Own-Price Elasticities
Marketdemand
Marketsupply
p
t
CS
pb
p
Tax
ps
PS
Deadweight loss
q
qt
D(p), S(p)
105
Deadweight Loss and Own-Price Elasticities
Marketdemand
Marketsupply
p
t
pb
p
ps
Deadweight loss
q
qt
D(p), S(p)
106
Deadweight Loss and Own-Price Elasticities
Marketdemand
Marketsupply
p
Deadweight loss falls as market demand becomes
less own- price elastic.
t
pb
p
ps
q
qt
D(p), S(p)
107
Deadweight Loss and Own-Price Elasticities
Marketdemand
Marketsupply
p
Deadweight loss falls as market demand becomes
less own- price elastic.
t
pb
p
ps
q
qt
D(p), S(p)
108
Deadweight Loss and Own-Price Elasticities
Marketdemand
Marketsupply
p
Deadweight loss falls as market demand becomes
less own- price elastic.
t
pb
ps p
qt q
D(p), S(p)
When eD 0, the tax causes no deadweight loss.
109
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 eD 0 or eS 0 then the deadweight
  loss is zero.