Download Chapter Sixteen

Chapter 16
Equilibrium
Market Equilibrium

A market is in equilibrium when total quantity
demanded by buyers equals total quantity
supplied by sellers.
2
Market
Equilibrium
Market
Market
p
demand
supply
q=S(p)
q=D(p)
D(p), S(p)
3
Market
Equilibrium
Market
Market
p
demand
supply
q=S(p)
p*
q=D(p)
q*
D(p), S(p)
4
Market
Equilibrium
Market
Market
p
demand
supply
q=S(p)
D(p*) = S(p*): the market
is in equilibrium.
p*
q=D(p)
q*
D(p), S(p)
5
Market
Equilibrium
Market
Market
p
demand
supply
q=S(p)
D(p’) < S(p’): an excess
of quantity supplied over
quantity demanded.
q=D(p)
p’
p*
D(p’)
S(p’)
D(p), S(p)
6
Market
Equilibrium
Market
Market
p
demand
supply
q=S(p)
D(p’) < S(p’): an excess
of quantity supplied over
quantity demanded.
q=D(p)
p’
p*
D(p’)
S(p’)
D(p), S(p)
Market price will fall towards p*.
7
Market
Equilibrium
Market
Market
p
demand
supply
q=S(p)
D(p”) > S(p”): an excess
of quantity demanded
over quantity supplied.
q=D(p)
p*
p”
S(p”)
D(p”)
D(p), S(p)
8
Market
Equilibrium
Market
Market
p
demand
supply
q=S(p)
D(p”) > S(p”): an excess
of quantity demanded
over quantity supplied.
q=D(p)
p*
p”
S(p”)
D(p”)
D(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
Equilibrium
Market
Market
p
demand
supply
S(p) = c+dp
p*
D(p) = a-bp
q*
D(p), S(p)
11
Market
Equilibrium
Market
Market
p
demand
supply
S(p) = c+dp
What are the values
of p* and q*?
p*
D(p) = a-bp
q*
D(p), S(p)
12
Market Equilibrium
D(p)  a  bp
S(p)  c  dp
At the equilibrium price p*, D(p*) = S(p*).
That is,
a  bp*  c  dp*
which gives
* ac
p 
bd
ad  bc
*
*
*
and q  D(p )  S(p ) 
.
bd
13
Market Equilibrium
p Market
demand
*
p 
ac
bd
Market
supply
S(p) = c+dp
D(p) = a-bp
ad  bc
q 
bd
*
D(p), S(p)
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 Equilibrium
aq
q  D(p)  a  bp  p 
 D 1 ( q),
b
the equation of the inverse market
demand curve. And
cq
q  S(p)  c  dp  p 
 S 1 ( q),
d
the equation of the inverse market
supply curve.
16
Market
Equilibrium
Market
-1
D (q),
S-1(q)
inverse
demand
Market inverse supply
S-1(q) = (-c+q)/d
p*
D-1(q) = (a-q)/b
q*
q
17
Market
Equilibrium
-1
Market
D (q),
S-1(q)
Market inverse supply
S-1(q) = (-c+q)/d
demand
At equilibrium,
D-1(q*) = S-1(q*).
p*
D-1(q) = (a-q)/b
q*
q
18
Market Equilibrium
cq
aq
1
.
p  D ( q) 
and p  S ( q) 
d
b
At the equilibrium quantity q*, D-1(p*) = S-1(p*).
That is,
a  q*  c  q*
1

b
which gives
*
and p  D
d
ad  bc
q 
bd
*
1
*
1
(q )  S
ac
(q ) 
.
bd
*
19
Market
Equilibrium
-1
Market
Market
D (q),
S-1(q)
demand
*
p 
ac
bd
supply
S-1(q) = (-c+q)/d
D-1(q) = (a-q)/b
ad  bc
q 
bd
*
q
20
Market Equilibrium

Two special cases:
 quantity
supplied is fixed, independent of the
market price, and
 quantity supplied is extremely sensitive to the
market price.
21
Market Equilibrium
Market quantity supplied is
p
fixed, independent of price.
S(p) = c+dp, so d=0
and S(p)  c.
q* = c
q
22
Market
Equilibrium
Market
Market quantity supplied is
p
demand
fixed, independent of price.
S(p) = c+dp, so d=0
and S(p)  c.
p*
D-1(q) = (a-q)/b
q* = c
q
23
Market
Equilibrium
Market
Market quantity supplied is
p
demand
p* =
(a-c)/b
fixed, independent of price.
S(p) = c+dp, so d=0
and S(p)  c.
p* = D-1(q*); that is,
p* = (a-c)/b.
D-1(q) = (a-q)/b
q* = c
q
24
Market
Equilibrium
Market
Market quantity supplied is
p
demand
fixed, independent of price.
S(p) = c+dp, so d=0
and S(p)  c.
p* =
(a-c)/b
p* = D-1(q*); that is,
p* = (a-c)/b.
D-1(q) = (a-q)/b
ac
p 
bd
q* = c
q
*
ad  bc
q 
bd
*
ac
p 
b
*
with d = 0 give
q*  c.
25
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.
26
Market Equilibrium
Market quantity supplied is
p
extremely sensitive to price.
S-1(q) = p*.
p*
q
27
Market
Equilibrium
Market
Market quantity supplied is
p
demand
extremely sensitive to price.
S-1(q) = p*.
p*
D-1(q) = (a-q)/b
q*
q
28
Market
Equilibrium
Market
Market quantity supplied is
p
demand
extremely sensitive to price.
S-1(q) = p*.
p* = D-1(q*) = (a-q*)/b so
q* = a-bp*
p*
D-1(q) = (a-q)/b
q* =
a-bp*
q
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.
pb  ps  t
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(pb )  S(ps )
33
Quantity Taxes
pb  ps  t
and
D(pb )  S(ps )
describe the market’s equilibrium.
Notice that these two conditions apply no
matter if the tax is levied on sellers or on
buyers.
Hence, a sales tax rate $t has the same effect
as an excise tax rate $t.
34
Quantity
Market
Eqm
Market Taxes &
Market
p
demand
supply
No tax
p*
q*
D(p), S(p)
35
Quantity
Market
Eqm
Market Taxes &
Market
p
demand
supply
$t
p*
q*
A quantity tax levied
on sellers raises the
market supply curve
by $t.
D(p), S(p)
36
Quantity
Market
Eqm
Market Taxes &
Market
p
demand
supply
$t
pb
p*
qt q*
A quantity tax levied
on sellers raises the
market supply curve
by $t, raises the buyers’
price and lowers the
quantity traded.
D(p), S(p)
37
Quantity
Market
Eqm
Market Taxes &
Market
p
demand
supply
$t
pb
p*
ps
qt q*
A quantity tax levied
on sellers raises the
market supply curve
by $t, raises the buyers’
price and lowers the
quantity traded.
D(p), S(p)
And sellers receive only ps = pb - t.
38
Quantity
Market
Eqm
Market Taxes &
Market
p
demand
supply
No tax
p*
q*
D(p), S(p)
39
Quantity
Market
Eqm
Market Taxes &
Market
p
demand
supply
p*
A quantity tax levied
on buyers lowers
the market demand
curve by $t.
$t
q*
D(p), S(p)
40
Quantity
Market
Eqm
Market Taxes &
Market
p
demand
p*
ps
supply
$t
qt q*
A quantity tax levied
on buyers lowers
the market demand
curve by $t, lowers
the sellers’ price and
reduces the quantity
traded.
D(p), S(p)
41
Quantity
Market
Eqm
Market Taxes &
Market
p
demand
pb
p*
ps
supply
$t
qt q*
A quantity tax levied
on buyers lowers
the market demand
curve by $t, lowers
the sellers’ price and
reduces the quantity
traded.
D(p), S(p)
And buyers pay pb = ps + t.
42
Quantity
Market
Eqm
Market Taxes &
Market
p
demand
supply
$t
pb
p*
ps
$t
qt q*
A quantity tax levied
on sellers at rate $t has
the same effects on the
market’s equilibrium
as does a quantity tax
levied on buyers at rate
$t.
D(p), S(p)
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
Market
Eqm
Market Taxes &
Market
p
demand
supply
pb
p*
ps
qt q*
D(p), S(p)
45
Quantity
Market
Eqm
Market Taxes &
Market
p
pb
p*
ps
demand
supply
Tax paid by
buyers
qt q*
D(p), S(p)
46
Quantity
Market
Eqm
Market Taxes &
Market
p
pb
p*
ps
demand
supply
Tax paid by
buyers
Tax paid by
sellers
qt q*
D(p), S(p)
47
Quantity Taxes & Market Eqm

E.g. suppose the market demand and supply
curves are linear.
D(pb )  a  bpb
S(ps )  c  dps
48
Quantity Taxes & Market Eqm
D(pb )  a  bpb and S(ps )  c  dps .
With the tax, the market equilibrium satisfies
pb  ps  t and D(pb )  S(ps ) so
pb  ps  t and a  bpb  c  dps .
Solving these two equations gives
a  c  bt
ps 
bd
Therefore,
a  c  dt
pb 
bd
ad  bc  bdt
q 
bd
t
49
Quantity Taxes & Market Eqm
a  c  bt
ps 
bd
a  c  dt
pb 
bd
ad  bc  bdt
q 
bd
t
As t  0, ps and pb  a  c  p*, the
bd
equilibrium price if
ad  bc
*
t

q
there is no tax (t = 0) and q 
bd
the quantity traded at equilibrium
when there is no tax.
50
Quantity Taxes & Market Eqm
a  c  bt
ps 
bd
a  c  dt
pb 
bd
As t increases,
and
ad  bc  bdt
q 
bd
t
ps falls,
pb rises,
qt falls.
51
Quantity Taxes & Market Eqm
a  c  bt
ps 
bd
a  c  dt
pb 
bd
ad  bc  bdt
q 
bd
t
The tax paid per unit by the buyer is
a  c  dt a  c
dt
pb  p 


.
bd
bd bd
*
The tax paid per unit by the seller is
a  c a  c  bt
bt
p  ps 


.
bd
bd
bd
*
52
Quantity Taxes & Market Equm
a  c  bt
ps 
bd
a  c  dt
pb 
bd
ad  bc  bdt
q 
bd
t
The total tax paid (by buyers and sellers combined)
is
ad  bc  bdt
T  tq  t
.
bd
t
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
Market
Market
Elasticities
p
demand
supply
$t
pb
p*
ps
qt q*
D(p), S(p)
55
Tax Incidence and Own-Price
Market
Market
Elasticities
p
demand
supply
$t
pb
p*
ps
qt q*
Change to buyers’
price is pb - p*.
Change to quantity
demanded is Dq.
D(p), S(p)
Dq
56
Tax Incidence and Own-Price
Elasticities
Around p = p* the own-price elasticity
of demand is approximately
Dq
*
q
D 
pb  p*
 pb  p* 
Dq  p*
 D  q*
.
p*
57
Tax Incidence and Own-Price
Market
Market
Elasticities
p
demand
supply
$t
pb
p*
ps
qt q*
D(p), S(p)
58
Tax Incidence and Own-Price
Market
Market
Elasticities
p
demand
supply
$t
pb
p*
ps
qt q*
Change to sellers’
price is ps - p*.
Change to quantity
demanded is Dq.
D(p), S(p)
Dq
59
Tax Incidence and Own-Price
Elasticities
Around p = p* the own-price elasticity
of supply is approximately
Dq
*
q
S 
ps  p*
 ps  p* 
Dq  p*
 S  q*
.
p*
60
Tax Incidence and Own-Price
Market
Market
Elasticities
p
demand
supply
pb
p*
ps
Tax paid by
buyers
Tax paid by
sellers
qt q*
D(p), S(p)
61
Tax Incidence and Own-Price
Market
Market
Elasticities
p
demand
supply
pb
p*
ps
Tax paid by
buyers
Tax paid by
sellers
qt q*
D(p), S(p)
*
Tax incidence =
pb  p
*
p  ps
.
62
Tax Incidence and Own-Price
Elasticities
*
pb  p
Tax incidence =
*
pb  p 
So
*
p  ps
*
Dq  p
D  q
*
*
pb  p
*
p  ps
.
.
*
ps  p 
*
Dq  p
 S q
*
.
S
 
.
D
63
Tax Incidence and Own-Price
Elasticities
Tax incidence is
*
pb  p
*
p  ps
S
 
.
D
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
Market
Market
Elasticities
p
demand
supply
$t
pb
p*
ps
qt q*
As market demand
becomes less ownprice elastic, tax
incidence shifts more
to the buyers.
D(p), S(p)
65
Tax Incidence and Own-Price
Market
Market
Elasticities
p
demand
supply
$t
pb
p*
ps
qt q*
As market demand
becomes less ownprice elastic, tax
incidence shifts more
to the buyers.
D(p), S(p)
66
Tax Incidence and Own-Price
Market
Market
Elasticities
p
demand
supply
pb
ps= p*
$t
qt = q*
As market demand
becomes less ownprice elastic, tax
incidence shifts more
to the buyers.
D(p), S(p)
67
Tax Incidence and Own-Price
Market
Market
Elasticities
p
demand
supply
pb
ps= p*
$t
As market demand
becomes less ownprice elastic, tax
incidence shifts more
to the buyers.
D(p), S(p)
qt = q*
When D = 0, buyers pay the entire tax, even
though it is levied on the sellers.
68
Tax Incidence and Own-Price
Elasticities
Tax incidence is
*
pb  p
*
p  ps
S
 
.
D
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
Market
Market
Elasticities
p
demand
supply
No tax
p*
q*
D(p), S(p)
71
Deadweight Loss and Own-Price
Market
Market
Elasticities
p
demand
supply
p*
No tax
CS
q*
D(p), S(p)
72
Deadweight Loss and Own-Price
Market
Market
Elasticities
p
demand
supply
p*
No tax
CS
PS
q*
D(p), S(p)
73
Deadweight Loss and Own-Price
Market
Market
Elasticities
p
demand
supply
p*
No tax
CS
PS
q*
D(p), S(p)
74
Deadweight Loss and Own-Price
Market
Market
Elasticities
p
demand
supply
pb CS
p*
ps PS
$t
qt q*
The tax reduces
both CS and PS
D(p), S(p)
75
Deadweight Loss and Own-Price
Market
Market
Elasticities
p
demand
supply
pb CS
p* Tax
ps PS
$t
qt q*
The tax reduces
both CS and PS,
transfers surplus
to government
D(p), S(p)
76
Deadweight Loss and Own-Price
Market
Market
Elasticities
p
demand
supply
pb CS
p* Tax
ps PS
$t
qt q*
The tax reduces
both CS and PS,
transfers surplus
to government
D(p), S(p)
77
Deadweight Loss and Own-Price
Market
Market
Elasticities
p
demand
supply
pb CS
p* Tax
ps PS
$t
qt q*
The tax reduces
both CS and PS,
transfers surplus
to government
D(p), S(p)
78
Deadweight Loss and Own-Price
Market
Market
Elasticities
p
demand
supply
pb CS
p* Tax
ps PS
$t
qt q*
The tax reduces
both CS and PS,
transfers surplus
to government,
and lowers total
D(p), S(p) surplus.
79
Deadweight Loss and Own-Price
Market
Market
Elasticities
p
demand
supply
$t
pb
p*
ps
Deadweight loss
qt q*
D(p), S(p)
80
Deadweight Loss and Own-Price
Market
Market
Elasticities
p
demand
supply
$t
pb
p*
ps
qt q*
Deadweight loss falls
as market demand
becomes less ownprice elastic.
D(p), S(p)
81
Deadweight Loss and Own-Price
Market
Market
Elasticities
p
demand
supply
$t
pb
p*
ps
qt q*
Deadweight loss falls
as market demand
becomes less ownprice elastic.
D(p), S(p)
82
Deadweight Loss and Own-Price
Market
Market
Elasticities
p
demand
supply
pb
ps= p*
$t
Deadweight loss falls
as market demand
becomes less ownprice elastic.
D(p), S(p)
qt = q*
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