Download (p*).

16
© 2010 W. W. Norton & Company, Inc.
Equilibrium
Market Equilibrium
A
market is in equilibrium when total
quantity demanded by buyers equals
total quantity supplied by sellers.
© 2010 W. W. Norton & Company, Inc.
2
Market Equilibrium
Market
p
demand
q=D(p)
D(p)
© 2010 W. W. Norton & Company, Inc.
3
Market Equilibrium
p
Market
supply
q=S(p)
S(p)
© 2010 W. W. Norton & Company, Inc.
4
Market Equilibrium
Market
p
demand
Market
supply
q=S(p)
q=D(p)
D(p), S(p)
© 2010 W. W. Norton & Company, Inc.
5
Market Equilibrium
Market
p
demand
Market
supply
q=S(p)
p*
q=D(p)
q*
© 2010 W. W. Norton & Company, Inc.
D(p), S(p)
6
Market Equilibrium
Market
p
demand
Market
supply
q=S(p)
D(p*) = S(p*); the market
is in equilibrium.
p*
q=D(p)
q*
© 2010 W. W. Norton & Company, Inc.
D(p), S(p)
7
Market Equilibrium
Market
p
demand
Market
supply
q=S(p)
D(p’) < S(p’); an excess
of quantity supplied over
quantity demanded.
q=D(p)
p’
p*
D(p’)
© 2010 W. W. Norton & Company, Inc.
S(p’)
D(p), S(p)
8
Market Equilibrium
Market
p
demand
Market
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 must fall towards p*.
© 2010 W. W. Norton & Company, Inc.
9
Market Equilibrium
Market
p
demand
Market
supply
q=S(p)
D(p”) > S(p”); an excess
of quantity demanded
over quantity supplied.
q=D(p)
p*
p”
S(p”)
© 2010 W. W. Norton & Company, Inc.
D(p”)
D(p), S(p)
10
Market Equilibrium
Market
p
demand
Market
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 must rise towards p*.
© 2010 W. W. Norton & Company, Inc.
11
Market Equilibrium
 An
example of calculating a market
equilibrium when the market demand
and supply curves are linear.
D(p)  a  bp
S(p)  c  dp
© 2010 W. W. Norton & Company, Inc.
12
Market Equilibrium
Market
p
demand
Market
supply
S(p) = c+dp
p*
D(p) = a-bp
q*
© 2010 W. W. Norton & Company, Inc.
D(p), S(p)
13
Market Equilibrium
Market
p
demand
Market
supply
S(p) = c+dp
What are the values
of p* and q*?
p*
D(p) = a-bp
q*
© 2010 W. W. Norton & Company, Inc.
D(p), S(p)
14
Market Equilibrium
D(p)  a  bp
S(p)  c  dp
At the equilibrium price p*, D(p*) = S(p*).
© 2010 W. W. Norton & Company, Inc.
15
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*
© 2010 W. W. Norton & Company, Inc.
16
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
© 2010 W. W. Norton & Company, Inc.
ac
p 
bd
*
17
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
*
© 2010 W. W. Norton & Company, Inc.
*
*
18
Market Equilibrium
Market
p
demand
*
Market
supply
S(p) = c+dp
p 
ac
bd
D(p) = a-bp
ad  bc
q 
bd
*
© 2010 W. W. Norton & Company, Inc.
D(p), S(p)
19
Market Equilibrium
 Can
we calculate the market
equilibrium using the inverse market
demand and supply curves?
© 2010 W. W. Norton & Company, Inc.
20
Market Equilibrium
 Can
we calculate the market
equilibrium using the inverse market
demand and supply curves?
 Yes, it is the same calculation.
© 2010 W. W. Norton & Company, Inc.
21
Market Equilibrium
aq
1
q  D(p)  a  bp  p 
 D ( 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.
© 2010 W. W. Norton & Company, Inc.
22
Market Equilibrium
D-1(q),
S-1(q)
Market
inverse
demand
Market inverse supply
S-1(q) = (-c+q)/d
p*
D-1(q) = (a-q)/b
q*
© 2010 W. W. Norton & Company, Inc.
q
23
Market Equilibrium
D-1(q), Market
S-1(q) demand
Market inverse supply
S-1(q) = (-c+q)/d
At equilibrium,
D-1(q*) = S-1(q*).
p*
D-1(q) = (a-q)/b
q*
© 2010 W. W. Norton & Company, Inc.
q
24
Market Equilibrium
pD
1
aq
cq
1
( q) 
.
and p  S ( q) 
d
b
At the equilibrium quantity q*, D-1(p*) = S-1(p*).
© 2010 W. W. Norton & Company, Inc.
25
Market Equilibrium
pD
1
aq
cq
1
( q) 
.
and p  S ( q) 
d
b
At the equilibrium quantity q*, D-1(p*) = S-1(p*).
That is,
a  q*  c  q*

b
d
© 2010 W. W. Norton & Company, Inc.
26
Market Equilibrium
pD
1
aq
cq
1
( q) 
.
and p  S ( q) 
d
b
At the equilibrium quantity q*, D-1(p*) = S-1(p*).
That is,
a  q*  c  q*

b
d
* ad  bc
which gives q 
bd
© 2010 W. W. Norton & Company, Inc.
27
Market Equilibrium
pD
1
aq
cq
1
( q) 
.
and p  S ( q) 
d
b
At the equilibrium quantity q*, D-1(p*) = S-1(p*).
That is,
a  q*  c  q*

b
d
* ad  bc
which gives q 
bd
*
and p  D
© 2010 W. W. Norton & Company, Inc.
1
*
1
(q )  S
ac
(q ) 
.
bd
*
28
Market Equilibrium
D-1(q), Market
S-1(q) demand
*
Market
supply
S-1(q) = (-c+q)/d
p 
ac
bd
D-1(q) = (a-q)/b
ad  bc
q 
bd
*
© 2010 W. W. Norton & Company, Inc.
q
29
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.
© 2010 W. W. Norton & Company, Inc.
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?
© 2010 W. W. Norton & Company, Inc.
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
© 2010 W. W. Norton & Company, Inc.
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 )
© 2010 W. W. Norton & Company, Inc.
33
Quantity Taxes
D(pb )  S(ps )
pb  ps  t
and
describe the market’s equilibrium.
Notice these conditions apply no
matter if the tax is levied on sellers or on
buyers.
© 2010 W. W. Norton & Company, Inc.
34
Quantity Taxes
D(pb )  S(ps )
pb  ps  t
and
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.
© 2010 W. W. Norton & Company, Inc.
35
p
Quantity Taxes & Market
Market Equilibrium
Market
demand
supply
No tax
p*
q*
© 2010 W. W. Norton & Company, Inc.
D(p), S(p)
36
p
Quantity Taxes & Market
Market Equilibrium
Market
demand
supply
$t
An excise tax
raises the market
supply curve by $t
p*
q*
© 2010 W. W. Norton & Company, Inc.
D(p), S(p)
37
p
Quantity Taxes & Market
Market Equilibrium
Market
demand
supply
$t
pb
p*
qt q*
© 2010 W. W. Norton & Company, Inc.
An excise tax
raises the market
supply curve by $t,
raises the buyers’
price and lowers the
quantity traded.
D(p), S(p)
38
p
Quantity Taxes & Market
Market Equilibrium
Market
demand
supply
$t
pb
p*
ps
qt q*
An excise tax
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.
© 2010 W. W. Norton & Company, Inc.
39
p
Quantity Taxes & Market
Market Equilibrium
Market
demand
supply
No tax
p*
q*
© 2010 W. W. Norton & Company, Inc.
D(p), S(p)
40
p
Quantity Taxes & Market
Market Equilibrium
Market
demand
supply
An sales tax lowers
the market demand
curve by $t
p*
$t
q*
© 2010 W. W. Norton & Company, Inc.
D(p), S(p)
41
p
Quantity Taxes & Market
Market Equilibrium
Market
demand
p*
ps
supply
$t
qt q*
© 2010 W. W. Norton & Company, Inc.
An sales tax lowers
the market demand
curve by $t, lowers
the sellers’ price and
reduces the quantity
traded.
D(p), S(p)
42
p
Quantity Taxes & Market
Market Equilibrium
Market
demand
pb
p*
ps
supply
$t
qt q*
An sales tax 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.
© 2010 W. W. Norton & Company, Inc.
43
p
Quantity Taxes & Market
Market Equilibrium
Market
demand
supply
$t
pb
p*
ps
$t
qt q*
© 2010 W. W. Norton & Company, Inc.
A sales tax levied at
rate $t has the same
effects on the
market’s equilibrium
as does an excise tax
levied at rate $t.
D(p), S(p)
44
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.
© 2010 W. W. Norton & Company, Inc.
45
p
Quantity Taxes & Market
Market Equilibrium
Market
demand
supply
pb
p*
ps
qt q*
© 2010 W. W. Norton & Company, Inc.
D(p), S(p)
46
p
pb
p*
ps
Quantity Taxes & Market
Market Equilibrium
Market
demand
supply
Tax paid by
buyers
qt q*
© 2010 W. W. Norton & Company, Inc.
D(p), S(p)
47
p
Quantity Taxes & Market
Market Equilibrium
Market
demand
pb
p*
ps
supply
Tax paid by
sellers
qt q*
© 2010 W. W. Norton & Company, Inc.
D(p), S(p)
48
p
pb
p*
ps
Quantity Taxes & Market
Market Equilibrium
Market
demand
supply
Tax paid by
buyers
Tax paid by
sellers
qt q*
© 2010 W. W. Norton & Company, Inc.
D(p), S(p)
49
Tax Incidence and Own-Price
Elasticities
 The
incidence of a quantity tax
depends upon the own-price
elasticities of demand and supply.
© 2010 W. W. Norton & Company, Inc.
50
Tax Incidence and Own-Price
Elasticities
Market
Market
p
demand
supply
$t
pb
p*
ps
qt q*
© 2010 W. W. Norton & Company, Inc.
D(p), S(p)
51
Tax Incidence and Own-Price
Elasticities
Market
Market
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
© 2010 W. W. Norton & Company, Inc.
52
Tax Incidence and Own-Price
Elasticities
Around p = p* the own-price elasticity
of demand is approximately
Dq
*
q
D 
pb  p*
p*
© 2010 W. W. Norton & Company, Inc.
53
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*
© 2010 W. W. Norton & Company, Inc.
54
Tax Incidence and Own-Price
Elasticities
Market
Market
p
demand
supply
$t
pb
p*
ps
qt q*
© 2010 W. W. Norton & Company, Inc.
D(p), S(p)
55
Tax Incidence and Own-Price
Elasticities
Market
Market
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
© 2010 W. W. Norton & Company, Inc.
56
Tax Incidence and Own-Price
Elasticities
Around p = p* the own-price elasticity
of supply is approximately
Dq
*
q
S 
*
ps  p
*
p
© 2010 W. W. Norton & Company, Inc.
57
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*
© 2010 W. W. Norton & Company, Inc.
58
Tax Incidence and Own-Price
Elasticities
Market
Market
p
pb
p*
ps
demand
supply
Tax paid by
buyers
Tax paid by
sellers
qt q*
© 2010 W. W. Norton & Company, Inc.
D(p), S(p)
59
Tax Incidence and Own-Price
Elasticities
Market
Market
p
pb
p*
ps
demand
supply
Tax paid by
buyers
Tax paid by
sellers
qt q*
D(p), S(p)
*
Tax incidence =
© 2010 W. W. Norton & Company, Inc.
pb  p
*
p  ps
.
60
Tax Incidence and Own-Price
Elasticities
Market
Market
p
demand
supply
$t
pb
p*
ps
qt q*
© 2010 W. W. Norton & Company, Inc.
As market demand
becomes less ownprice elastic, tax
incidence shifts more
to the buyers.
D(p), S(p)
61
Tax Incidence and Own-Price
Elasticities
Market
Market
p
demand
supply
$t
pb
p*
ps
qt q*
© 2010 W. W. Norton & Company, Inc.
As market demand
becomes less ownprice elastic, tax
incidence shifts more
to the buyers.
D(p), S(p)
62
Tax Incidence and Own-Price
Elasticities
Market
Market
p
demand
supply
$t
pb
ps= p*
qt = q*
© 2010 W. W. Norton & Company, Inc.
As market demand
becomes less ownprice elastic, tax
incidence shifts more
to the buyers.
D(p), S(p)
63
Tax Incidence and Own-Price
Elasticities
Market
Market
p
demand
pb
ps= p*
supply
$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.
© 2010 W. W. Norton & Company, Inc.
64
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.
© 2010 W. W. Norton & Company, Inc.
65
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.
© 2010 W. W. Norton & Company, Inc.
66
Deadweight Loss and Own-Price
Elasticities
Market
Market
p
demand
supply
No tax
p*
q*
© 2010 W. W. Norton & Company, Inc.
D(p), S(p)
67
Deadweight Loss and Own-Price
Elasticities
Market
Market
p
demand
supply
No tax
p*
CS
q*
© 2010 W. W. Norton & Company, Inc.
D(p), S(p)
68
Deadweight Loss and Own-Price
Elasticities
Market
Market
p
demand
supply
No tax
p*
PS
q*
© 2010 W. W. Norton & Company, Inc.
D(p), S(p)
69
Deadweight Loss and Own-Price
Elasticities
Market
Market
p
demand
supply
No tax
p*
CS
PS
q*
© 2010 W. W. Norton & Company, Inc.
D(p), S(p)
70
Deadweight Loss and Own-Price
Elasticities
Market
Market
p
demand
supply
No tax
p*
CS
PS
q*
© 2010 W. W. Norton & Company, Inc.
D(p), S(p)
71
Deadweight Loss and Own-Price
Elasticities
Market
Market
p
demand
supply
$t
pb CS
p*
ps PS
qt q*
© 2010 W. W. Norton & Company, Inc.
The tax reduces
both CS and PS
D(p), S(p)
72
Deadweight Loss and Own-Price
Elasticities
Market
Market
p
demand
supply
$t
pb CS
p* Tax
ps PS
qt q*
© 2010 W. W. Norton & Company, Inc.
The tax reduces
both CS and PS,
transfers surplus
to government
D(p), S(p)
73
Deadweight Loss and Own-Price
Elasticities
Market
Market
p
demand
supply
$t
pb CS
p* Tax
ps PS
qt q*
© 2010 W. W. Norton & Company, Inc.
The tax reduces
both CS and PS,
transfers surplus
to government
D(p), S(p)
74
Deadweight Loss and Own-Price
Elasticities
Market
Market
p
demand
supply
$t
pb CS
p* Tax
ps PS
qt q*
© 2010 W. W. Norton & Company, Inc.
The tax reduces
both CS and PS,
transfers surplus
to government
D(p), S(p)
75
Deadweight Loss and Own-Price
Elasticities
Market
Market
p
demand
supply
$t
pb CS
p* Tax
ps PS
qt q*
© 2010 W. W. Norton & Company, Inc.
The tax reduces
both CS and PS,
transfers surplus
to government,
and lowers total
surplus.
D(p), S(p)
76
Deadweight Loss and Own-Price
Elasticities
Market
Market
p
demand
supply
$t
pb CS
p* Tax
ps PS
Deadweight loss
qt q*
© 2010 W. W. Norton & Company, Inc.
D(p), S(p)
77
Deadweight Loss and Own-Price
Elasticities
Market
Market
p
demand
supply
$t
pb
p*
ps
Deadweight loss
qt q*
© 2010 W. W. Norton & Company, Inc.
D(p), S(p)
78
Deadweight Loss and Own-Price
Elasticities
Market
Market
p
demand
supply
$t
pb
p*
ps
qt q*
© 2010 W. W. Norton & Company, Inc.
Deadweight loss falls
as market demand
becomes less ownprice elastic.
D(p), S(p)
79
Deadweight Loss and Own-Price
Elasticities
Market
Market
p
demand
supply
$t
pb
p*
ps
qt q*
© 2010 W. W. Norton & Company, Inc.
Deadweight loss falls
as market demand
becomes less ownprice elastic.
D(p), S(p)
80
Deadweight Loss and Own-Price
Elasticities
Market
Market
p
demand
pb
ps= p*
supply
$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.
© 2010 W. W. Norton & Company, Inc.
81
Deadweight Loss and Own-Price
Elasticities
 Deadweight
loss due to a quantity
tax rises as either market demand or
market supply becomes more ownprice elastic.
 If either D = 0 or S = 0 then the
deadweight loss is zero.
© 2010 W. W. Norton & Company, Inc.
82