Title: Chapter 16 Equilibrium
1Chapter 16Equilibrium
2Market Equilibrium
- A market is in equilibrium when total quantity
demanded by buyers equals total quantity supplied
by sellers.
3Market Equilibrium
Marketdemand
Marketsupply
p
qS(p)
qD(p)
D(p), S(p)
4Market Equilibrium
Marketdemand
Marketsupply
p
qS(p)
p
qD(p)
D(p), S(p)
q
5Market Equilibrium
Marketdemand
Marketsupply
p
qS(p)
D(p) S(p) the marketis in equilibrium.
p
qD(p)
D(p), S(p)
q
6Market 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)
7Market 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 will fall towards p.
8Market 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)
9Market 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 will rise towards p.
10Market Equilibrium
- An example of calculating a market equilibrium
when the market demand and supply curves are both
linear.
11Market Equilibrium
Marketdemand
Marketsupply
p
S(p) cdp
p
D(p) a-bp
D(p), S(p)
q
12Market Equilibrium
Marketdemand
Marketsupply
p
S(p) cdp
What are the valuesof p and q?
p
D(p) a-bp
D(p), S(p)
q
13Market Equilibrium
At the equilibrium price p, D(p) S(p).That
is,
which gives
and
14Market Equilibrium
Marketdemand
Marketsupply
p
S(p) cdp
D(p) a-bp
D(p), S(p)
15Market Equilibrium
- Can we calculate the market equilibrium using the
inverse market demand and supply curves? - Yes, it is the same calculation.
16Market Equilibrium
the equation of the inverse marketdemand curve.
And
the equation of the inverse marketsupply curve.
17Market 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
18Market 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
19Market Equilibrium
and
At the equilibrium quantity q, D-1(p)
S-1(p).That is,
which gives
and
20Market Equilibrium
Marketdemand
Marketsupply
D-1(q),S-1(q)
S-1(q) (-cq)/d
D-1(q) (a-q)/b
q
21Market Equilibrium
- Two special cases
- quantity supplied is fixed, independent of the
market price, and - quantity supplied is extremely sensitive to the
market price.
22Market Equilibrium
Market quantity supplied isfixed, independent of
price.
p
S(p) cdp, so d0 and S(p) º c.
q
q c
23Market 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
24Market 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
25Market 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
26Market 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
27Market Equilibrium
Market quantity supplied isextremely sensitive
to price.
p
S-1(q) p.
p
q
28Market Equilibrium
Marketdemand
Market quantity supplied isextremely sensitive
to price.
p
S-1(q) p.
p
D-1(q) (a-q)/b
q
q
29Market 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
30Quantity 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.
31Quantity 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?
32Quantity Taxes
- A tax rate t makes the price paid by buyers, pb,
higher by t from the price received by sellers,
ps.
33Quantity 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.
34Quantity 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 the same effect as
an excise tax rate t.
35Quantity Taxes Market Eqm
Marketdemand
Marketsupply
p
No tax
p
q
D(p), S(p)
36Quantity Taxes Market Eqm
Marketdemand
Marketsupply
p
A quantity tax levied on sellers raises the
market supply curve by t.
t
p
q
D(p), S(p)
37Quantity Taxes Market Eqm
Marketdemand
Marketsupply
p
A quantity tax levied on sellers raises the
market supply curve by t, raises the
buyersprice and lowers thequantity traded.
t
pb
p
q
qt
D(p), S(p)
38Quantity Taxes Market Eqm
Marketdemand
Marketsupply
p
A quantity tax levied on sellers raises the
market supply 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.
39Quantity Taxes Market Eqm
Marketdemand
Marketsupply
p
No tax
p
q
D(p), S(p)
40Quantity Taxes Market Eqm
Marketdemand
Marketsupply
p
A quantity tax levied on buyers lowersthe
market demandcurve by t.
p
t
q
D(p), S(p)
41Quantity Taxes Market Eqm
Marketdemand
Marketsupply
p
A quantity tax levied on buyers lowersthe
market demandcurve by t, lowersthe sellers
price andreduces the quantitytraded.
p
ps
t
q
qt
D(p), S(p)
42Quantity Taxes Market Eqm
Marketdemand
Marketsupply
p
A quantity tax levied on buyers 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.
43Quantity Taxes Market Eqm
Marketdemand
Marketsupply
p
A quantity tax levied on sellers at rate t has
the same effects on themarkets equilibriumas
does a quantity taxlevied on buyers at rate t.
t
pb
pb
pb
p
ps
t
q
qt
D(p), S(p)
44Quantity 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.
45Quantity Taxes Market Eqm
Marketdemand
Marketsupply
p
pb
pb
pb
p
ps
q
qt
D(p), S(p)
46Quantity Taxes Market Eqm
Marketdemand
Marketsupply
p
Tax paid by buyers
pb
pb
pb
p
ps
q
qt
D(p), S(p)
47Quantity Taxes Market Eqm
Marketdemand
Marketsupply
p
Tax paid by buyers
pb
pb
pb
p
Tax paid by sellers
ps
q
qt
D(p), S(p)
48Quantity Taxes Market Eqm
- E.g. suppose the market demand and supply curves
are linear.
49Quantity Taxes Market Eqm
and
With the tax, the market equilibrium satisfies
so
and
and
Solving these two equations gives
Therefore,
50Quantity Taxes Market Eqm
theequilibrium price ifthere is no tax
(t 0) and qt the quantity traded at
equilibrium when there is no tax.
As t 0, ps and pb
51Quantity Taxes Market Eqm
As t increases, ps falls, pb rises,
and qt falls.
52Quantity Taxes Market Eqm
The tax paid per unit by the buyer is
The tax paid per unit by the seller is
53Quantity Taxes Market Equm
The total tax paid (by buyers and sellers
combined) is
54Tax Incidence and Own-Price Elasticities
- The incidence of a quantity tax depends upon the
own-price elasticities of demand and supply.
55Tax Incidence and Own-Price Elasticities
Marketdemand
Marketsupply
p
t
pb
p
ps
q
qt
D(p), S(p)
56Tax 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
57Tax Incidence and Own-Price Elasticities
Around p p the own-price elasticityof demand
is approximately
58Tax Incidence and Own-Price Elasticities
Marketdemand
Marketsupply
p
t
pb
p
ps
q
qt
D(p), S(p)
59Tax 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
60Tax Incidence and Own-Price Elasticities
Around p p the own-price elasticityof supply
is approximately
61Tax 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)
62Tax 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
63Tax Incidence and Own-Price Elasticities
Tax incidence
So
64Tax Incidence and Own-Price Elasticities
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.
65Tax 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)
66Tax 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)
67Tax 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)
68Tax 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.
69Tax 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.
70Deadweight 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.
71Deadweight Loss and Own-Price Elasticities
Marketdemand
Marketsupply
p
No tax
p
q
D(p), S(p)
72Deadweight Loss and Own-Price Elasticities
Marketdemand
Marketsupply
p
No tax
CS
p
q
D(p), S(p)
73Deadweight Loss and Own-Price Elasticities
Marketdemand
Marketsupply
p
No tax
CS
p
PS
q
D(p), S(p)
74Deadweight Loss and Own-Price Elasticities
Marketdemand
Marketsupply
p
No tax
CS
p
PS
q
D(p), S(p)
75Deadweight 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)
76Deadweight 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)
77Deadweight 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)
78Deadweight 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)
79Deadweight 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)
80Deadweight Loss and Own-Price Elasticities
Marketdemand
Marketsupply
p
t
pb
p
ps
Deadweight loss
q
qt
D(p), S(p)
81Deadweight 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)
82Deadweight 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)
83Deadweight 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.
84Deadweight 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.