Updated: 21 Feb 2007
MICRO ECONOMICS: ECON 601
Lecture 1
Topics to Be Covered:
a. Output Restriction
b. Constant Elasticities
c. Price Controls and Shortages
d. Black Markets
e. Tax Incidence Analysis
f. Marginal Burden
g. Trade Restrictions
h. Alternative Ways of Subsidizing
ECON 601: ADVANCED MICRO ECONOMICS
Applied Competitive Analysis
Nicholson Chapter 11
–
Up to this point we have been developing the tools to undertake the analysis of real world
policy issues.
–
A competitive equilibrium yields a solution that maximizes economic welfare. i.e.
Consumer and producer surplus is maximized when a market has reached its competitive
equilibrium.
P
A
S
P1
F
P*
P2
E
G
D
B
Q*
Q1
Q
Maximum consumer surplus = P*AE
Maximum producer surplus = P*EB
Suppose something (e.g. tax or monopolist) causes only Q1 to be demanded and supplied. At this
point consumers would value the output at P1 (points F) and the marginal cost of producing more
of the goods is only at P2 (Point G).
The economy can be made better off by the triangle FEG is output is expanded to Q*.
1
Example
Welfare cost Consumptions
Output Restriction
Linear demand and supply
Demand function = QD = 10 – Pd
Supply Function = QS = Ps – 2
P
10
S
QS = P – 2
7
6
5
QD = 10 – P
B
2
3
10
4
Welfare loss = ½ P. Q = ½ (2) (1) = 1
2
Q
Constant Elasticities
P
QD = 200 P – 1.2
QS = 1.3P
11.1
9.87
8.46
D
Q
12.8
11
Automobile restriction to control emissions:
.5 (11.1 – 8.46) (12.8 – 11) = 2.38 billions of dollar
Price Controls and Shortages
P
S.S.
A
Pb
G
L.S.
P2
P3
C
F
P1
E
D’
D
Q1
Q3
Q4
Shortage Q4-Q1
3
Q
With price ceiling of P1 the firms will continue to produce Q1. As compared to the long run
equilibrium of (P3, Q3) the price controls cause an economic loss of EAF. The amount CAF is a
loss in consumer surplus and the area ECF is a loss in producer surplus. As prices are held down
at P1 there is a transfer from producers to consumers of P1P3CE. This is not part of the economic
losses but is a transfer from one group to another in society.
Price controls and black markets
With price controls, black markets tend to develop where people are willing to pay up to P b for
the good. Black markets usually develop rather quickly as soon as shortages develop as a
consequence of price controls.
Tax Incidence Analysis
Suppose we impose a unit tax on a good:
P
S
PD
P0
F
t
E
PS
D
Q0
Q1
4
Q
PD – PS = t
dPD – dPS = dt
dQD = dQS
Q D
Q S
dPD =
dPS
PD
PS
Q D
Q S
dPD =
(dPd – dt)
PD
PS
(dPS = dPD – dt)
Divided by dt,
Q D dPD Q S dPD
Q S
=
(
)–
PD dt
PS
PS
dt
(
Q D Q S dPD
Q S
)(
)= –
PD PS
PS
dt
Q s P0
s
 xpx
Ps Q0
dPD
=
= s
d
 xpx   xpx
dt
Q s P0 Q D P0

Ps Q0 PD Q0
In the same way we find,
dPD
>0
dt
P
d
 xpx
dPs
= s
d
 xpx   xpx
dt
dPs
<0
dt
S1
D
S0
PD
t
PS
Q
Q0
5
If dxp = 0
s
 xpx
dPD
= s
d
 xpx   xpx
dt
dPD
=1
dt
If dxpx = –
dPs
dPD
= 0 but
= –1
dt
dt
because
d
 xpx
dPs

= s
=
= –1
d
 xpx   xpx  
dt
P
S
PD
t
PS
Q
The relative change in supply and demand prices,
d
s
 xpx
 xpx
dPs dPD
d
–(
)/
= –( s
)/(
)=
–
d
s
d
s
 xpx   xpx
 xpx
  xpx
dt
dt
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Tax Incidence Analysis
P
S
F
Pd
t
P0
Ps
H
E
G
D
Q0
Q1
Consumers lose P0PdFE
Q
Tax Revenues = P0PdFH
+
Producers lose PsP0EG
Tax Revenues = PsP0HG
+1
Total Taxes
FEG is “deadweight” loss an economic cost of taxation.
The loss in producers surplus is in fact a loss of the factors of production used to produce the
output.
DW = ½ dt (dQ)
P0
, Therefore
dP Q0
d = dQ
dQ = d dPD (
dQ =  (
d
Q0
)
P0
s
s d
)dt (
Q0
)
P0
7
DW = –½ (
dt 2  d  s
) ( s
)P0Q0
P0
 d
Let us consider a 10 percent tax on new houses in North Cyprus. Assume,
d = –1.5, s = 2.0, Q0
= 2000 new houses each year P = 35,000 pounds each,
DW
= –½ (0.10)2 (
= –½ (0.01) (
( 1.5)( 2)
) (35,000) (2,000)
2  1 .5
3
)(35,000) (2,000)
3 .5
= –½ (0.01) –3.0 (10,000) (2,000)
= 0.005 (60,000,000)
= 300,000/yr.
Marginal Burden
Suppose tax rate was increased to 15% i.e. from 0.1 to 0.15
DW
= –½ (0.15)2 (
( 1.5)( 2)
) (35,000) (2,000)
2  1 .5
= 0.01125 (60,000,000)
= 675,000/yr.
The tax rate rose by 50% but the DW increase by 125%.
Same DW costs are associated with transactions costs imposed by business, fees, trade
restrictions.
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Trade Restrictions
(1)
Gains from Trade
P
S
P0
Pw
E0
A
E1
D
Q2
Q1
Q0
Q
P0Q0 if no trade. Now open up to trade that will allow imports at world price of PW.
Demand will increase firm Q0 to Q1. Domestic suppliers will reduce production to Q2.
Imports will come in to fill gap of (Q1 – Q2). Consumers will gain consumer surplus
PwP0E0E1, producers of the item will lose PWP0E0A. The economy will have a net gain of
AE0E1.
(2)
Tariff Protection
Suppose domestic suppliers of the item ask for protection from imports. As suppliers are
usually fewer and better organized than the economic who benefit from trade, the
suppliers might get a protection tariff.
9
P
S
DW2
DW1
B
PR=Pw(1+t)
P wt
Pw
E2
C
A
E1
F
D
Q2
Q3
Q4
Q1
Q
Tariff Revenue = CB E2F
Loss to Consumers = Pw PR E2 E1
Gain Domestic Producers = PW PR BA
DW2 loss in consumer supplies through inefficient production = ABC
DW1 loss in consumer surplus through inefficient consumption =FE2E1
Quantitative Estimates of DW Loss
Q3  Q1
Q1
=
PR  Pw
Pw
d1 = t d
DW1 = - .5 (PR – Pw) (Q3 – Q1)
= -.5 (Pw (1 + t) – Pw) Q1 t d
= -.5 (Pw + tPw – Pw) Q1 t d
= -.5 t2 Pw Q1 d
DW2 = .5 (PR – Pw) (Q4 – Q2)
Q4  Q 2
Q2
=(
PR  Pw s
) = t s
Pw
PRs =(Pw (1 + t))
DW2 = .5 (t Pw) . t s Q2
= .5 t2 s Q2 Pw
10
Quota to limit imports Q3 – Q4.
In this case the area BCFE2 that was being collected as revenue will go to the fortunate people
who get the import licences or quota permits.
Let us consider a Tariff on Automobiles in US.
Typical case of Turkey, Malaysia, … etc.
QD = 42 P–½
QS = 1.3 P
P = $9,000
P
S
DW2
Tariff revenues
E0
9.87 = P0
9.5
9=Pw
A
DW1
E1
D
1 million
Q
11.7 12.4 12.8 13.4
14.3
2.6 million
Gain in consumer surplus = PwP0E0E1 = $ 11.8 billion/year
Suppose put on a Tariff of $500 / car imported
PR = Pw + 500 = 9.5 thousand
DW1 = .5 (.5) (14.3 – 13.4) = 0.225 billion
DW2 = .5 (.5) (12.4 – 11.7) = 0.175 billion
Total DW loss = 0.4 billion
Tariff revenue = 500 (1 million) = 0.5 billion
DW = loss 80 percent of tariff revenue
An automobile quota of 1 million cars would have an identical effect to that tariff of $500.
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The only difference is that the 500 of tariff revenue would go to whoever got the right to import
the cars.
Other Example
Subsidize the cost of capital from 10 percent to 2 percent in production of electricity.
R
0.13 v2
DW
0.05 v1
DK
K2
K1
100 billion
Q
v = r+ d
r = real rate of reduction, d = rate of depreciation = 0.3 percent per year
kf = elasticity of substitution of capital for fuel
dkk = Sk epx – (1 – Sk) kf
epx = –0.6 Sk = 0.4
kf = 0.3
dkk = 0.4 (–0.6) – (0.6) (0.3) = – 0.24 – 0.18 = –0.42
1 = 0.2 + 0.3 = 0.5
2 = 0.10 + 0.03 = 0.13
Capital is subsidized from 0.10 to 0.02, t = u/v1
Rate of subsidy = u per year
DW1 = – 0.5 (t2) dkk 1 K1
0.0064
= –0.5 (
) (–0.42) (0.05) ($100 B)
0.0025
= –0.5 (2.86) (–0.42) (0.05) ($100 B) = 3.003 billion loss
12
Alternative Ways of Subsidizing
Barley farming in North Cyprus desire to have farmers receive a price of Pmin/bushel.
(1)
Set minimum price and government purchase barley and sell surplus at a loss to
Turkey.
(2)
Subsidize people who purchase barley for annual feed and bread.
(3)
Restrict amount of land that can be planted.
(1)
Minimum price and Government Purchase
Government will sell what it purchases to Turkey
P
S
DW1 = loss caused by reduced
consumption = Q2ABQ0
A
Pmin
C
DW2 = loss caused too much production
= Q0BCQ1
B
B
Reduction in DW loss by value of sale
of Barley to Turkey by PT (Q1 – Q2)
F
D
PT
Q2
Q
Q1
Q0
Revenue Cost
Pmin (Q1 – Q2) – PTurkey (Q1 – Q2)
(2)
Subsidize people who purchase barley for annual feed and bread.
P
S
A
Pmin
e
B
Subsidy
PD
C
f
D
Q2
Q1
DW loss = Bef
Revenue Cost
(Pmin – PD) (Q1)
13
Q
Question: How would the economic cost and revenue cost changes if the demand
function were less elastic ?
Question: How would the economic cost and revenue cost change of the supply function
were less elastic ?
Question: How does the economic loss and revenue cost change if the demand curve
were less elastic ? If the supply curve were less elastic ?
(3)
Restrict amount of land that can be planted.
P
SS1
S
A
Pmin
SS0
B
C
D
G
Q1
Q0
Q
DW = ABC + GAC
Revenue Cost = 0
ABC is the loss due to the fact that consumers value output firm (Q0 – Q1) at Q1ABQ0 while the
resource saved are only Q1CBQ0. An additional efficiency cost is imposed because farmers tend
to farm the land more intensely and use more other factors such as fertilizer, irrigation etc.
Question: How does economic loss change is the supply function is more elastic ? If the demand
function is more elastic?
The End
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