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Market Equilibrium
&
Comparative Statics
Dr. Jennifer P. Wissink
©2011 John M. Abowd and Jennifer P. Wissink, all rights reserved.
Market Equilibrium


We will consider the market
for compact disc players.
Recall that we will define
the following for our market:
–
–
–
–

Demanders are the buyers of CD
disc players.
–

QxD = f(PX, Ps, Pc, I, T&P, Pop)
Suppliers are the sellers of CD
players.
–

The type and style of CD players.
The quality of the CD players.
All other attributes of the generic CD
player.
A time frame that applies to our market
for CD players.
QXS = g(PX, Pfop, Poc, S&T, N)
The CD player market is a perfectly
competitive market.
Px
Market Equilibrium (Verbal)
A
place of “rest”.
 Equilibrium: a price where the quantity demanded
equals the quantity supplied.
 In notation:
– Find a PX* so that: QXD(PX*) = QXS(PX*)
Market Equilibrium (Table)
Price
0
5
10
15
17
20
25
30
35
40
Market Equilibrium
Quantity
Quantity
Demanded
Supplied
40
6
35
11
30
16
25
21
23
23
20
26
15
31
10
36
5
41
0
46
 At
P* = $17, the
QD = QS=23
 So
Q*=23
Market Equilibrium (Table)
Market Equilibrium
Quantity
Quantity
Price
Demanded
Supplied
0
40
6
5
35
11
10
30
16
15
25
21
17
23
23
20
20
26
25
15
31
30
10
36
35
5
41
40
0
46



Note: If P>17 you are
not at an equilibrium.
Why?
Suppose P=$30
– QD=10 and Qs=36
– surplus=26 units


Price would tend to fall.
There would be an
increase in quantity
demanded and a
decrease in quantity
supplied as the price
falls.
Market Equilibrium (Table)
Market Equilibrium
Quantity
Quantity
Price
Demanded
Supplied
0
40
6
5
35
11
10
30
16
15
25
21
17
23
23
20
20
26
25
15
31
30
10
36
35
5
41
40
0
46



Note: If P<17 you are not
at an equilibrium.
Why?
Suppose P=$15
– QD=25 and Qs=21
– shortage=4 units


Price would tend to rise.
There would be an
increase in quantity
supplied and a decrease
in quantity demanded as
the price rises.
Market Equilibrium (Graph)


The market
equilibrium occurs
at the intersection
of the supply and
demand curves.
Let’s drop the
subscript X, ok?
Price
Demand
Supply
Phigh
surplus
P*=17


At P* = $17,
QD = QS = 23
So Q* = 23
Plow
shortage
23
Quantity
Market Equilibrium (Equations)

Two equations and Two unknowns
– Equations: Demand and Supply Curves
– Unknowns: P and Q

To find P*, set QD = QS
–
–
–
–
–

Recall: QD = 40 - P and QS = 6 + P
So for an equilibrium: (40 - P*) = (6 + P*)
34 = 2P* or P* = 34/2 so... P*=$17
To find Q*, plug P* into either the demand or supply equation.
Q*=23 = 40 - 17 or Q*=23 = 6 + 17
SIMPLE AS THAT!? Then what....
Comparative Statics


Use the model to make predictions.
Something changes in the market.
–
–
–
–



Something that changes demand.
Something that changes supply.
Something that changes both!
Something the government does to prevent a natural market
equilibrium.
Would get a new equilibrium.
Compare one equilibrium with another equilibrium and
see what happens to P* and Q*.
Compare two equilibria - compare two static situations comparative statics!
Recall Demand & Supply Curves



The demand curve
– QD = f(P)
given Ps, Pc, I,
T&P, Pop
The supply curve
– QS = g(P)
given Pfop, Poc,
S&T, N
Comparative Statics
Summary:
EVENT
↑D
P*
Up
Q*
Up
↓D
Down
Down
↑S
Down
Up
↓S
Up
Down
↑D ↑ S
?
Up
Comparative Statics:
Increase in Demand  increase in P* and Q*





D shifts to right.
No longer in equilibrium: At
P=$17 there’s a shortage
Price will rise.
As price rises, there is a
reduction in quantity
demanded along new
demand curve
AND
an increase in quantity
supplied along original
supply curve.
Get new P* and Q* at P*=22
and Q*=28.
Price
Demand
New Demand
Supply
22
17
23
28
Quantity
Comparative Statics:
Decrease in Demand  decrease in P* and Q*





D shifts to left.
No longer in equilibrium:
At P=$17 there’s a
surplus.
Price will fall.
As price falls, there is an
increase in quantity
demanded along new
demand curve
AND
a decrease in quantity
supplied along original
supply curve.
Get new P* and Q* at
P*=14.5 and Q*=20.5.
Price
Demand
Supply
17
14.5
New Demand
20.5 23
Quantity
Comparative Statics:
Increase in Supply  decrease in P* & increase in Q*





S shifts to right.
No longer in equilibrium:
At P=$17 there’s a
surplus.
Price will fall.
As price falls, there is a
reduction in quantity
supplied along new
supply curve
AND
an increase in quantity
demanded along
original demand curve.
Get new P* and Q* at
P*=14.50 and Q*=25.5.
Price
Demand
Supply
New Supply
17
14.5
23 25.5
Quantity
Demand Generated Examples:
3 Different Markets – 3 Different Stories
Question
 How
would an increase in family
income change the demand for air
travel?
 What would happen to the market price
and quantity?
Air Travel Market



Increased family
income increases the
demand for air travel –
assuming it’s a normal
good.
New price = P* and
new quantity
supplied = new
quantity demanded
= Q*.
Price
P*
P
Equilibrium price
and quantity both
rise.
Q
Q*
Quantity
Question
 How
would an increase in the price of
software change the demand for
computers?
 What would happen to the market price
and quantity?
Computer Market



An increase in the
price of software, a
complement,
decreases the
demand for
computers.
New price = P* and
new quantity supplied
= new quantity
demanded = Q*.
Price
P
P*
Equilibrium price and
quantity both fall.
Q*
Q
Quantity
Question
 How
would an increase in the price of
Cornell men’s hockey tickets change
the demand for women’s basketball
tickets?
 What would happen to the market price
and quantity?
Cornell Women’s BB Market



An increase in the
price of CU men’s
hockey tickets, a
substitute, increases
the demand for
women’s basketball
tickets.
New price = P* and
new quantity
supplied = new
quantity demanded
= Q*.
Equilibrium price
and quantity both
rise.
Price
P*
P
Q
Q*
Quantity
Supply Generated Examples:
2 Different Markets – 2 Different Stories
Question
 How
would heavy rains in the Gironde
valley in September change the supply
of fine red wine?
 What would happen to the market price
and quantity?
Red Wine Market



Bad weather ruins
grapes and leads to a
decreased supply that
intersects the original
demand curve to the left
of the original
equilibrium.
New price = P* and
new quantity supplied
= quantity demanded
= Q*.
Price
P*
P
Equilibrium price
rises and equilibrium
quantity falls.
Q*
Q
Quantity
Question
 How
would a decrease in the price of
wood pulp change the supply of paper?
 What would happen to the market price
and quantity?
Paper Market



The decreased price
of wood pulp, an
input price,
increases the supply
of paper.
New price = P* and
new quantity
supplied = quantity
demanded = Q*.
Price
P
P*
Equilibrium price
falls and equilibrium
quantity rises.
Q Q*
Quantity
Review of Results

Increased demand: equilibrium price and
quantity both increase.

Decreased demand: equilibrium price and
quantity both decrease.

Increased supply: equilibrium price decreases
while quantity increases.
 Decreased
supply: equilibrium price increases
while quantity decreases.
Other Applications...



Many such application exist. Could go on and on and on.....
How about this: Suppose more than one thing happens at the
same time????
Last case...
– The Market:
» Automobile Gasoline Market in U.S. = gas
» Regular Grade
» The first two weeks of September
– The Events:
» Heavy Labor Day weekend and back to college travel expected AND AT
THE SAME TIME
» Some Persian Gulf event increases crude oil prices (crude oil is an input in
making gas)
– The Consequences
» Labor Day & back to school travel plans  increase in the demand for gas
» higher crude oil prices  decrease in the supply of gas
– Comparative Statics Result?
– What’s your prediction on what happens to P* and Q*?
Answer!
 Predict
that equilibrium gas prices go up for sure!
 Prediction on equilibrium quantity depends on
what is assumed about the relative magnitudes of
the shifts.
– IF demand shifts more than supply
» Q* will also increase
– IF supply shifts more than demand
» Q* will decrease
 Important
to know what you know and know what
you DON’T KNOW.
 Draw the pictures for yourself and check it out.