Supply and Demand
Aggregated Behavior of
Producers and Consumer
Scarcity and Individual
Preferences


y
x = units of sheep
y = units of tobacco sticks
(x1,y1)
U(x,y) grows
(x3,y3)
(x2,y2)
x
Individual Demand

Valuation
P
p1
y
P: price per unit
q: quantity
x
p2
q
Aggregated Demand
P: Price per unit
P
P
+
q1
P
P
… +
Q: Total Quantity
=
q2
qn
QT
n
q1  q2  ...  qn  QT   qi
i 1
How to Represent Aggregated
Demand Functions
P

Two features
 Downward
 Highest willingness
to pay
Q
P
Indirect Demand Function
a
“P” is function of “Q”
P (Q ) = a - bQ
1
a: Highest willingnes to pay
b: Slope
b
Is there a Direct
Demand Function ?
Q
If Q increases in one unit
in the market
The price P decreases in
“b” units
From Indirect to Direct Demand
Functions (Math. Remark)
2 =1
2
y
= x
1
2
1 2
2
2
(y ) = ( x )
y(x)
2
y = x
1
x=y
2
x(y)
x
y
From Indirect to Direct
Demand Functions
P a
Q+ b = b
Indirect Demand Function:
P
P = a - bQ
P a - bQ
b = b
P a
b =b
-
bQ
b
-
Q +Q
P a
Q+ b = b
P P a
Q+ b - = b
b
-
P
b
A Direct Demand Function:
P a
b =b
Q
-
Q
a
Q =b
-
P
b
The Aggregated Demand
ai
qi = b
i
P = a - bQ
P
P
P
P
n
+
=
+
q1
q2
-
P
bi
qn
QT   qi  q1  q2  ...  qn
i 1
QT
Changes in Demand (Scarcitiy)

Substitute Goods
If price of a substitute good rises
P
The demand incrases (shifts to the right)
And viceversa
Q
Changes in Demand (Scarcitiy)

Complementary Goods
If price of a complementary good rises
P
The demand decreases (shifts to the left)
And viceversa
Q
Aggregated Supply

The structure of the supply function
P
The costs of the k-th unit ck
Fixed cost per unit
c0
The cost of the first unit c1
qi
1
k
Market Mechanism
If the demand and the supply are fixed (stable),
an equilibrium (q*,p*) is reached.

P
QS Quantity supplied
QS
QD Quantity demanded
Q* Optimal Quantity in the market
p*
p* Optimal price in the market
QD
Q*
Q
(Q*,p*)  Qs = QD
P
QS
Market Mechanism
p*
QD
Q*
Q
(Q*,p*)  Qs = QD = =Q*
P = a - bQD ; P =  + QS
 + QS = a - bQD
 + QS -  = a - bQD - 
QS = a - bQD - 
QS + bQD = a -  - bQD + bQD
QS + bQD = a - 
Q* + bQ* = ( + b)Q* = a - 
( + b)Q* = a - 
( + b)
( + b)
Q* = (a -+b)
P =  + QS =  + ( a -  )
+b
Elasticity (Introduction)

Percentage
p
If one price falls from 19€ to 15€
then the percentual change of
the price is:
19 - 15
19
19€
15€
4
=
* 100 = 21,05%
* 100
19
We say:
The % change of the price is:
Pf - Pi
P
=
Pi * 100
P * 100
0
Elasticity
p
Pf - Pi
P
Pi * 100 = P * 100
Let consider the mentioned
change takes place in a market
19€
?
15€
How much is the percentual
change of the demand?
The Elasticity measures this change
in percentage

:
Q
Q * 100
P
P * 100
=
Q
Q
P
P
=
P
Q
.
Q
P
0
Q
Q
P
: The slope of the Demand
function
Arc Elasticity

The Arc elasticity measures the changes in a market, not in a point but
within an interval.
P

(P2,Q2)
P1 + P2
2
=
P
(P1,Q1)
0
Q
Q
=
Q1 + Q2
2
:
P
Q
.
Q
P