Supply and Demand
Aggregated Behavior of
Producers and Consumer
Scarcity and Individual
Preferences
y
(x1,y1)
x = units of sheep
y = units of tobacco sticks
U(x,y) grows
(x3,y3)
(x2,y2)
x
Individual Demand
Valuation
P
p1
y
P: price per unit
q: quantity
x
p2
q
1
Aggregated Demand
P: Price per unit
P
P
P
+
… +
q1
Q: Total Quantity
P
=
qn
q2
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
a: Highest willingnes to pay
1
b: Slope
b
If Q increases in one unit
in the market
Is there a Direct
Demand Function ?
The price P decreases in
“b” units
Q
From Indirect to Direct Demand
Functions (Math. Remark)
2 =1
2
1
y
= x2
1 2
2
( y ) = ( x2 )
y(x)
2
y = x
1
x=y
2
x(y)
x
y
2
From Indirect to Direct
Demand Functions
P a
Q+ b = b
Indirect Demand Function:
P = a - bQ
P a
b =b
-
Q +Q
P a
Q+ b = b
P a - bQ
b = b
P
-
P P a
Q+ b - = b
b
bQ
b
-
P
b
A Direct Demand Function:
P a
b =b
-
Q
a
Q =b
-
P
b
Q
The Aggregated Demand
a
qi = bi
i
P = a - bQ
P
P
P
-
P
bi
P
n
+
=
+
q1
QT =
q2
∑q
i
= q1 + q 2 + ... + q n
i =1
qn
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
3
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
c0
Fixed cost per unit
The cost of the first unit c1
1
k
qi
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*,p*) ⇐ Qs = QD
Q
4
P
QS
Market Mechanism
p*
QD
Q*
Q
(Q*,p*) ⇐ Qs = QD = =Q*
βQ* + bQ* = (β + b)Q* = a - α
P = a - bQD ; P = α + βQS
(β + b)Q* = a - α
(β + b)
(β + b)
α + β QS = a - bQD
α + β QS - α = a - bQD - α
Q* = (aβ -+αb)
βQS = a - bQD - α
P = α + βQS = α + β( a - α )
βQS + bQD = a - α - bQD + bQD
β+b
βQS + bQD = a - α
Elasticity (Introduction)
Percentage
p
If one price falls from 19€ to 15€
19€
then the percentual change of
the price is:
19 - 15
19
15€
4
* 100 = 19* 100 = 21,05%
We say:
0
The % change of the price is:
Pf - Pi
∆P
Pi * 100 = P * 100
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
ε
:
∆Q
Q * 100
∆P
P * 100
=
∆Q
Q
∆P
P
=Q.
P
∆Q
∆P
0
Q
∆Q
∆P
: The slope of the Demand
function
5
Arc Elasticity
The Arc elasticity measures the changes in a market, not in a point but
within an interval.
P
ε
(P2,Q2)
P1 + P2
2
=
:
P
Q
.
∆Q
∆P
P
(P1,Q1)
0
Q
Q
=
Q1 + Q2
2
6