Supply and Demand
Aggregated Behavior of Producers and Consumer
Scarcity and Individual Preferences
xx
yy
xx = units of sheep yy = units of tobacco sticks
(x2,y2)
(x1,y1)
(x3,y3)
U(x,y) grows
Individual Demand
ValuationP: price per unit
q: quantity
xx
yy P
q
p1
p2
Aggregated Demand
P: Price per unit
Q: Total Quantity
+ … + =
P
q1
P
q2
P
qn
P
QT
n
iiTn qQqqq
121 ...
How to Represent Aggregated Demand Functions Two features
Downward Highest willingness
to pay
P
Q
Q
P
P( )Q“P” is function of “Q”
= a - bQa: Highest willingnes to pay
b: Slope
IndirectIndirect Demand Function
Is there a DirectDirect Demand Function ?
a
1
b If Q increases in one unit in the market
The price P decreases in “b” units
From Indirect to Direct Demand Functions (Math. Remark)
y = x12
y(x)
x
x(y)
y
y = x12( )2 ( )2
22
= 1
y = x2 1 x = y2
From Indirect to Direct Demand Functions
P
Q
A DirectDirect Demand Function:
IndirectIndirect Demand Function: P = a - bQ
Pb =
=
a - bQb
Pb
ab
- bQb
=Pb
ab
- Q
=ab
Pb
- Q +Q+Q
=ab
Pb+Q - P
b- Pb
=abQ - P
b
=ab
Pb+Q
The Aggregated Demand
n
n
iiT qqqqQ
...211+ + =
P
q1
P
q2
P
qn
P
QT
P = a - bQ =aii
biiqii
- Pbii
Changes in Demand (Scarcitiy)
Substitute Goods
P
Q
If price of a substitute good rises
The demand incrases (shifts to the right)
And viceversa
Changes in Demand (Scarcitiy)
Complementary Goods
P
Q
If price of a complementary good rises
The demand decreases (shifts to the left)
And viceversa
Aggregated Supply
The structure of the supply function
Fixed cost per unit
P
qii
ck
c1
1
The cost of the first unit
k
The costs of the k-th unit
c0
Market Mechanism If the demand and the supply are fixed (stable),
an equilibrium (q*,p*) is reached.
P
QQ*
p*
QSQS Quantity supplied
QD
QD Quantity demanded
Q* Optimal Quantity in the market
p* Optimal price in the market
(Q*,p*) Qs = QD
Market Mechanism
P
QQ*
p*
QS
QD
(Q*,p*) Qs = QD = =Q*
P = a - bQP = a - bQDD ;; P = P = + + QQSS
+ + QQSS = = a - bQa - bQDD
+ + QQSS - - = = a - bQa - bQDD - -
QQSS = = a - bQa - bQDD - -
QQSS ++ bQbQDD = = a a - - - bQbQDD + bQ+ bQDD
QQSS ++ bQbQDD = = a a - -
QQ** ++ bbQQ** = (= ( + + bb))QQ** = = a a - -
(( + + bb))QQ** = = a a - - (( + + bb)) (( + + bb))
a a - - (( + + bb))==Q*
P = P = + + QQSS = = + + ( )( )a - a - + b+ b
Elasticity (Introduction)
Percentage p
0
If one price falls from 19€ to 15€
19€
15€then the percentual change of the price is:
19 - 15
19* 100 =
419
* 100 = 21,05%
We say:
The % change of the price is:
Pf - Pi
Pi PP=* 100 * 100
Elasticityp
0
19€
15€
Pf - Pi
Pi PP=* 100 * 100
Q
Let consider the mentioned change takes place in a market
How much is the percentual change of the demand?
?
The Elasticity measures this change in percentage
:QQPP
* 100
* 100=
QQPP
=P
Q. Q
P
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
0 Q
(P2,Q2)
(P1,Q1)
Q1 + Q2Q = 2
:P
Q. Q
PP1 + P2
P=2
