Supply and Demand Aggregated Behavior of Producers and Consumer.

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