Download CHAPTER 6: LINEAR PROGRAMMING

CHAPTER 9:
DEMAND and SUPPLY
MODELLING
[1] DEMAND CURVE

In general, the demand for a product is dependent
upon the specifc unit price that is charged.




The selling price falls then the demand will rise ;
The selling price rises then the demand will fall;
An inverse relationship between demand and selling
price.
This type of relationship can be represented by:

qd = f(p)




qd stands for the quantity demanded ;
p stands for the unit price ;
f() is notational shorthand for saying 'depends upon ‘
Example : Cycle Safety-Helmet

A company manufactures and sells a particular
type of bicycle safety-helmet. The demand for
the company's product is given by :


qd = 900 - 30p — — ( 9.2 )
where p is in £'s and qd is in units of output per time
period.
How should we define the two axes ?
In terms of the x-axis , what range is
appropriate ?
How should the x-axis range be calibrated ?



p
qd
qs
0
900
0
5
750
100
10
600
200
15
450
300
20
300
400
25
150
500
30
0
600
SUPPLY CURVE



Demand curve describes the behaviour of
customers
Supply curve presents behaviour about the
supplier/manufacturer of the products
the quantity supplied and the price of a product that
can be captured as follows :

qs = g(p)



qs stands for the quantity supplied
p stands for the price
g( ) is notational convenience for saying 'depends upon'.

Cycle safety-helmet example, the supply
curve as follows :

qs = 20*p

The system of equations looks as follows :
qd = 900 - 30*p
qs = 0+ 20*p

EQUILIBRIUM point: the point of
intersection of two curve




( pe , qe )
At pe, consumers want to buy at this price are
able to do so.
At qe suppliers are able to sell all and are not
left with any unsold stocks.
EQUILIBRIUM CONDITION

The equality between demand and supply can
be written as :

qd = qs

Summary, the system of equations of
Demand-Supply model:

qd = 900-30*p
qs= 0 -20*p
qd = qs
(Demand curve )
( Supply curve )
( Equilibrium condition )

p1< pe: qd(p1) >qs(p1)



Quantity demanded will start to fall, reflecting
the fundamental behaviour of consumers
Quantity supplied will start to rise , reflecting
the fundamental behaviour of suppliers.
p2 > pe: qs(p2) >qd(p2)


Quantity demanded will increase , reflecting
the fundamental behaviour of consumers
Quantity supplied will decrease , reflecting the
fundamental behaviour of suppliers
SHIFTS in DEMAND and
SUPPLY


Some outside force was to come along and
influence the behaviour of either consumers
or producers, then the market equilibrium
would change.
Our problem now is to identify potential
sources of market disturbance.
Demand Curve Analysis

The range of factors that may typically
influence the demand

qd = f( p , adv , y , psub , pcomp )






qd-- the amount demanded ,
p--the price of the product,
adv--the amount of advertising spent on the product
y-- the income of consumers
psub--the price of a substitute product
pcomp--the price of a complementary product

Advertising

level of advertising to have a positive influence
on the demand for a product



For ANY given product price an increase in
advertising causes an increase in product demand
for ANY given product price a decrease in
advertising causes a decrease in product demand
The market research department has
estimated that the impact of this campaign will
be to increase product demand by 100 units at
each and every price level

Table 9.2

qd1 = 900 -30*p ( the initial demand curve)
qd2 = qd1 + 100
= 900 - 30*p +100
= 1000 -30p
(the demand curve AFTER the advertising campaign)
p
qdl
qd2
qd3
0
900
1000
850
5
750
850
700
10
600
700
550
15
450
550
400
20
300
400
250
25
150
250
100

Income




The analysis of changes follows a similar line of
reasoning to the advertising
consumer income increases - - more purchasing
power-- at any given product price, increase in product
demand-- outward shift in the demand curve.
consumer income decreases--reduction in demand--inward shift in the demand curve.
for example, increases income tax--the after-tax or
disposable income of consumers will fall-- inward shift
in product demand; Similarly , decrease in tax rates -increase disposable income – outward shift in demand
curves

Price of Substitutes


Substitutes are products with essentially the
same characteristics
the influence of the price of a substitute
product upon the demand :


for ANY given price of the PRODUCT of INTEREST
an INCREASE in the PRICE of the SUBSTITUTE
PRODUCT causes an INCREASE in the demand for
the product of interest.
for ANY given price of the PRODUCT of INTEREST
a DECREASE in the PRICE of the SUBSTITUTE
PRODUCT causes a DECREASE in the demand for
the product of interest.


a decrease in the price of a substitute product
will cause a reduction in the demand for the
product of interest,and hence an inward shift of
the relevant product demand curve.
an increase in the price of a substitute product
gives rise to an increase in the demand for the
product of interest, and hence to an outward
shift of the relevant demand curve.

Price of Complements

Complementary goods are products that
almost by definition have to be purchased in
conjunction. For example ,bicycles and safetyhelmets


for ANY given price of the PRODUCT of INTEREST
a DECREASE in the PRICE of a
COMPLEMENTARY good causes an INCREASE in
the demand for the product of interest.
for ANY given price of the PRODUCT of INTEREST
an INCREASE in the PRICE of a
COMPLEMENTARY good causes a DECREASE in
the demand for the product of interest.


a decrease in the price of a complement -- an
increase in the demand for the product-outward shift of the relevant demand curve.
an increase in the price of a complement-- a
decrease in the demand for the product -inward shift of the relevant demand curve.

Two types of demand curve movements

A SHIFT OF a DEMAND CURVE


changes in factors such as Advertising , Income , Price of
a Substitute , Price of a Complement will cause the whole
demand curve to sfift in the ( price , quantity ) space. This
type of change is often called a shift in the product
demand curve.
A SHIFT ALONG an EXISTING DEMAND CURVE.


if the price of a product falls , with all other factors being
held constant at some level , then there will be a
downward movement along the demand curve such that
the quantity demanded is increased.
This type of movement is often called an increase in the
quantity demanded. Similarly , a price increase gives to a
decrease in the quantity demanded.
Supply Curve Analysis

The range of factors that may typically
influence the Supply

qs = g( p , price of inputs , tax , innovation )





qs -- the supply of the product;
p-- the price of the product ;
price of inputs -- the prices of the factor inputs that
companies tend to use in output production.
tax -- the influence of sales type taxes upon the
behaviour of suppliers
Innovation-- the impact of changes in working processes
that influence output efficiency.

Price of Inputs



an increase in input prices -- a reduction in
product supply.
A decrease in input prices – an increase in
product supply.
Example




qs1=20p
qs2 = 40p
qs3 = 15p
p
qsl
qs2
qs3
0
0
0
0
5
100
200
75
10
200
400
150
15
300
600
225
20
400
800
300
25 '
500
1000
375
30
600
1200
450

Tax


If the supplier is suddenly faced with a higher
sales tax bill then they can afford to supply less
units of output, and thus the supply curve will
shift downwards.
For a reduction in sales tax any output level
can be supplied at a lower price and thus the
supply curve will shift upwards.

Innovation

Innovation --some form of technical innovation
which makes output production more efficient.



Modern computerised piece of machinery
Training and educating the workforce
An efficiency increasing investment upward
shift in the supply curve

Two type of supply curve movements


an increase (decrease ) in quantity supplied is
associated with a movement up (down ) an existing
supply curve , and is caused by an increase (decrease)
in the price of the product of interest with all other
factors being held constant.
a change in supply involves a complete shift in the
supply curve such that at any given price the amount
supplied changes. This is caused by a change in one of
the other factors of supply and the exact supply curve
movement is dependent upon the specific factor being
analysed.
MODELLING A CHANGING
MARKET

Two strands



demand and supply interact to establish a market
equilibrium.
external factors could cause the demand or
supply curve to shift.
These two strands is put together, some
issues should be addressed.



Given a change in external conditions , we
must be able to identify which relationship(s) is
affected.
QUALITATIVE prediction : to predict the
correct direction of change given a movement
in demand or supply.
Give correct numerical answers to the problem

Old Demand-Supply model




qd = 900-30*p (Demand curve )
qs= 0 +20*p ( Supply curve )
qd = qs
( Equilibrium condition )
Reduction in consumer income, then
demand for its product will fall by 100 units



qd = 800-30*p (Demand curve )
qs= 0 +20*p ( Supply curve )
qd = qs
( Equilibrium condition )



The equilibrium price has fallen -- pe2 < pel
The equilibrium quantity has fallen -- qe2 < qel
The change in the equilibrium price:


The change in the equilibrium quantity:


the change in pe = pe = pe2 – pel
The change in qe = qe = qe2 - qel
two types of movements :


the fall in price will cause a reduction in quantity
supplied as suppliers find the product less profitable.
the fall in price will cause a rise in quantity
demanded as the consumers move along their new
demand curve.

Numerical solution
Variable
Initial
Equilibrium
Value
New Equilibrium
Value
Change in
Equilibrium
Value
pe
18
16
pe=-2
qe
360
320
qe=-40

CPW for Demand and Supply
Modelling