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 l

eft 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 (Demand curve )

qs= 0 -20*p ( Supply curve )

qd = qs ( Equilibrium condition )

p1< pe: qd(p1) >qs(p1) Quantity demanded will start to fall, reflecting t

he fundamental behaviour of consumers Quantity supplied will start to rise , reflecting th

e 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 in

fluence 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

qd1 = 900 -30*p ( the initial demand curve) qd2 = qd1 + 100

= 900 - 30*p +100 = 1000 -30p

(the demand curve AFTER the advertising campaign)

Table 9.2

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 safety-helmets 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 h

eld 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 comp

anies tend to use in output production. tax -- the influence of sales type taxes upon the behavio

ur 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 associat

ed 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 pe = pe = pe2 – pel The change in the equilibrium quantity:

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