CHAPTER 9 DEMAND and SUPPLY MODELLING 1 DEMAND

CHAPTER 9: DEMAND and SUPPLY MODELLING

[1] DEMAND CURVE n In general, the demand for a product is dependent upon the specifc unit price that is charged. q q n n The selling price falls then the demand will rise ; The selling price rises then the demand will fall; An inverse relationship between demand selling price. This type of relationship can be represented by:

q qd = f(p) n n qd stands for the quantity demanded ; p stands for the unit price ; f() is notational shorthand for saying 'depends upon ‘ Example : Cycle Safety-Helmet q A company manufactures and sells a particular type of bicycle safety-helmet. The demand for the company's product is given by : n n qd = 900 - 30 p — — ( 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 ? q q q p qd qs 0 900 0 5 750 10 600 200 15 450 300 20 300 400 25 150 500 30 0 600

SUPPLY CURVE n n n 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 : q qs = g(p) n n n qs stands for the quantity supplied p stands for the price g( ) is notational convenience for saying 'depends upon'.

n Cycle safety-helmet example, the supply curve as follows : q qs = 20*p

n The system of equations looks as follows : qd = 900 - 30*p qs = 0+ 20*p

n EQUILIBRIUM point: the point of intersection of two curve q q q n ( pe , qe ) At pe, consumers want to buy at this price are able to do so. At qe suppliers are able to sell and are not left with any unsold stocks. EQUILIBRIUM CONDITION q The equality between demand supply can be written as : n qd = qs

n Summary, the system of equations of Demand-Supply model: q qd = 900 -30*p qs= 0 -20*p qd = qs (Demand curve ) ( Supply curve ) ( Equilibrium condition )

n p 1< pe: qd(p 1) >qs(p 1) q q n Quantity demanded will start to fall, reflecting the fundamental behaviour of consumers Quantity supplied will start to rise , reflecting the fundamental behaviour of suppliers. p 2 > pe: qs(p 2) >qd(p 2) q q 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 n n 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 n The range of factors that may typically influence the demand q qd = f( p , adv , y , psub , pcomp ) n n n 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

n Advertising q level of advertising to have a positive influence on the demand for a product n n q 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

n Table 9. 2 n qd 1 = 900 -30*p ( the initial demand curve) qd 2 = qd 1 + 100 = 900 - 30*p +100 = 1000 -30 p (the demand curve AFTER the advertising campaign) p qdl qd 2 qd 3 0 900 1000 850 5 750 850 700 10 600 700 550 15 450 550 400 20 300 400 25 150 250 100

n Income q q 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

n Price of Substitutes q q Substitutes are products with essentially the same characteristics the influence of the price of a substitute product upon the demand : n n 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.

q q 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.

n Price of Complements q Complementary goods are products that almost by definition have to be purchased in conjunction. For example , bicycles and safetyhelmets n n 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.

q q 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.

n Two types of demand curve movements q A SHIFT OF a DEMAND CURVE n q 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. n n 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 n The range of factors that may typically influence the Supply q qs = g( p , price of inputs , tax , innovation ) n n n 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.

n Price of Inputs q q q an increase in input prices -- a reduction in product supply. A decrease in input prices – an increase in product supply. Example n n qs 1=20 p qs 2 = 40 p qs 3 = 15 p

p qsl qs 2 qs 3 0 0 5 100 200 75 10 200 400 15 300 600 225 20 400 800 300 25 ' 500 1000 375 30 600 1200 450

n Tax q q 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.

n Innovation q Innovation --some form of technical innovation which makes output production more efficient. n n q Modern computerised piece of machinery Training and educating the workforce An efficiency increasing investment upward shift in the supply curve

n Two type of supply curve movements q q 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 n Two strands q q n demand 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.

q q q 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

n Old Demand-Supply model q q q n 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 q qd = 800 -30*p (Demand curve ) qs= 0 +20*p ( Supply curve ) qd = qs ( Equilibrium condition )

q q q The equilibrium price has fallen -- pe 2 < pel The equilibrium quantity has fallen -- qe 2 < qel The change in the equilibrium price: n q The change in the equilibrium quantity: n q the change in pe = pe 2 – pel The change in qe = qe 2 - qel two types of movements : n n 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.

n Numerical solution

Variable Initial Equilibrium Value New Equilibrium Value Change in Equilibrium Value pe 18 16 pe=-2 qe 360 320 qe=-40

n CPW for Demand Supply Modelling