CHAPTER 9: DEMAND and SUPPLY MODELLING

1. CHAPTER 9: DEMAND and SUPPLY MODELLING

2. [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:

3. 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.

5. p qd qs 0 900 0 5 750 100 10 600 200 15 450 300 20 300 400 25 150 500 30 0 600 • 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 ?

6. 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'.

7. Cycle safety-helmet example, the supply curve as follows : • qs = 20*p

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

9. 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

10. 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 )

11. 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

13. 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.

14. 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

15. 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

16. 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 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)

18. 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

19. 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.

20. 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.

21. 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.

22. 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.

23. 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.

24. 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.

25. 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

26. 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

28. 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.

29. 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

30. 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.

31. 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.

32. 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

33. 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 )

35. 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.

36. Numerical solution

38. CPW for Demand and Supply Modelling