SYSTE

M OF

LINEAR

EQUATIO

NS

VI V

I AN

AN

D A

SH

L EY

LINEAR DEMAND FUNCTIONS

• Shows the relationship between QUANTITY DEMANDED of the product and PRICE

QD= a – bP• ‘a’ = quantity demanded if price is 0

• ‘b’ = slope of curve

EXAMPLE: CHANGE IN ‘A’

Q D = 500 – 10P

Prices ($) Calculation

QD

0 600 - (10X0) 600

10 600 - (10X10) 500

20 600 - (10X20) 400

30 600 - (10X30) 300

40 600 - (10X40) 200

Q D = 600 – 10PPrices ($)

Calculation QD

0 500 - (10X0) 500

10 500 - (10X10) 400

20 500 - (10X20) 300

30 500 - (10X30) 200

40 500 - (10X40) 100

GRAPHICAL REPRESENTATION

100 200 300 400 500 600 7000

10

20

30

40

50

Quantity

Pri

ce

CHANGE IN ‘A’ =

HORIZONTAL SHIFT OF THE DEMAND CURVE

EXAMPLE: CHANGE IN ‘B’

Q D = 500 – 10P

Prices ($) Calculation

QD

0 500 – (20X0) 500

10 500 – (20X10) 300

20 500 – (30X10) 100

Q D = 500 – 20PPrices ($)

Calculation QD

0 500 - (10X0) 500

10 500 - (10X10) 400

20 500 - (10X20) 300

30 500 - (10X30) 200

40 500 - (10X40) 100

GRAPHICAL REPRESENTATION

100 200 300 400 5000

10

20

30

40

50

Quantity

Pri

ce

CHANGE IN ‘B’ =

CHANGE IN SLOPE OF THE DEMAND CURVE

*CHANGE IN SLOPE IS DIFFERENT FROM CHANGE IN ELASTICITY

SUMMARY

• ‘a’ and ‘b’ will be affected by changes in the non-price determinants of demand

• Examples of non-price determinants of demand• Income• Price of other products• Tastes/Preferences

LINEAR SUPPLY FUNCTIONS

• Shows the relationship between QUANTITY SUPPLIED of the product and PRICE

QS= c – dP• ‘c’ = quantity demanded if price is 0

• ‘d’ = slope of curve

SUMMARY

• Almost identical to the demand linear function

• Change in ‘c’ = parallel shift in curve

• Change in ‘d’ = change in slope of the curve

SUMMARY

• ‘c’ and ‘d’ will be affected by changes in the non-price determinants of supply

• Examples of non-price determinants of supply• The cost of factors of production• The state of technology• Expectations

MARKET EQUILIBRIUM

• The intersection between demand curve and supply curve

QD= QS

a – bP = c – dP

Prices ($)

Calculation

QD

0 2000 – 0 2000

1 2000 – 200 1800

2 2000 – 400 1600

3 2000 – 600 1400

4 2000 – 800 1200

5 2000 – 1000 1000

6 2000 – 1200 800

EXAMPLEQD = 2000 – 20P Qs = -400 – 400P

Prices ($)

Calculation

QS

0 –400 + 0 –400 1 –400 + 400 0

2 –400 + 800 400

3 –400 + 1200 800

4 –400 + 1600 1200

5 –400 + 2000 1600

6 –400 + 2400 2000

QD = 2000 – 200(4)

QD = 1200 units

QS = –400 +400(4)

QS = 1200 units

EXAMPLE

2000 – 20P = –400 – 400P2400 = 600P

P = $4

or

GRAPHICAL REPRESENTATION

400 600 800 1000120014001600180020000

1

2

3

4

5

6

7

Quantity

Pri

ce