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
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