St. Philomena’s College, Mysore-15
Module II : Economic application of linear functions:
ByMs. Rashmi P
Maharaja’s College,
Mysore
I part A -2 marks questions:
1. The demand for function for a commodity is D=36-3P what is the quantity demand, if
price is Rs 3:and if it is a free goods what is the quantity demand?
We have demand equation:
D=36-3P at P=3
D=36-3(3)
=36-9
= 27 units
If it is a free good put P=0
D=36-3(0)
=36 units
2. The supply function is given as S=5P-10,find the quantity supplied if price is Rs 6, if
supply is zero, what is the price?
S=5P-10
S=5P-10
S=5(6)-10
S=20
If S=0
0=5P-10
10
P=
=2
5
Ap=6, S=20
P=2
3. The demand function is given as qd=12-2P construct the demand schedule?
Qd = 12-2(6)=0
Qd = 12-2(5)=2
Qd = 12-2(4)=4
Qd = 12-2(3)=6
Qd = 12-2(2)=8
Qd = 12-2(1)=10
Qd = 12-2(0)=12
File: ECO WORKSHOP-2005
X
0
2
4
6
8
10
12
P
6
5
4
3
2
1
0
1
St. Philomena’s College, Mysore-15
4. The specific supply function is QS=20P construct the supply schedule?
X
120
100
80
60
40
20
0
Qs=20 (6)= 120
Qs=20 (5)= 100
Qs=20 (4)= 80
Qs=20 (3)= 60
Qs=20 (2)= 40
Qs=20 (1)= 20
Qs=20 (0)= 0
P
6
5
4
3
2
1
0
5. The specific demand function is Qd=15-3P construct a demand schedule?
Qd=15-3P
15-3(0)=15
15-3(1)=12
15-3(2)=9
15-3(3)=6
15-3(4)=3
15-3(5)=0
P
0
1
2
3
4
5
Qd
15
12
9
6
3
0
6. The demand function is 5-2P construct a demand schedule?
5-2p
5-2(0)=5
P
Qd
5-2(1)=3
0
5
5-2(2)=1
1
3
5-2(3)=-1
2
1
5-2(4)=-3
3
-1
5-2(5)=-5
4
-3
5
-5
7. If the demand function is Qd=-1.5P+10 construct a demand schedule?
-1.5P+10
-1.5(0)+10=10
-1.5(1)+10=8.5
-1.5(2)+10=7
-1.5(3)+10=5.5
-1.5(4)+10=4
-1.5(5)+10=2.5
File: ECO WORKSHOP-2005
Qd
10
8.5
7
5.5
4
2.5
P
0
1
2
3
4
5
2
St. Philomena’s College, Mysore-15
8. If the demand function is Qd=-3P+14 construct a demand schedule?
Q d –3P+14
Q d= -3(0)+14=14
Q d= -3(1)+14=11
Q d= -3(2)+14=8
Q d= -3(3)+14=5
Q d= -3(4)+14=2
Q d= -3(5)+14=-1
1.
Qd
14
11
8
5
2
-1
P
0
1
2
3
4
5
If the demand function for any commodity is 100P-88=P what is the price
at which quality demand is 0.04?
100D-88=P
100(0.04)-88=P
P=84
10. If the demand function is D=25-3X construct a demand schedule?
S=25-3x
S=25-3(0)=25
S=25-3(1)=22
S=25-3(2)=19
S=25-3(3)=16
S=25-3(4)=13
X
0
1
2
3
4
Y
25
22
19
16
13
11. If the supply function is S=15X+8 construct a supply schedule?
S=15x+8
S=15(0)+8=8
S=15(1)+8=23
S=15(2)+8=38
S=15(3)+8=53
S=15(4)+8=68
X
0
1
2
3
4
Y
8
23
38
53
68
12. Given straight-line 3Y+X=15 find the intercept of a slope?
3Y+X=15
15  X 1
 5
Y=
3
3
1
1
Y=  5
Y= x  5
3
3
File: ECO WORKSHOP-2005
3
St. Philomena’s College, Mysore-15
13. If the function is in the form of
3  4 X 4Y  8

prove that it is a linear demand equation?
3
3
3  4 X 4Y  8
3
3
9-12X=16Y-32
12X-16Y=9+32
12X-16Y=41
16Y=-12X+41
PART – B: 5 Marks Questions:
1) Calculate the slope of the line given as: C-10, 20 and D= 40,30?
Ans : Find the co-ordinates. Write it as:
C = (10,20)
x1 y1
Slope :
D : (40-30)
x2 y2
x2  y1
x1  y 2
=
30  20
40  10
=
10
3
=
1
3
2) Given the equation 4x + 2y = 7. Find the in intercept on both axes?
4x
7
2y
7
+
=1
y
x
+
=1
7
7
4
2
Intercept on ‘x’ axis is 7
Intercept on ‘y’ axis is 7
4
2
3) Graph the two equations P=25-3x and S=15x+8. Find graphically their interaction.
y = 25 – 3x
y = 25 – 3(0)=25
y = 25 – 3(1)=22
y = 25 – 3(2)=19
y = 25 – 3(3)=16
y = 25 – 3(4)=13
File: ECO WORKSHOP-2005
x
0
1
2
3
4
y
25
22
19
16
13
4
St. Philomena’s College, Mysore-15
Supply Curve :
y = 15x + 8
y = 15 (0) + 8 = 8
y = 15 (1) + 8 =23
y = 15 (2) + 8 =38
y = 15 (3) + 8 =53
x
0
1
2
3
y
8
23
38
53
150
S
140
120
100
Demand
and
supply
80
60
40 D
E
20
S
1
D
2
3
4
5
6
Price
4) Some 100 students wish to participate in excursion when the fee is Rs. 50, if fee is brought
down to 25, some 150 students are ready to take part. Construct the demand equation for the
trip. Find the two coordinates.
(50,100)
x1 y1
Slope :
x  50
y  100
x  50
y  100
File: ECO WORKSHOP-2005
(25 - 150)
x2 y2
=
=
25  50
x  50
=
150  100
y  100
=
 25
1
=
50
2
1
2
5
St. Philomena’s College, Mysore-15
2 (x-50) = -1(y-100)
2x – 100 = - y + 100
2x – 100 – 100 = - y
- y = 2x - 200
y = - 2x + 200
5) In a market, commodity mango is supplied by 50 units at price Rs. 1. if price raises by 2,
Supply increases to 75units. Construct the supply equation if x is quantity supplied, and ‘y’ is
price.
Ans: Co-ordinates: (50,1)
(75, 2)
Apply two-point formula.
 y  y1 

y – y1  2
 x2  x1 
x1 =50 y1 =1
x2 =75 y2 =2
2 1
75  50
(y-1) =
y–1= 1
= (x – x1)
(x – 50)
(x – 50)
25
x = 25y + 25
s = 25p + 25
6) The demand for apple is 40 if price 2, suppose price rises to Rs. 5 demand for apple is 20 in
the market, construct the demand equation?
Coordinates
40, 2
Apply the two-point formula
 52 

 (x – 40)
 20  40 
y–2
y=2
y=
20, 5
3
20
(x – 40)
 3x
+4
20
3x = 80 – 20y
File: ECO WORKSHOP-2005
6
St. Philomena’s College, Mysore-15
7) The price of the ice creams Rs. 1, 100. Ice cream will be demanded if the price increases to
Rs. 2,
50 ice creams will be demanded construct the demand schedule for the above
information.
Co ordinates
100,1 50,2
Apply the two-point method formula:
X1=100
X2=50
Y1=1 Y2=2
Y-1 =
2 1
( X  100)
50  100
Y = 1-
1
( X  100)
50
Y=
X
1 2
50
Y=
X
3
50
X=50-50Y
File: ECO WORKSHOP-2005
7
St. Philomena’s College, Mysore-15
8. If the demand function is in the form of Qd=15-3P construct the demand schedule and
curve?
P
0
1
2
3
4
5
Qd=15-3(0)=15
Qd=15-3(1)=12
Qd=15-3(2)=9
Qd=15-3(3)=6
Qd=15-3(4)=3
Qd=15-3(5)=0
Y
Qd
15
12
9
6
3
0
D
15
0.5
14
13
12
1.12
11
10
9
8
7
6
2.9
5
4
3.6
3
2
4.3
1
0
1
2
3
4
D
5 X
9. Demand function is given as 12-2Pconstruct a schedule graph?
Qd=12-2(6)=0
Qd=12-2(5)=2
Qd=12-2(4)=4
Qd=12-2(3)=6
Qd=12-2(2)=8
Qd=12-2(1)=10
Qd=12-2(0)=12
File: ECO WORKSHOP-2005
X
0
2
4
6
8
10
12
P
6
5
4
3
2
1
0
8
St. Philomena’s College, Mysore-15
0.6
6
5
(2.5)
4
(4.4)
3
(6.3)
2
(8.2)
1
(10.1)
1
2
3
4
5
6
7
8
9
10
11
(12.0)
12
10 Marks Questions:1) Consider the following demand and supply functions. Qd = 50 – p, Qs = 2p – 25,
where ‘P’ represents price per unit, Qd & Qs – quantity demand & supply. If the govt.
decides to levy a specific tax of Rs.5 per unit find the new equilibrium price and
quantity. Illustrate your results on the graph
Effect of tax:
i) Price increases P1 - P
ii) Fall in quantity demand x – x1
equilibrium Qd  Qs Before the tax
50-p=2p-25
– p - 2p = -50 –25
-3p = -75
3p = 75
Before tax
75
p 
P  25
3
Qd  25
Substitute the value of ‘p’ in the demand equation we have:
Qd = 50 –p
Qs = 2p –25
Qd = 50 –25 = 25.
Qs = 2(25) – 25 = 25.
Effect of tax:
(x) Qd = 50 –p.
File: ECO WORKSHOP-2005
tax - Rs.5 per unit price tax.
9
St. Philomena’s College, Mysore-15
After the tax:
x = 50 –p.
the tax is on supplier and also it is per unit price tax.
Supply function:
x = 2p –25.
-2p = -x – 25
2p = x +25.
x 25
p 
 perunit
2 2
Price of the commodity
After the tax the new supply function is
 x 25 
p      5 (tax)
2
2
Equilibrium price & quantity after the tax:
Qd  Qs
x = 50 –p
D = p = 50 –x
 x 25 
s p    5
2 2 
x 35
p 
2 2
x 35
50  x  
2 2
x
35
  50 
2
2
3
 100  35  65
x

2
2
2
x
3
 65
x
2
2
3
65
x
2
2
After the tax
65
x1 
3
1
65 2

2 3
1
65
x
3
x
After the tax the new equilibrium quantity is x1
File: ECO WORKSHOP-2005
p1
85
3
65
3
10
St. Philomena’s College, Mysore-15
Substituting the value of x is the
p = 50 – x we have
65
p  50 
3
65 85
p  150  
3
3
Graph:Before tax:
Demand
x  50  p
supply
x  2 p  25
p  50  x
x
p
x 25
p 
2 2
x
p
0
50
0
25
25
25
25
12.5
2
25
30
20
35
30
After the tax
x  50  p
x 35
s 
2 2
(5 tax)
x
y
35
2
85
28.3
3
25
0
21.6 65
3
35
Y (0.50)
S
50
E1
40
S1
25,25
E
30
S
E
S1
20
0,12
S
10
M
0
5
File: ECO WORKSHOP-2005
10
15
20
M1
25
30
35
40
X
11
St. Philomena’s College, Mysore-15
2) Given the demand & supply function:
D : x = 200 –5p
S : x = 4p –79
If the Govt. imposes a specific tax of Rs. 2 per unit on the supplier find the new equilibrium price
Quantity? Show your result on the graph?
Equilibrium before the tax :
x = 200 –5p
 5P  200  X
200 x

5
5
x
D  40 
5
x  4 p  79
p
 4 p   x  79
x 79

4 4
x 79
SP 
D=S-Before
4 4
p
D=S
40-
Before Tax Market equilibrium Q.D  QS
x x 79
 
4 4 4
x x

5
4
= - 40 +
79
4
x x
79
  40 
5 4
4
4 x  5x
160  79
81


20
4
4

x  45

p  31
9 x 81

20 4
9
x
5
81 20

 45
4 9
1 1
Substitute the value of ‘x’ in any equation
File: ECO WORKSHOP-2005
12
St. Philomena’s College, Mysore-15
P  40 
x
5
45
5
P  40  9  31
40 
After the tax, if tax of Rs. 2 is levied as specific tax.
x
5
 x 79 
S= P=     2
4 4 
x 87
P= 
4 4
P: 40 
After the tax equilibrium is at D=S.
x x 87
 
5 4 4
 x x 87
 
 40
5
4 4
x x 87
 
 40
5 4 4
P  40 
5 x  4 x  87 160

20
4
9
73
x
20
4
5
73 20 365
x


4 9
9
1
After the tax
x
1
365
9
P1 
287
9
Substitute the value with demand equation:
P  40 
365
9
P  40 
365
45
File: ECO WORKSHOP-2005
13
St. Philomena’s College, Mysore-15
287
1800  365 1435
P

45
45
9
GRAPH:
Before Tax:
Demand:
S=
P  40  9
x 79

4 4
5
Qd
X
P
0
79
45
31
0
45
50
(19.35)
4
P
40
31
30
After the tax
87
Px 
4 4
x
y
0
87
(40.5) 365
(21.75)
4
287 (32)
9
9
Y
50
45
S1
D (0.40)
(40.532)
40
S
E1
E
35
D
(45.31)
30
Qd
and
Qs
25 (0.21.75)
(0,19.35)
s1
20
S
15
10
5
0
10
20
30
40
50
X
Price
File: ECO WORKSHOP-2005
14
St. Philomena’s College, Mysore-15
3) The demand supply functions are:
D:P=100-2x, S:P=3x-50 and Specific tax on the supplier is Rs. 5 per unit find the new
equilibrium price and quantity.
Illustrate your results on the graph:
Before tax:
Qd  QS
100-2x=3x-50
-2x-3x=-100-50
5x=150
150
 30
x=
5
x  30
P  40
Substitute the value of x in demand equation we have:
P=100-2(30)
P=40
After the tax:
D=100-2x
S=
P=(3x-50)+5:
Equilibrium: Qd  QS:
x 29
p 42
1
1
100-2x = 3x-45
-2x-3x = -45-100
= - 5x = -145
5x = 145
x=
145
 29
5
Substitute the Value of ‘x’ with the equation we have:
P=100-2 (29)
P= 100-58
P=42
Graph:
Before tax:
File: ECO WORKSHOP-2005
15
St. Philomena’s College, Mysore-15
Demand
Supply
x-y
x-y
P= 100-2(10) = 70
P= 100-2(30) = 40
P= 100-2(40) = 20
10- 70
30- 40
40- 20
10 - 20
30 - 40
S= P= 3x-50
3(10)-50
30-50=20
3(30)-80=40
After the tax:
S=3x-45
3(15)-45=0
3(29)-45=42
X
15
29
Y
0
42
Y
S1
70 D
S
60
E
E1
50
(4.2)
40
(3.6)
S1
D
30
S
(0, 12)
20
10
0
10
20
30
40
50
X
4) The demand law is D=15-3y and the supply law is S=2y-3, find the new equilibrium price
and quantity if an additive specific tax of Rs. 2 per unit is imposed, graph your results?
Before Tax
15-3y = 2y – 3:
-3y – 2y = -15-3
= -5y = -18
18
 3 .6
y=
5
File: ECO WORKSHOP-2005
Qd  QS
Before Tax
x  4 .2
p  3 .6
16
St. Philomena’s College, Mysore-15
Substitute the value in either demand or supply equation
Qd= 15-3y
15-3 (3.6) =4.2
Supply: S = 2(3.6) – 3 = 4.2
After the Tax:
Demand function remains as it is.
D = 15 – 3y
Add the tax Rs. 2 to the supply function:
S = (2y-3) 2
S = 2y-1
Equilibrium after the tax Qd  Qs
15 – 3y = 2y – 1
P1 = 3.2
- 3y – 2y = -15 - 1
X1 = 5.4
= - 5y = - 16
16
y=
=3.2
5
Substitute the value in the demand function:
D = 15 – 3 (3.2) = 5.4
F–
S =2(3.2) – 1 =5.4
Graph:
Before Tax
Demand:
D = 15 – 3y
= 15 – 3(0) =12
= 15 – 3(3.6) = 4.2
x
0
3.6
y
12
4.2
Supply Function:
S = 2y – 3
2(2) – 3 =
2(3.6) – 3 = 4.2
After the tax
2y – 1
2(1) – 1
2–1=1
2(3.2) – 1 = 5.4
File: ECO WORKSHOP-2005
x
1
3.2
y
1
5.4
17
St. Philomena’s College, Mysore-15
Y
Y
D
12
11
10
S1
9
S
8
7
6
P1
5
P
4
E1
E
3
2
S1
1
0
D
S
1
2
x
3
x
4
5
6
X
Problems on Subsidy:
1) The demand function is P = 50 – x and supply function is P = 2x- 25. if the government
offers a subsidy of Rs. 15 per unit. Find the changes in price and quantity demanded
and graph it
The effects of subsidy:
i) Price goes down
ii) Quantity demanded increases.
Equilibrium before subsidy Qd  Qs
50 – x = 2x – 25
- x – 2x = -50 - 25
= - 3x = - 75
3x = 75
75
x=
=25
3
File: ECO WORKSHOP-2005
x1 = 25
p1 = 25
18
St. Philomena’s College, Mysore-15
Substitute the value either in the equation we have:
P = 50 – x
P = 50 – 25
P = 25
After subsidy:
Take the demand function:
P = 50 – x
But supply observe the subsidy
P = (2x - 25) - 15
P = 2x – 40
Equilibrium after the tax Qd = Qs
50 – x = 2x – 40
- x – 2x = -50 - 40
= - 3x = - 90
3x = 90
90
x=
= 30
3
x1 = 20
p1 = 30
Substitute the value
50 – 30 = 20
The reduction in price P – P1 = 25 – 20 = 5. Increase in the quantity demanded.
x1 – x = 30 – 25 = 5
File: ECO WORKSHOP-2005
19
St. Philomena’s College, Mysore-15
Graph : -
Before equilibrium:
Demand
P = 50 – x
50 – 0 = 50
50 – 25 = 25
2x – 25
2(20) – 25
40 – 25 = 15
2 (25) – 25 = 25
x y
0 50
25 25
Supply
x y
20 15
25 25
After subsidy
Supply function
P = 2x – 40
2(20) – 40
2(30) – 40 =20
x
y
20 0
30 20
Y
S
S
S1
50
40
30
E
E1
20
D
10
0
File: ECO WORKSHOP-2005
S
10
S1
20
30
40
50
60
70
X
20