MODEL-1econstudents.weebly.com/uploads/8/7/4/4/8744298/mod… · Web viewX Y 0 25 1 22 2 19 3 16 4 13 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

St. Philomena’s College, Mysore-15

Module II : Economic application of linear functions:

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=3D=36-3(3) =36-9 = 27 units

If it is a free good put P=0D=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 Ap=6, S=20S=5P-10S=5(6)-10S=20

If S=0 P=20=5P-10

P= = 2

3. The demand function is given as qd=12-2P construct the demand schedule?

Qd = 12-2(6)=0Qd = 12-2(5)=2Qd = 12-2(4)=4Qd = 12-2(3)=6Qd = 12-2(2)=8Qd = 12-2(1)=10Qd = 12-2(0)=12

File: ECO WORKSHOP-2005 1

X P0 62 54 46 38 210 112 0

By-Ms. Rashmi PMaharaja’s College, Mysore


4. The specific supply function is QS=20P construct the supply schedule?

Qs=20 (6)= 120Qs=20 (5)= 100Qs=20 (4)= 80Qs=20 (3)= 60Qs=20 (2)= 40Qs=20 (1)= 20Qs=20 (0)= 0

5. The specific demand function is Qd=15-3P construct a demand schedule?

Qd=15-3P15-3(0)=1515-3(1)=1215-3(2)=915-3(3)=615-3(4)=315-3(5)=0

6. The demand function is 5-2P construct a demand schedule?5-2p5-2(0)=55-2(1)=35-2(2)=15-2(3)=-15-2(4)=-35-2(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


X P120 6100 580 460 340 220 10 0

P Qd0 151 122 93 64 35 0

P Q d0 51 32 13 -14 -35 -5

Qd P10 08.5 17 2

5.5 34 4

2.5 5


8. If the demand function is Qd=-3P+14 construct a demand schedule?

Q d –3P+14Q d= -3(0)+14=14Q d= -3(1)+14=11Q d= -3(2)+14=8Q d= -3(3)+14=5Q d= -3(4)+14=2Q d= -3(5)+14=-1

1. If the demand function for any commodity is 100P-88=P what is the price at which quality demand is 0.04?

100D-88=P100(0.04)-88=PP=84

10. If the demand function is D=25-3X construct a demand schedule?

S=25-3xS=25-3(0)=25 S=25-3(1)=22S=25-3(2)=19S=25-3(3)=16S=25-3(4)=13

11. If the supply function is S=15X+8 construct a supply schedule?

S=15x+8S=15(0)+8=8S=15(1)+8=23S=15(2)+8=38S=15(3)+8=53S=15(4)+8=68

12. Given straight-line 3Y+X=15 find the intercept of a slope?

3Y+X=15

Y=

Y= Y=


Qd P14 011 18 25 32 4-1 5

X Y0 251 222 193 164 13

X Y0 81 232 383 534 68


13. If the function is in the form of prove that it is a linear demand equation?

9-12X=16Y-3212X-16Y=9+3212X-16Y=4116Y=-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) D : (40-30) x1 y1 x2 y2

Slope : = = =

2) Given the equation 4x + 2y = 7. Find the in intercept on both axes?

+ = 1

+ = 1

Intercept on ‘x’ axis is

Intercept on ‘y’ axis is

3) Graph the two equations P=25-3x and S=15x+8. Find graphically their interaction.

y = 25 – 3x x yy = 25 – 3(0)=25 0 25y = 25 – 3(1)=22 1 22y = 25 – 3(2)=19 2 19y = 25 – 3(3)=16 3 16y = 25 – 3(4)=13 4 13



Supply Curve :

y = 15x + 8 x yy = 15 (0) + 8 = 8 0 8y = 15 (1) + 8 =23 1 23y = 15 (2) + 8 =38 2 38y = 15 (3) + 8 =53 3 53

150 S

140

120

100

80

60

40 D

E20

S D 1 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) (25 - 150) x1 y1 x2 y2

Slope : = = = =


Demandand

supply


=

2 (x-50) = -1(y-100)2x – 100 = - y + 1002x – 100 – 100 = - y - y = 2x - 200y = - 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 = (x – x1)

x1 =50 y1 =1x2 =75 y2 =2

(y-1) = (x – 50)

y – 1 = (x – 50)

x = 25y + 25s = 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 20, 5Apply the two-point formula

y – 2 (x – 40)

y = 2 (x – 40)

y = + 4

3x = 80 – 20y



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 =

Y = 1-

Y =

Y=

X=50-50Y



8. If the demand function is in the form of Qd=15-3P construct the demand schedule and curve?

Qd=15-3(0)=15Qd=15-3(1)=12Qd=15-3(2)=9Qd=15-3(3)=6Qd=15-3(4)=3Qd=15-3(5)=0

Y 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 D

0 1 2 3 4 5 X

9. Demand function is given as 12-2Pconstruct a schedule graph?

Qd=12-2(6)=0Qd=12-2(5)=2Qd=12-2(4)=4Qd=12-2(3)=6Qd=12-2(2)=8Qd=12-2(1)=10Qd=12-2(0)=12


P Qd0 151 122 93 64 35 0

X P0 62 54 46 38 210 112 0


0.66

5

(2.5)

4

(4.4)

3

(6.3)

2

(8.2)

1

(10.1)

(12.0)1 2 3 4 5 6 7 8 9 10 11 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 - Pii) Fall in quantity demand x – x1

Qd = 50 –p equilibrium Qd Qs Before the taxQs = 2p –25 50-p=2p-25

– p - 2p = -50 –25-3p = -75

3p = 75

Substitute the value of ‘p’ in the demand equation we have:

Qd = 50 –25 = 25.Qs = 2(25) – 25 = 25.

Effect of tax:(x) Qd = 50 –p. tax - Rs.5 per unit price tax.


Before tax


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.

Price of the commodityAfter the tax the new supply function is

Equilibrium price & quantity after the tax:

x = 50 –pD = p = 50 –x

1

1

After the tax the new equilibrium quantity is

Substituting the value of x is the

p = 50 – x we have


After the tax


Graph:-

Before tax:

Demand supply

After the tax

Y (0.50) S

50

40 E1

25,25S1

30 E E

S

S1 20

S 0,12

10 M M1

0 5 10 15 20 25 30 35 40 X

2) Given the demand & supply function: D : x = 200 –5p

S : x = 4p –79If 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 :


St. Philomena’s College, Mysore-15x = 200 –5p

D=S-Before

D=S Before Tax Market equilibrium Q.D QS

40-

= - 40 +

9 5

1 1

Substitute the value of ‘x’ in any equation

After the tax, if tax of Rs. 2 is levied as specific tax.

P:



S= P=

P=

After the tax equilibrium is at D=S.

5

1

After the tax

Substitute the value with demand equation:

287

9

GRAPH:

Before Tax:

S=

X P


Demand:

Qd P0 4045 3150 30


0 (19.35)

45 31

After the tax

x y0 (21.75)

(40.5)

Y

50

45 D (0.40) S1

40 (40.532)E1 E

S

35 (45.31) D

30

25s1

(0.21.75)(0,19.35)

20

S 15

10

5

0 10 20 30 40 50 X

Price


QdandQs


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:

100-2x=3x-50-2x-3x=-100-505x=150

x=

Substitute the value of x in demand equation we have:

P=100-2(30)P=40

After the tax:

D=100-2xS= P=(3x-50)+5:

Equilibrium: Qd QS:

100-2x = 3x-45

-2x-3x = -45-100

= - 5x = -145

5x = 145

x=

Substitute the Value of ‘x’ with the equation we have:

P=100-2 (29)P= 100-58P=42

Graph:

Before tax:


After the tax:S=3x-453(15)-45=03(29)-45=42


Demand Supply x-y x-y

P= 100-2(10) = 70 10- 70 10 - 20P= 100-2(30) = 40 30- 40P= 100-2(40) = 20 40- 20 30 - 40

Y

S1

70 D S

60

E1 E50

(4.2)40

S1

(3.6)

D30

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 Qd QS Before Tax

15-3y = 2y – 3:-3y – 2y = -15-3= -5y = -18

y=


S= P= 3x-503(10)-5030-50=203(30)-80=40

X Y15 029 42


Substitute the value in either demand or supply equationQd= 15-3y

15-3 (3.6) =4.2Supply: 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) 2S = 2y-1

Equilibrium after the tax Qd Qs15 – 3y = 2y – 1 P1 = 3.2- 3y – 2y = -15 - 1 X1 = 5.4= - 5y = - 16

y = =3.2

Substitute the value in the demand function:D = 15 – 3 (3.2) = 5.4F – S =2(3.2) – 1 =5.4

Graph:

Before TaxDemand: D = 15 – 3y x y = 15 – 3(0) =12 0 12 = 15 – 3(3.6) = 4.2 3.6 4.2

Supply Function: S = 2y – 3 2(2) – 3 = 2(3.6) – 3 = 4.2

After the tax 2y – 1 x y2(1) – 1 1 12 – 1 = 1 3.2 5.42(3.2) – 1 = 5.4



YY

D12

11

10

9

S1 S

8

7

6P1

E 1

5P

E4

3

2

S1 D1

S x x 0 1 2 3 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 x1 = 25- x – 2x = -50 - 25 p1 = 25


St. Philomena’s College, Mysore-15= - 3x = - 753x = 75

x = =25



Substitute the value either in the equation we have:

P = 50 – xP = 50 – 25P = 25

After subsidy:

Take the demand function:

P = 50 – x

But supply observe the subsidy

P = (2x - 25) - 15P = 2x – 40

Equilibrium after the tax Qd = Qs

50 – x = 2x – 40 x1 = 20- x – 2x = -50 - 40 p1 = 30= - 3x = - 903x = 90

x = = 30

Substitute the value50 – 30 = 20

The reduction in price P – P1 = 25 – 20 = 5. Increase in the quantity demanded.

x1 – x = 30 – 25 = 5



Graph : -

Before equilibrium:

Demand SupplyP = 50 – x x y 50 – 0 = 50 0 50 50 – 25 = 25 25 25

2x – 25 2(20) – 2540 – 25 = 152 (25) – 25 = 25

x y20 1525 25

After subsidy

Supply function

P = 2x – 40 x y 2(20) – 40 20 02(30) – 40 =20 30 20

Y

SS

S150

40

30 E

E120

D10 S

S1

0 10 20 30 40 50 60 70 X


Documents

MODEL-1econstudents.weebly.com/uploads/8/7/4/4/8744298/mod… · Web viewX Y 0 25 1 22 2 19 3 16 4 13 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