Elasticity

Exercise 1:Suppose that as a result of an improvement in technologythe producer's supply change from: (S1) Qs=-40+20P to (S2) Qs=-10+20P1. From S1 to S2, Supply increase or decrease? Why?2. Derive this producer's old and new supply schedule?3. On one axes, draw this producer's supply curves beforeand after the improvement in technology?4. How much of commodity X does this producer supply at the price of 4$ before and after the improvement in technology?commodity X in the market. Draw, on one axes, the three producer's supply cuver and derive geometriallly the marketsupply curve for commodity X.

Exercise 2:Tablele 2.1 gives the supply schedule of the three producer of the three producers of commodity X in the market. Draw, on oneset of axes, the three producer's supply curves and derice geometricallythe market supply curve for commodity X

Quantity Supplied (Kg, Per time period)market supply Producer 1 Producer 2 Producer 3 market

0.00 0.00 0.00 10.00 10.001.00 0.00 0.00 25.00 25.002.00 0.00 20.00 35.00 55.003.00 10.00 30.00 42.00 82.004.00 16.00 36.00 46.00 98.005.00 20.00 40.00 50.00 110.006.00 22.00 42.00 53.00 117.00

Exercise 3:

commodity X, each with a demand function given by

1. Find the market demand function and the market supplyfunction for commodity X? Q=120000-20000P Qs=20000P2. Find the market demand schedule and the market supply Pschedule of commodity X and from them find the equilibrium 0price and the equilibrium quantity? 13. Plot, on one set of axes, the market demand curve and the 2market supply curve for commodity X and show the equilibrium 3point? 44. Obtain the equilibrium price and the equilibrium quantity math 5

P ($/Kg)

There are 10,000 identical individual in the market for

(D1) Qd=12-2P, and 1,000 identical producers of commodity X,each with a function given by (S1) Qs=20P.

Exercise 4:Suppose that from the condition of equilibrium in exercise 3, there is anincrease in consumer's income (ceteris paribus) so that a new market demand

1. Derive the new market demand schedule2. Show the new market demand curve on the graph of exercise 3 (3)3.State the new equilibrium price and the new equilibrium quantity forcommodity X.4. Obtain the equilibrium price and the equilibrium quantity mathematically?

Exercise 5:Commodity X have:(D1) Q=100-2P(S1) Q=3P-501. Find the equilibrium price Pe1and the equilibrium quantity Qe1P=30, Q=402 Demand increase 50% become (D2), so demand D2 have:(D2) Q=??? Qd2=150-3PFind the equilibrium price Pe2 and the equilibrium quantity Qe2 between D2 and S1?3 Supply increase 40% become (S2), so supply S2 have:(S2) Q=??? Qs2= 4.2P-70Find the equilibrium price Pe3 and the equilibrium quantity Qe3 between D2 and S2?4. Derive the demand schedule and supply schedule5. Plot, on one set of axes, the demand curve (D1, D2) and thesupply curve (S1, S2) for commodity X and show the equilibriumpoint (E1, E2, and E3)?

Exercise 6:Commodity X have:(D1) P=100-(1/4)Q Qd1=-4P+400(S1) P=(3/4)Q-50 Qs1=4/3P+200/31. Find the equilibrium price, Pe1and the equilibrium quantity, Qe1?2 Demand increase 50% become (D2), so demand D2 have:(D2) Q=??? Qd2=-6P+600Find the equilibrium price Pe2 and the equilibrium quantity Qe2 between D2 and S1?3 Supply increase 40% become (S2), so supply S2 have:(S2) Q=??? Qs2=28/15P+280/3Find the equilibrium price Pe3 and the equilibrium quantity Qe3 between D2 and S2?4. Derive the demand schedule and supply schedule5. Plot, on one set of axes, the demand curve (D1, D2) and thesupply curve (S1, S2) for commodity X and show the equilibriumpoint (E1, E2, and E3)?

curve is given by (D2) Qd=140,000-20,000P

Exercise 7:

commodity X, each with a demand function given byQ=120-PQ=-2P

1. Find the market demand function and the market supplyfunction for commodity X? Qd1=1200000-10000P Qs1=-2000P2. Find the market demand schedule and the market supply schedule of commodity X and from them find the equilibriumprice and the equilibrium quantity?3. Plot, on one set of axes, the market demand curve and themarket supply curve for commodity X and show the equilibriumpoint?4. Obtain the equilibrium price and the equilibrium quantity mathematically?

ee


(D1) P=120-Q, and 1,000 identical producers of commodity X,each with a function given by (S1) P=(1/2)Q

Qd Qs120,000 0100,000 20,000

80,000 40,00060,000 60,00040,000 80,00020,000 100,000

Find the equilibrium price Pe2 and the equilibrium quantity Qe2 between D2 and S1? P=33.3, Q=50

Find the equilibrium price Pe3 and the equilibrium quantity Qe3 between D2 and S2? P=30.55, Q=58.33

P=-20, Q=480



Exercise 1:The following table presents hypothetical data for the market demandfor a good. Complete the table:

Qd P AR TR MR Ed Type of Demand1.00 50.00 50.00 50.00 0.00 -5.00 elastic2.00 40.00 40.00 80.00 30.00 -2.00 elastic3.00 30.00 30.00 90.00 10.00 -1.00 unit elastic4.00 20.00 20.00 80.00 -10.00 -0.71 inelastic5.00 13.00 13.00 65.00 -15.00 -0.52 inelastic6.00 8.00 8.00 48.00 -17.00 -0.27 inelastic

7.00 8.00 8.00 56.00 infinity #NAME?Exercise 2:Given: The demand equation is P=40-2Q Q=20-0.5P TR=40Q-2Q^2a. What is the equation for MR?MR=40-4Qb. At what output is MR=0? Q=10, P=20c. At what output is TR maximum? Q=10,P=20d. Determine the price elasticity of demand at the output where TR is maximumComplete the table:

Q P TR MR Ed0.00 40 0 40 Infinity

40 0 40 #DIV/0!40 0 40 #DIV/0!

………… ………… ………… …………………… ………… ………… …………

40 0 40 #DIV/0!Draw, on one set of axes the P, TR, MRExercise 3:Suppose that the demand equation for a good is Q=20-2P P=10-0.5QComplete the table:

Q P TR MR Ed TR=10Q-0.5Q^20 10 0 10 Infinity MR=10-Q2 9 18 8 -9 Q'=-24 8 32 6 -4

………… ………… ………… ………… …………………… ………… ………… ………… …………

20 0 0 -10 0

Exercise 4:

(dQ/dP)=9-4Pcalculate the price elasticity of demand at a price of $4 and at a price $3

Exercise 5:

Suppose that the demand equation for a good is Q=16+9P-2P2,

(dP/dQ)=3-8Qa. Determine price elasticity of demand at Q=10b. Determine the equation for TR and MR MR=dTR/dQ= 1000+6Q-12Q^2

Exercise 6:

where Qa=Units of product A demanded by consumers each day and Pb=Sellingprice of product B.

a. Determine the cross-elasticity coefficient for the two products when the price Edxy=(dQx/dPy)*(Py/Qx)of product B=$10b. Are products A and B complements, subtitutes, or independent, and how "strong"is the relationship? substitute, very trong, 93%

Exercise 7:The Fairfax Apparel Company manufactures sports, shirts for men; during 1987

2.502.17>>>>>>>>. Co dãn điểm

and March 1988.a. Calculate the cross elasticity of demand between Fairfax's sports shirts andLafayette's sports shirts during February and March. Are the two companies' sports shirts good or poor substitutes? goodb. Suppose that the coeffient of the price elasticity of demand for Fairfax'ssports shirts is -2.0. Assuming that Lafayette keeps its price at $12, by how P1much must Fairfax cut its price to build its sales of shirts back up to 23,000 Q1per month? (Use the arc formula for price elasticity) p=9.83$ P2

Q2Exercise 8:Find the price elasticity of demand (Ed) for the curvilinear demand function

Exercise 9:Suppose that two prices and their corresponding quantities (Table 9) are observed in the market for commodity X. Find the price elasticity of demandfor commodity X between point A and point B (Moving from A to B, from B to A, and Midway between A and B)

Point Px Qx Ed1= -4.29A 6.10 32,180 Ed2=-3.13B 5.70 41,230 Ed3= -3.64

If the demand equation for an item is P=1000+3Q-4Q2

Given: The relationship between product A and product B is Qa=80Pb-0.5Pb2,

Fairfax sold an average of 23,000 sports shirts for $13 per shirt. In early January1988, Fairfax's major competitor, Lafayyete Manufacturing Co., cut the price ofits sports shirts from $15 to $12. The orders Fairfax received for its own sports shirts dropped sharly, from 23,000 per month to 13,000 per month for February

of the form Q=aP-b

Exercise 10:

Commodity Before AfterP Q P Q Exy=1

Hamburgers (Y) 3.00 30.00 2.00 40.00Hot dogs (X) 1.00 15.00 1.00 10.00 Exz= -0.78Mustard (Z) 1.50 10.00 2.00 9.00Hot dogs (X) 1.00 15.00 1.00 12.00

Exercise 11:From the supply schedule in Table 11, find arc elasticity for a movementa. From poit A to point C E1=0.75b. From poit C to point A E2=2/3c. Midway between A and C E3=5/7d. At point B EBA=11/23 EBC=9/10 EBD=20/17 EBE=7/3

Point A B C D EPx 6 5 4 3 2Qx 6,000 5,500 4,500 3,000 0

Exercise 12:With reference to Fig 12, consider the following two farm-aid programs forwheat farmers.I. The government sets the price of wheat at P2 and purchases the resultingsurplus of wheat at P2.II. The government allows wheat to be sold at the equilibrium price of P1and grants each farmer a cash subsidy of P2-P1 on each unit sold. Whichof the two programs is more expensive to the government? B

Find the cross elasticity of demand between hot dogs (X) and hamburgers (Y) (Exy)and between hot dogs (X) and mustard (Z) (Exz) for the data in Table 10

P1

P2

Pw

Qw

Dw

A

E

Sw

Type of Demand

TR=10Q-0.5Q^2

Ed=(dQ/dP)*(P/Q) Q P Ed20.00 4.00 -1.4025.00 3.00 -0.36

Ed=(%∆Q)/(%∆P)=(∆Q/Q)/(∆P/P)=[1/(∆P/∆Q)*(p/Q)]=(∆Q/∆P)*(P/Q)

Ed=[1/(dP/dQ)]*(p/q) 10.00 630.00 -0.82

MR=dTR/dQ= 1000+6Q-12Q^2 TR=P*Q=1000Q+3Q^2-4Q^3 >>>>> MR=0

Q Qa Pb Ed

Edxy=(dQx/dPy)*(Py/Qx) dQa/dQb = 80-Pb 10.00 750.00 10.00 0.93

>>>>>> co dãn chéo Tb Ed=(dQ/dP)*(P/Q)2.17>>>>>>>>. Co dãn điểm

Fairf Lafa13.00 15.00 27.78 =(Q2-Q1)/(Q2+Q1)

23,000.00 %∆PTb -13.8912.00 Ed -2.00

13,000.00 P 9.82

Trmax >>>>> (TR)n <0

%∆QTb =(P2-P1)/(P2+P1)

0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.000.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

Producer 1

Producer 2

Producer 3

market

0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.000.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

Producer 1

Producer 2

Producer 3

market

price012345

Qd1 Qs Qd2120000 0 140000100000 20000 120000

80000 40000 10000060000 60000 8000040000 80000 6000020000 100000 40000

0 20000 40000 60000 80000 1000001200001400000

20000

40000

60000

80000

100000

120000

Column T

0 20000 40000 60000 80000 100000 120000 140000 1600000

1

2

3

4

5

6

Qd1QsQd2

0 20000 40000 60000 80000 1000001200001400000

20000

40000

60000

80000

100000

120000

Column T

0 20000 40000 60000 80000 100000 120000 140000 1600000

1

2

3

4

5

6

Qd1QsQd2

Price (USDQd1 Qd2 Qs1 Qs20 100 150 -50 -70

20 60 90 10 1440 20 30 70 9860 -20 -30 130 18280 -60 -90 190 266

100 -100 -150 250 350

Price Qd1 Qd2 Qs1 Qs20 400 600 66.66667 93.33333

20 320 480 93.33333 130.666740 240 360 120 16860 160 240 146.6667 205.333380 80 120 173.3333 242.6667

100 0 0 200 280 -200 -100 0 100 200 300 4000

20

40

60

80

100

120

Qd1

Qd2

Qs1

Qs2

-200 -100 0 100 200 300 4000

20

40

60

80

100

120

Qd1

Qd2

Qs1

Qs2

Q P=AR TR MR Ed0 40 0 40 x

0.5 39 19.5 38 2.052632 -21 38 38 36 1.055556 -2

1.5 37 55.5 34 0.72549 -22 36 72 32 0.5625 -2

2.5 35 87.5 30 0.466667 -23 34 102 28 0.404762

3.5 33 115.5 26 0.3626374 32 128 24 0.333333

4.5 31 139.5 22 0.3131315 30 150 20 0.3

5.5 29 159.5 18 0.2929296 28 168 16 0.291667

6.5 27 175.5 14 0.2967037 26 182 12 0.309524

7.5 25 187.5 10 0.3333338 24 192 8 0.375

8.5 23 195.5 6 0.450989 22 198 4 0.611111

9.5 21 199.5 2 1.10526310 20 200 0 x

10.5 19 199.5 -2 -0.90476211 18 198 -4 -0.409091

11.5 17 195.5 -6 -0.24637712 16 192 -8 -0.166667

12.5 15 187.5 -10 -0.1213 14 182 -12 -0.089744

13.5 13 175.5 -14 -0.06878314 12 168 -16 -0.053571

14.5 11 159.5 -18 -0.04214615 10 150 -20 -0.033333

15.5 9 139.5 -22 -0.02639316 8 128 -24 -0.020833

16.5 7 115.5 -26 -0.01631717 6 102 -28 -0.012605

17.5 5 87.5 -30 -0.00952418 4 72 -32 -0.006944

18.5 3 55.5 -34 -0.00476919 2 38 -36 -0.002924

19.5 1 19.5 -38 -0.0013520 0 0 -40 0

Q P=AR TR MR Ed MR C20 10 0 X 102 9 18 -0.5 84 8 32 -0.5 66 7 42 -0.5 48 6 48 -0.5 2

10 5 50 -0.5 012 4 48 -0.5 -214 3 42 -0.5 -416 2 32 -0.5 -618 1 18 -0.5 -820 0 0 -0.5 -10

Exercise 3:

commodity X, each with a demand function given by

1. Find the market demand function and the market supplyfunction for commodity X?P Qd Qs

0 120,000 01 100,000 20,0002 80,000 40,0003 60,000 60,0004 40,000 80,0005 20,000 100,000

2. Find the market demand schedule and the market supply schedule of commodity X and from them find the equilibriumprice and the equilibrium quantity?3. Plot, on one set of axes, the market demand curve and themarket supply curve for commodity X and show the equilibriumpoint? See Exercise 44. Obtain the equilibrium price and the equilibrium quantity mathematically?(D1): Qd=12-2P

(S1): Qs=20P

Qd=Qs

Exercise 4:Suppose that from the condition of equilibrium in exercise 3, there is anincrease in consumer's income (ceteris paribus) so that a new market demand

1. Derive the new market demand scheduleP Qd Qs Qd'

0 120,000 0 1400000.5 110,000 10000 130000

1 100,000 20000 1200001.5 90,000 30000 110000

2 80,000 40000 1000002.5 70,000 50000 90000

3 60,000 60000 80000


(D1) Qd=12-2P, and 1,000 identical producers of commodity X,each with a function given by (S1) Qs=20P.

ð Market demand function: (D): Qd=120,000-20,000P

ð Market supply function: (S): Qs=20,000P

ó 120,000-20,000P=20,000Pó 40,000P= 120,000ó P = 3 (Units of currency)

ð Q= 20,000x3 = 60,000 (Units of quantity)

curve is given by (D2) Qd=140,000-20,000P

3.5 50,000 70000 700004 40,000 80000 60000

2. Show the new market demand curve on the graph of exercise 3 (3)

3.State the new equilibrium price and the new equilibrium quantity forcommodity X.

P'=3.5Q'=70,0004. Obtain the equilibrium price and the equilibrium quantity mathematically?

Qd’=Qs

Exercise 6:Commodity X have:(D1) P=100-(1/4)Q(S1) P=(3/4)Q-50

(D1) P=100-1/4Q or (D1): Qd1 = -4P + 400 (S1) P=(3/4)Q-50 or (S1): Qs1 = 4/3P + 200/3

1. Find the equilibrium price, Pe1and the equilibrium quantity, Qe1?Qd1=Qs1

2 Demand increase 50% become (D2), so demand D2 have:

ó 140,000-20,000P = 20,000Pó 40,000P = 140,000ó P = 3.5 ( Units of currency)

ð Q’ = 3.5 x 20,000 = 70,000

ó -4P + 400 = 4/3P + 200/3ó 16/3P = 1000/3ó P = 62.5 ( Units of currency)

ð Q = (-4) x 62.5 + 400 = 150 ( Units of quantity)

0 20000 40000 60000 80000 100000 120000 140000 1600000

0.5

1

1.5

2

2.5

3

3.5

4

4.5

8

4

Market demand and supply curve of commodity X

QdQsQd'

Quantity

Price

(D2) = 150% (D1)

Find the equilibrium price Pe2 and the equilibrium quantity Qe2 between D2 and S1?Qd2 = Qs1

Qs2=28/15P+280/3

3 Supply increase 40% become (S2), so supply S2 have:(S2) = 140% (S1)

4. Derive the demand schedule and supply scheduleP Qd1 Qd2 Qs1 Qs2

0 400 600 66.6666666666667 93.3333331.25 275 412.5 108.333333333333 151.6667

62.5 150 225 150 21093.75 25 37.5 191.666666666667 268.3333

125 -100 -150 233.333333333333 326.6667

5. Plot, on one set of axes, the demand curve (D1, D2) and thesupply curve (S1, S2) for commodity X and show the equilibriumpoint (E1, E2, and E3)?

ó (D2): 1.5Qd1 = -6P + 600ó (D2): Qd2 = -6P +600

ó -6P +600 = 4/3P + 200/3ó 22/3P = 1600/3óð Q= 1800/11

ó (S2): 1.4Qs1 = 28/15 P +280/3ó (S2): Qs2 = 28/15P + 280/3

-200 -100 0 100 200 300 400 500 600 7000

20

40

60

80

100

120

140

33

4

Demand and supply curves of commodity X

Qd1

Qd2

Qs1

Qs2