FTU2 - Microeconomics 2 - Trần Thông Tú - 1201017440

7/29/2019 FTU2 - Microeconomics 2 - Trn Thng T - 1201017440

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Exercise 1: T

Suppose that as a result of an improvement in technology

the 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 before

and 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?

P 2 3 4 5

Q(S1) 0 20 40 60

Q(S2) 30 50 70 90

P=4, Q(S1)=40, Q(S2)=70

Q(s2)-Q(s1)=30 => Supply increased

0

2

4

6

0 10 20 30 40 50 60 70 80 90 100

P

Q

X

S1 S2


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Exercise 2:

Tablele 2.1 gives the supply schedule of the three producer of

commodity X in the market. Draw, on one set of axes,

the three producer's supply curves and derice geometricallythe market supply curve for commodity XP ($/Kg) Quantity Supplied (Kg, Per time period)

Producer 1 Producer 2 Producer 3 Market Supply

0 0 0 10 10

1 0 0 25 25

2 0 20 35 55

3 10 30 42 824 16 36 46 98

5 20 40 50 110

6 22 42 53 117

0

1

2

3

4

5

6

7

P

X

D1

D2

D3

S


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Exercise 3:

There are 10,000 identical individual in the market for

commodity X, each with a demand function given by

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

1. Find the market demand function and the market supply

function for commodity X?

2. Find the market demand schedule and the market supply

schedule of commodity X and from them find the equilibrium

price 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 equilibrium

point?

4. Obtain the equilibrium price and the equilibrium quantity mathematically?

(S1) P=a+bQ -> S2 P=a+b/(1+x%)Q

P Qd Qs

1 100,000 20,000

2 80,000 40,000

3 60,000 60,000

4 40,000 80,000

5 20,000 100,0006 0 120,000

Ex1: Qd=120000-20000P; Qs=20000P

S1 -> S2 increase x%

S1->S2 increase x%

(S1) Q=c+dP=>Q=(1+x%)(c+dP)


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Exercise 4:

Suppose that from the condition of equilibrium in exercise 3, there is an

increase in consumer's income (ceteris paribus) so that a new market demand

curve is given by (D2) Qd=140,000-20,000P1. Derive the new market demand schedule

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 for

commodity X.

4. Obtain the equilibrium price and the equilibrium quantity mathematically?

P Qs Qd0 0 140,000

0.5 10,000 130,000

1.0 20,000 120,000

1.5 30,000 110,000

2.0 40,000 100,000

2.5 50,000 90,000

3.0 60,000 80,0003.5 70,000 70,000

4.0 80,000 60,000

4.5 90,000 50,000

5.0 100,000 40,000

4

5

6

X


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Exercise 5:

Commodity X have:

(D1) Q=100-2P

(S1) Q=3P-501. Find the equilibrium price Pe1and the equilibrium quantity Qe1?

Pe1= 50.00

Qe1= 0.00

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

Pe2= 33.33Qe2= 50.00

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

(S2) Q=1,4Q(S1)=1,4(3P-50)=4,2P-70


Pe3= 30.56

Qe3= 58.33

4. Derive the demand schedule and supply scheduleQ Pd1 Ps1 Pd2 Ps2

0.00 50.00 16.67 50.00 16.67

5.00 47.50 18.33 48.33 17.86

.. .. .. .. ..

. . . . .

75.00 12.50 41.67 25.00 34.52

80.00 10.00 43.33 23.33 35.71

Q Pd1 Ps1 Pd2 Ps2

0.00 50.00 16.67 50.00 16.67

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

(D2) 1.5Q(D1)=1.5(100-2P)=150-3P


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5. Plot, on one set of axes, the demand curve (D1, D2) and the

supply curve (S1, S2) for commodity X and show the equilibrium

point (E1, E2, and E3)?

E1

E3

E2E4

0.00

10.00

20.00

30.00

40.00

50.00

60.00

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00

X

D1 S1 D2 S2


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Exercise 6:

Commodity X have:

(D1) P=100-(1/4)Q

(S1) P=(3/4)Q-501. Find the equilibrium price, Pe1and the equilibrium quantity, Qe1?

Qe1=150

Pe1=62,5

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


Pe2=800/11Qe2=1800/11

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


4. Derive the demand schedule and supply schedule

5. Plot, on one set of axes, the demand curve (D1, D2) and the

supply curve (S1, S2) for commodity X and show the equilibriumpoint (E1, E2, and E3)?

P Qs1 Qd1 Qs2 Qd2

45.00 126.67 220.00 177.33 330.00

52.27 136.36 190.91 190.91 286.36

61.00 148.00 156.00 207.20 234.00

62.50 150.00 150.00 210.00 225.00

64.00 152.00 144.00 212.80 216.0064.41 152.54 142.37 213.56 213.56

72.73 163.64 109.09 229.09 163.64

75.00 166.67 100.00 233.33 150.00

(D1) Q=400-4P => (D2) Q= (1+0,5)(400-4P)=600-6P

(S1) Q=4P/3+200/3 => (S2) Q=(1+0,4)(4P/3+200/3) Q=28/15P+280/3


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Exercise 7:

There are 10,000 identical individual in the market for

commodity X, each with a demand function given by

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

1. Find the market demand function and the market supply

function for commodity X?

2. Find the market demand schedule and the market supply

schedule of commodity X and from them find the equilibrium

price and the equilibrium quantity?

P Qs Qd

98 196,000 220,000

99 198,000 210,000100 200,000 200,000

101 202,000 190,000

102 204,000 180,000

103 206,000 170,000

Pd= 120-1/10000Q

Ps= 1/2000Q

E

98

100

102

104

X


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Exercise 1: TThe following table presents hypothetical data for the market demand

for a good. Complete the table:

Qd P AR TR MR Ed Type of Demand1.00 50.00 50.00 50.00 40.00 -5.00 Elastic

2.00 40.00 40.00 80.00 20.00 -2.00 Elastic3.00 30.00 30.00 90.00 0.00 -1.00 Unitary Elastc4.00 20.00 20.00 80.00 -20.00 -0.50 Inelastic5.00 10.00 10.00 50.00 -40.00 -0.20 Inelastic6.00 0.00 0.00 0.00 -60.00 0.00 Inelastic

AR=TR/Q=P=Doanh thu trung bnh=Average RevenueMR=TR/Q==dTR/dQ=Doanh thu bin=Marginal RevenueEd=Ep=Edp=(%Q/%P)=(Q/P)*(P/Q)=[1/((P/Q)]*(P/Q)Ed=Ep=Edp=(%Q/%P)=(dQ/dP)*(P/Q)=[1/(dP/dQ)]*(P/Q)

Ed= -1Unitary Elastic P= 60.00 + -10.00 *QEd< -1Elastic (Co gin nhiu) P=60-10QEd> -1Inelastic (Co gin t) TR=PQ=60Q-10Q^2Ed= 0Perfectly Inelastic (HT kg co gin) MR=TR'=60-20QEd= -Perfectly Elastic (HT co gin) Ed=1/-10*P/Q


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Exercise 2:Given: The demand equation is P=40-2Q Q=20-P/2a. What is the equation for MR?

b. At what output is MR=0?

c. At what output is TR maximum?

d. Determine the price elasticity of demand at the output where TR is maximumComplete the table:

Q P TR MR Ed Type of Demand

0.00 40.00 0.00 40.00 Perfect Elastic

0.50 39.00 19.50 38.00 -39.00 Elastic

1.00 38.00 38.00 36.00 -19.00 Elastic

1.50 37.00 55.50 34.00 -12.33 Elastic

2.00 36.00 72.00 32.00 -9.00 Elastic

2.50 35.00 87.50 30.00 -7.00 Elastic

3.00 34.00 102.00 28.00 -5.67 Elastic3.50 33.00 115.50 26.00 -4.71 Elastic

4.00 32.00 128.00 24.00 -4.00 Elastic

4.50 31.00 139.50 22.00 -3.44 Elastic

5.00 30.00 150.00 20.00 -3.00 Elastic

5.50 29.00 159.50 18.00 -2.64 Elastic

6.00 28.00 168.00 16.00 -2.33 Elastic

6.50 27.00 175.50 14.00 -2.08 Elastic

7.00 26.00 182.00 12.00 -1.86 Elastic

7.50 25.00 187.50 10.00 -1.67 Elastic

8.00 24.00 192.00 8.00 -1.50 Elastic

8.50 23.00 195.50 6.00 -1.35 Elastic

9.00 22.00 198.00 4.00 -1.22 Elastic

9.50 21.00 199.50 2.00 -1.11 Elastic

10.00 20.00 200.00 0.00 -1.00 Inelastic

10.50 19.00 199.50 -2.00 -0.90 Inelastic

11.00 18.00 198.00 -4.00 -0.82 Inelastic

11.50 17.00 195.50 -6.00 -0.74 Inelastic

12.00 16.00 192.00 -8.00 -0.67 Inelastic

TR=PQ=40Q-2Q^2MR=(TR)'=40-4Q

MR=040-4Q=0Q=10TRmaxQ=-40/2(-2)=10


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12.50 15.00 187.50 -10.00 -0.60 Inelastic

13.00 14.00 182.00 -12.00 -0.54 Inelastic

13.50 13.00 175.50 -14.00 -0.48 Inelastic

14.00 12.00 168.00 -16.00 -0.43 Inelastic

14.50 11.00 159.50 -18.00 -0.38 Inelastic

15.00 10.00 150.00 -20.00 -0.33 Inelastic15.50 9.00 139.50 -22.00 -0.29 Inelastic

16.00 8.00 128.00 -24.00 -0.25 Inelastic

16.50 7.00 115.50 -26.00 -0.21 Inelastic

17.00 6.00 102.00 -28.00 -0.18 Inelastic

17.50 5.00 87.50 -30.00 -0.14 Inelastic

18.00 4.00 72.00 -32.00 -0.11 Inelastic

18.50 3.00 55.50 -34.00 -0.08 Inelastic

19.00 2.00 38.00 -36.00 -0.05 Inelastic

19.50 1.00 19.50 -38.00 -0.03 Inelastic20.00 0.00 0.00 -40.00 0.00 Perfectly Inelastic

Draw, on one set of axes the P, TR, MR

-40

10

60

110

160

0 5 10 15 20

Chart Title

-40.00

10.00

60.00

110.00

160.00

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00

X

P TR MR


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Exercise 3:Suppose that the demand equation for a good is Q=20-2P

Complete the table:


0.00

2.004.00

20.00

TR=PQ=20P-2P^2

MR=TR'=20-4P


0.00 10.00 0.00 -20.00 Perfect Elastic

2.00 9.00 18.00 -16.00 -2.25 Elastic4.00 8.00 32.00 -12.00 -1.00 Inelastic

6.00 7.00 42.00 -8.00 -0.58 Inelastic

8.00 6.00 48.00 -4.00 -0.38 Inelastic

10.00 5.00 50.00 0.00 -0.25 Inelastic

12.00 4.00 48.00 4.00 -0.17 Inelastic

14.00 3.00 42.00 8.00 -0.11 Inelastic

16.00 2.00 32.00 12.00 -0.06 Inelastic

18.00 1.00 18.00 16.00 -0.03 Inelastic

20.00 0.00 0.00 20.00 0.00 Perfectly Inelastic


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-100.00

-50.00

0.00

50.00

100.00

150.00

200.00

250.00

0.00 5.00 10.00 15.00 20.00 25.00

P

Q

X

TR MR


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Exercise 4:

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

calculate the price elasticity of demand at a price of $4 and at a price $3

Ed=dQ/dP*P/Q=(9-4P)*P/Q

Q P Ed

20.00 4.00 1.8025.00 3.00 1.08

Exercise 5:

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

a. Determine price elasticity of demand at Q=10

b. Determine the equation for TR and MR

Ed=1/(3-8Q)*P/Q

TR=PQ=1000Q+3Q^2-4Q^3

MR=TR'=1000+6Q-12Q^2Q P Ed

10.00 630.00 21.00

Exercise 6:

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

where Qa=Units of product A demanded by consumers each day and Pb=Selling

price of product B.

a. Determine the cross-elasticity coefficient for the two products when the price

of product B=$10b. Are products A and B complements, subtitutes, or independent, and how "strong"

is the relationship?

Qa Pb Ed

750.00 10.00 0.93

A and B are subtitues

The relationship is weak because Ed>-1


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Exercise 7:The Fairfax Apparel Company manufactures sports, shirts for men; during 1987 Qa1= 23,000.00

Fairfax sold an average of 23,000 sports shirts for $13 per shirt. In early January Pa= 13.00

1988, Fairfax's major competitor, Lafayyete Manufacturing Co., cut the price of Pb1= 15.00

its sports shirts from $15 to $12. The orders Fairfax received for its own sports Pb2= 12.00

shirts dropped sharly, from 23,000 per month to 13,000 per month for February Qa2= 13,000.00and March 1988.

a. Calculate the cross elasticity of demand between Fairfax's sports shirts and

Lafayette's sports shirts during February and March. Are the two companies'

sports shirts good or poor substitutes?

%Pb= -20.00% %Qa= -43.48%%Pb(tb)= -22.22% %Qa(tb)= -55.56% =Q/Qtb=(Q2-Q1)/[(Q1+Q2)/2]

Eab= 2.17Eab(tb)= 2.50

b. 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

much must Fairfax cut its price to build its sales of shirts back up to 23,000

per month? (Use the arc formula for price elasticity)

Ed=-2

Pb=12

Qa=23000

Pa=?

Eab(tb)=%Qa(tb)/%Pb(tb)=[(Qa3-Qa2)/(Qa3+Qa2)]/[(Pb3-Pb2)/(Pb3+Pb2)]

36.14


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

of the form Q=aP-b

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 QxA 6.10 32,180.00

B 5.70 41,230.00

A->B %P= -0.07 %Q= 0.28B->A %P= 0.07 %Q= -0.22

Midpoint %P= -0.07 %Q= 0.25

Exercise 10: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

Commodity Before AfterP Q P Q %P %Q

Hamburgers (Y) 3.00 30.00 2.00 40.00 -0.40 0.29Hot dogs (X) 1.00 15.00 1.00 10.00 0.00 -0.40Mustard (Z) 1.50 10.00 2.00 9.00 0.29 -0.11Hot dogs (X) 1.00 15.00 1.00 12.00 0.00 -0.22

Exy= 1.00

Exz= -0.78


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Exercise 11:From the supply schedule in Table 11, find arc elasticity for a movement

a. From poit A to point C

b. From poit C to point A

c. Midway between A and C

d. At point BPoint A B C D E

Px 6.00 5.00 4.00 3.00 2.00

Qx 6,000.00 5,500.00 4,500.00 3,000.00 0.00

Midway AC At point BMovement A->C C->A A->C C->A B->A B->C

%P -33.33% 50.00% -40.00% 40.00% 20.00% -20.00%

%Q -25.00% 33.33% -28.57% 28.57% 9.09% -18.18%

Ed 0.75 0.67 0.71 0.71 0.45 0.91


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Exercise 12:With reference to Fig 12, consider the following two farm-aid programs for

wheat farmers.

I. The government sets the price of wheat at P2 and purchases the resulting

surplus 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. Which

of the two programs is more expensive to the government?

Depending on elasticity of the demand function

Elastic I>IIInelastic I


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Exercise 13:We have:

%Q= 10.00%

%TR= 6.00%

Find:

%P= -3.64%Ed= -2.75


%P= 12.00%%TR= 8.00%

Find:

%Q= -3.57%

Ed= -0.30


%Q= 20.00%%P= -4.00%

Find:

%TR= 15.20%Ed= -5.00


%Q= 8.00%Ed= -4.00

Find:

%P= -2.00%%TR= 5.84%


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Exercise 17:At the equilibrium point we have:

Pe= 100.00Qe= 200.00Es= 4.00

Ed= -2.00Find:Demand function and Supply function:Q=a+bP and P=c+dQ

(D) Q = 600.00 - 4.00 P

(S) P = 75.00 + 1/8 PEs=1/(dP/dQ) * P/Q 1/(dP/dQ)*100/200=4 1/(dP/dQ)=8 d=1/8

Ed=dQ/dP*P/Q dQ/dP * 100/200=-2 dQ/dP=-4 => b=04


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Exercise 18:

Compare type of demand at poits A, B, and C1.00

Assume that: D1 Q= 9.00 + -1.00 *PD2 Q= 11.00 + -1.00 *P

Q P1 P2 Ed1 Ed2

1.00 8.00 10.00 -8.00 -10.00

2.00 7.00 9.00 -7.00 -4.50

3.00 6.00 8.00 -4.00 -2.67

4.00 5.00 7.00 -2.50 -1.75

5.00 4.00 6.00 -1.60 -1.20

6.00 3.00 5.00 -1.00 -0.83

7.00 2.00 4.00 -0.57 -0.57

8.00 1.00 3.00 -0.25 -0.38

Q P Ed Type of demandA 3.00 8.00 -2.67 ElasticB 3.00 6.00 -2.00 ElasticC 5.00 6.00 -1.20 Elastic

A

CB


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0.00

2.00

4.00

6.00

8.00

10.00

12.00

0.00 2.00 4.00 6.00 8.00 10.00

P

Q

X

P1

P2


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Exercise 19:


1.00

1.00

Assume that: D1 Q= -5.00 + -5.00 *PD2 Q= -1.00 + -1.00 *P

Q P1 P2 Ed1 Ed2

-30.00 5.00 29.00 0.83 0.97

-20.00 3.00 19.00 0.30 0.95

-10.00 1.00 9.00 0.20 0.90

1.00 -1.20 -2.00 2.40 2.00

10.00 -3.00 -11.00 0.60 1.10

20.00 -5.00 -21.00 0.50 1.05

30.00 -7.00 -31.00 0.47 1.03

50.00 -11.00 -51.00 0.44 1.02

Q P Ed Type of demand

A 10.00 -3.00 0.30 InelasticB 10.00 -11.00 1.10 InelasticC 50.00 -11.00 0.22 Inelastic

A

CB


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-60.00

-50.00

-40.00

-30.00

-20.00

-10.00

0.0010.00

20.00

30.00

40.00

-40.00 -20.00 0.00 20.00 40.00 60.00P

Q

X

P1

P2


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Exercise 20:


4.00

10.00

Assume that: D1 Q= 10.00 + -1.00 *PD2 Q= 10.00 + -4.00 *P

Q P1 P2 Ed1 Ed2

1.00 9.00 2.25 -9.00 -9.00

3.00 7.00 1.75 -2.33 -2.33

5.00 5.00 1.25 -1.00 -1.00

7.00 3.00 0.75 -0.43 -0.43

9.00 1.00 0.25 -0.11 -0.11

11.00 -1.00 -0.25 0.09 0.09

13.00 -3.00 -0.75 0.23 0.23

15.00 -5.00 -1.25 0.33 0.33

Q P Ed Type of demand

A 10.00 9.00 -0.90 InelasticB 10.00 2.25 -0.23 InelasticC 3.00 7.00 -2.33 Elastic

A

CB


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-6.00

-4.00

-2.00

0.00

2.00

4.00

6.00

8.00

10.00

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00

P

Q

X

P1

P2


27/65

Exercise 1: T

Demand and Supply for commodity X:

(D1) Q=500-2P

(S1) Q=3P-200

1. Find the equilibrium price and quantity (Pe1, Qe1) for commodity X,

elasticity of demand and supply at equilibrium point (Ed1, Es1)?2. Demand for commodity X increase 50% in order to become D2,

(D2) Q=???

Pe1= 140.00 Ed1= -1.27

Qe1= 220.00 Es1= 1.91

(D2) Q=1.5*(500-2P)=750-3P

Find the equilibrium price and quantity (Pe2, Qe2) between D2 and S1

Pe2= 158.33 Ed2= -1.73

Qe2= 275.00 Es2= 1.73

3. Supply for commodity X increase 40% in order to become S2,

(S2) Q=1.4*(3P-200)=4.2P-280


Pe3= 143.06 Ed3= -1.34

Qe3= 320.83 Es3= 1.87

4. From D2 and S2, the government set the price control (Pct)

4.1 Price control=120%*Pe3

Pct=??? 171.67

What is type of price?

Floor price

Result of that price:

Qd=1.5*(500-2P)=750-3P

Qs=1.4*(3P-200)=4.2P-280

Qd=??? 235.00

Qs=??? 441.00

Excess demand or excess supply?

Excess supply

206.00


28/65

Government spending (B) ???

B=??? 35,363.33


Pct=??? 114.44


Ceiling priceResult of that price?

Qd=1.5*(500-2P)=750-3P

Qs=1.4*(3P-200)=4.2P-280

Qd=??? 406.67

Qs=??? 200.67


Excess demand

206.00

Government spending ???

B=??? 206.00 * Pi

4.3 Tax (T)=10%Pe3

T=??? 14.31

4.3.1 If taxe on the demand side (buyers)

* Demand function and supply function after tax

* Equilibrium price and quantity after tax (Pe4, Qe4)

* Incidence of tax between buyers and selllers

* Total government tax revenue is?

(D2) Q==750-3P

(S2) Q==4.2P-280(D2Tx) Q=750-3P-3*Tx

(S2Tx) Q=4.2P-280

Pe4= 137.09

Qe4 338.72

Seller 5.96 Pe3-Pe4

Buyer 8.34 Tx-Seller

Tax revenue= Tx*Qe4


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4.3.2 If taxe on the supply side (sellers)


(D2) Q=750-3P

(S2Tx) Q=4.2P-280 +4.2*Tx


Pe5= 151.40Qe5= 295.80


Buyers 5.96

Sellers 8.34


4,231.56

(D) P=a+bQ (S) P=a+bQ

(D) Q=c+dP (S) Q=c+dP

Tx Tx

(DTx) P=a+bQ -Tx (STx) P=a+bQ +Tx

(DTx) Q=c+dP +dTx (STx) Q=c+dP -dTx

d0


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Exercise 2:

Demand and Supply for commodity X:

(D1) P= 500.00 + -0.33 Q

(S1) P= -200.00 + 0.75 Q

1. Find the equilibrium price and quantity (Pe1, Qe1) for commodity X,

elasticity of demand and supply at equilibrium point (Ed1, Es1)?Qe1= 646.15 Ed1= -1.32

Pe1= 284.62 Es1= 0.59

2. Demand for commodity X increase 50% in order to become D2,

(D2) P= 500.00 + -0.22 Q


Qe2= 720.00 Ed2= -4.13

Pe2= 660.00 Es2= 1.22

3. Supply for commodity X increase 40% in order to become S2,

(S2) P= -200.00 + 0.54 Q


Qe3= 923.56 Ed3= -1.44

Pe3= 294.76 Es3= 0.60

4. From D2 and S2, the government set the price control (Pct)


Pct=??? 353.72


Floor price

Result of that price:

Qd=??? 658.27Qs=??? 1,033.61


Excess supply

375.33

Government spending (B) ???

B=??? 132,761.88


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Pct=??? 235.81


Ceiling Price

Result of that price?

Qd=??? 1,188.85Qs=??? 813.51


Excess demand

375.33

Government spending ???

B=??? 375.33 *Pi

4.3 Tax (T)=10%Pe3

Tax=

T=??? 29.48

4.3.1 If taxe on the demand side (buyers)


(D2Tx) P= 470.52 + -0.22 Q

(S2Tx) P= -200.00 + 0.54 Q


Qe4= 884.67 Ed4= -1.39

Pe4= 273.93 Es4= 0.58


Seller= 20.83

Buyer= 8.64* Total government tax revenue is?

26,076.92


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4.3.2 If taxe on the supply side (sellers)


(D2Tx) P= 500.00 + -0.22 Q

(S2Tx) P= -170.52 + 0.54 Q


Qe5= 884.67 Ed5= -1.54Pe5= 303.41 Es5= 0.64


Buyer= 20.83

Seller= 8.64


26,076.92

Ecersice 3:

The price of commodity X before tax is 10$/Kg, Tax on supply side (sellers) 3$/Kg;

Ed of commodity X=-4, Es of commodity X=2. The price of commodity X after tax?

P1= 10.00

Tx= 3.00

Ed= -4.00

Es= 2.00

Pe= 1.00PTx= 11.00

Ecersice 4:

The price of commodity X before tax is 10$/Kg, the price of commodity X after tax is 12 $/Kg.

Ed of commodity X=-4, Es of commodity X=2. How much tax per unit of output?

P1= 10.00

P2= 12.00

Ed= -4.00

Es= 2.00

Tx= 6.00Pe=Tx*Es/(Es-Ed)


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Exercise 1: T

Complete the following table:

Units of

Output TFC TVC TC AFC AVC ATC MC

0.00 500.00 0.00 500.00

100.00 500.00 250.00 750.00 5.00 2.50 7.50 2.50

200.00 500.00 600.00 1,100.00 2.50 3.00 5.50 3.50

300.00 500.00 1,000.00 1,500.00 1.67 3.33 5.00 4.00

400.00 500.00 1,500.00 2,000.00 1.25 3.75 5.00 5.00

500.00 500.00 2,100.00 2,600.00 1.00 4.20 5.20 6.00

0.00

500.00

1,000.00

1,500.00

2,000.00

2,500.00

3,000.00

0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 450.00 500.00

P

Q

X

TFC TVC TC


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Exercise 2:

Complete the following table. Assume that units of fixed input cost $10 each and that units

of variable inputs cost $20 each.

Units of

Fixed

Input K

Units of

Variable

Input L

Units of

Variable

Output

QL

Marginal

Product of

VariableInput

MPL=Q/L

Average

Product of

Variable

Input AVL

=Q/L TFC TVC TC AFC ATC

100.00 0.00 0.00 1,000.00 0.00 1,000.00

100.00 20.00 600.00 30.00 30.00 1,000.00 400.00 1,400.00 1.67 2.33

100.00 40.00 1,500.00 45.00 37.50 1,000.00 800.00 1,800.00 0.67 1.20

100.00 60.00 2,000.00 25.00 33.33 1,000.00 1,200.00 2,200.00 0.50 1.10

100.00 80.00 2,200.00 10.00 27.50 1,000.00 1,600.00 2,600.00 0.45 1.18

100.00 100.00 2,300.00 5.00 23.00 1,000.00 2,000.00 3,000.00 0.43 1.30

Units of

Fixed

Input K

Units of

Variable

Input L

Units of

Variable

Output

QL

Marginal

Product of

Variable

Input

MPL=Q/L

Average

Product of

Variable

Input AVL

=Q/L MC AVC

100.00 0.00 0.00

100.00 20.00 600.00 30.00 30.00 0.67 0.67

100.00 40.00 1,500.00 45.00 37.50 0.44 0.53

100.00 60.00 2,000.00 25.00 33.33 0.80 0.60

100.00 80.00 2,200.00 10.00 27.50 2.00 0.73

100.00 100.00 2,300.00 5.00 23.00 4.00 0.87


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Exercise 3:

Given the total cost function TC=10000+9Q, where Q=units of output:

a. Determine the equations for TFC and TVC, and illustrate graphically the relationships among TFC, TVC, TC.

b.Determine the equation for AFC, AVC, ATC, and MC. Graphically illustrate their relationships to one another.

b.Determine the equation for AFC, AVC, ATC, and MC. Graphically illustrate their relationships to one another.

Relationship: AFC+AVC=ATC

TFC=10000 TVC=9Q TC=TFC+TVC

0.00

1,000.00

2,000.00

3,000.00

4,000.00

0.00 500.00 1,000.001,500.002,000.002,500.00

P

Q

X

TFC TVC TC

0.00

1.00

2.00

3.00

4.00

500.00 1,000.00 1,500.00 2,000.00

P

Q

X

AFC ATC MC AVC


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Exercise 4:

Given the total cost function TC=20000+4Q+0.5Q^2, where Q=units of output:

a. Determine the equations for TFC and TVC. Graph the TFC, TVC, and TC functions, and graphically show their

relationships to one another. How would you describe the behavior of TVC as output increases?

b. Determine the equations for AFC, AVC, ATC, and MC. Graph each of these functions, and graphically show

their relationships to one another.

Exercise 5:

Given the following information:

* Q=6X, where X=units of variable input and Q=units of output.

* There are 10 units of fixed input.

* Price of the fixed inputs = $10/unit.

* Price of the variable inputs = $5/unit.

Determine the corresponding equations for TFC, TVC, TC, AFC, AVC, ATC, and MC.

TFC= 100.00

TVC= 30.00 *Q

TC= 100.00 + 30.00 *Q

AFC= 100.00 /Q

AVC= 30.00

ATC= 30.00 + 100.00 /Q

MC= 30.00

TFC=20000 TVC= 4Q+0.5Q^2 AFC= 20000/Q AVC= 4+0.5Q ATC = 20000/Q +4+0.5Q MC=4+Q


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Exercise 6:

The total cost function of a shirt manufacturer is TC=10+26Q-5Q^2+0.5Q^3, where TC is in hundreds of

dollars per month and Q is output in hundreds of shirts per month.

a. What is the equation for TVC?

b. What is the equation for AVC?

c. What is the equation for ATC?

d. What is the equation for MC?

e. Plot the relationships among TFC, TVC, and TC

f. Plot the relationships among AFC, AVC, AC, and MC

TVC=26Q-5Q^2+0.5Q^3

AVC= 26-5Q+0.5Q^2

ATC=10/Q +26-5Q+0.5Q^2

MC=26-Q+1.5Q^2

TFC=10=TC-TVC

AC=AFC+AVC

MC=(AC.Q)'


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Exercise 7:

Given TC=2000+15Q-6Q^2+Q^3, where Q= units of output:

Complete the following table.

Q TFC TVC TC AFC AVC ATC MC

0.00 2,000.00 0.00 2,000.00

2.00 2,000.00 14.00 2,014.00 1,000.00 7.00 1,007.00 3.00

4.00 2,000.00 28.00 2,028.00 500.00 7.00 507.00 15.00

6.00 2,000.00 90.00 2,090.00 333.33 15.00 348.33 51.00

8.00 2,000.00 248.00 2,248.00 250.00 31.00 281.00 111.00

10.00 2,000.00 550.00 2,550.00 200.00 55.00 255.00 195.00

12.00 2,000.00 1,044.00 3,044.00 166.67 87.00 253.67 303.00

14.00 2,000.00 1,778.00 3,778.00 142.86 127.00 269.86 435.00

16.00 2,000.00 2,800.00 4,800.00 125.00 175.00 300.00 591.00

18.00 2,000.00 4,158.00 6,158.00 111.11 231.00 342.11 771.00

20.00 2,000.00 5,900.00 7,900.00 100.00 295.00 395.00 975.00

22.00 2,000.00 8,074.00 10,074.00 90.91 367.00 457.91 1,203.00

24.00 2,000.00 10,728.00 12,728.00 83.33 447.00 530.33 1,455.00

26.00 2,000.00 13,910.00 15,910.00 76.92 535.00 611.92 1,731.00

28.00 2,000.00 17,668.00 19,668.00 71.43 631.00 702.43 2,031.00

30.00 2,000.00 22,050.00 24,050.00 66.67 735.00 801.67 2,355.00

32.00 2,000.00 27,104.00 29,104.00 62.50 847.00 909.50 2,703.00

34.00 2,000.00 32,878.00 34,878.00 58.82 967.00 1,025.82 3,075.00

36.00 2,000.00 39,420.00 41,420.00 55.56 1,095.00 1,150.56 3,471.00

38.00 2,000.00 46,778.00 48,778.00 52.63 1,231.00 1,283.63 3,891.00

40.00 2,000.00 55,000.00 57,000.00 50.00 1,375.00 1,425.00 4,335.00


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Exercise 8:

Given the following cost information:

AFC for 5 units of output is $2000

AVC for 4 units of output is $850

TC rises by $1240 when the sixth unit of output is produced

ATC for 5 units of output is $2880

It costs $1000 more to produce 1 unit of output than to produce nothing.

TC for 8 units of output is $19040

TVC increases by $1535 when the seventh unit of output is produced.

AFC plus AVC for 3 units of output is $4185

ATC falls by $5100 when out rise from 1 to 2 units.

Using this information, complete the following table:

Output TFC TVC TC AFC AVC ATC MC

0.00 10,000.00 0.00 10,000.00

1.00 10,000.00 1,000.00 11,000.00 10,000.00 1,000.00 11,000.00 1,000.00

2.00 10,000.00 1,800.00 11,800.00 5,000.00 900.00 5,900.00 800.00

3.00 10,000.00 2,555.00 12,555.00 3,333.33 851.67 4,185.00 755.00

4.00 10,000.00 3,400.00 13,400.00 2,500.00 850.00 3,350.00 845.00

5.00 10,000.00 4,400.00 14,400.00 2,000.00 880.00 2,880.00 1,000.00

6.00 10,000.00 5,640.00 15,640.00 1,666.67 940.00 2,606.67 1,240.00

7.00 10,000.00 7,175.00 17,175.00 1,428.57 1,025.00 2,453.57 1,535.00

8.00 10,000.00 9,040.00 19,040.00 1,250.00 1,130.00 2,380.00 1,865.00


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Exercise 9:

9.1 Use the production function: %Q={[1+%TC]^(alpha+beta)}-1

Q=10K^(0.5)*L^(0.6)

K

6.00 24.49 37.13 47.35 56.27 64.34 71.77

5.00 22.36 33.89 43.23 51.37 58.73 65.52

4.00 20.00 30.31 38.66 45.95 52.53 58.60

3.00 17.32 26.25 33.48 39.79 45.49 50.75

2.00 14.14 21.44 27.34 32.49 37.14 41.44

1.00 10.00 15.16 19.33 22.97 26.27 29.30

1.00 2.00 3.00 4.00 5.00 6.00 L

a. Complete the production table.

b. For this production system, are returns to scale decreasing, constant, or increasing? Explain.

c. Suppose the wage rate is $28, the price of capital also is $28 per unit, and the firm currently is

producing 30.31 units of output per period using four units of capital and two units of labor. Is

this an efficient resource combination? Explain. What would be a more efficient combination?

%TC= 700.00%

%Q= 884.92%

Q2= 98.49


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9.2 Use the data from 9.1 to answer the following questions.

a. If the rate of capital input is fixed at three and if output sells for $5 per unit, determine the

total average, and marginal product functions and the marginal revenue product function for

labor in the following table.

L TPL

APL

MPL

MRPL

0.00 0.00

1.00 17.32 17.32 17.32 86.60

2.00 26.25 13.13 8.93 44.66

3.00 33.48 11.16 7.23 36.15

4.00 39.79 9.95 6.31 31.54

5.00 45.49 9.10 5.70 28.50

6.00 50.75 8.46 5.26 26.29

b. Using data from part a, if the wage rate is $ 28 per unit, how much labor should be employed?

c. If the rate of labor input is fixed at 5 and the price of output is $5 per unit, determine the total,

average, and marginal product functions for capital and the marginal revenue product of capital

in the following table 5.00

K TPK APK MPK MRPK0.00 0.00

1.00 26.27 26.27 26.27 131.33

2.00 37.14 18.57 10.88 54.40

3.00 45.49 15.16 8.35 41.74

4.00 52.53 13.13 7.04 35.19

5.00 58.73 11.75 6.20 31.00

6.00 64.34 10.72 5.61 28.03

d. Using the data from part c, if the price of capital is $40 per unit, how many units of capital

should be employed? 3.00


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Exercise 10:

International Publishing has kept the following data on labor input and production of textbook

for each of eight production periods.

Production period 1 2 3 4 5 6 7 8

Labor Input 4 3 6 8 2 7 5 1

Output of Books 260 190 900 800 110 1500 2100 50

a. Use the data on labor input and total product to compute the average and marginal product for labor input rate from one

to eight. (Assume that a zero labor input would resuld in zero output)

L QL APL MPL1.00 50.00 50.00

2.00 110.00 55.00 60.00

3.00 190.00 63.33 80.00

4.00 260.00 65.00 70.00

5.00 2,100.00 420.00 1,840.00

6.00 900.00 150.00 -1,200.00

7.00 1,500.00 214.29 600.00

8.00 800.00 100.00 -700.00

b. Draw, on one set of axes the QL, APL, MPL

-1,500.00

-1,000.00

-500.00

0.00

500.00

1,000.00

1,500.00

2,000.00

2,500.00

0.00 5.00 10.00

L

X

QL

APL

MPL


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Exercise 11: PK= 20.00

PL= 5.00

K 1.00 1.00 1.00 1.00 1.00 1.00

L 1.00 2.00 3.00 4.00 5.00 6.00

QL 6.00 13.00 21.00 28.00 34.00 39.00

APL 6.00 6.50 7.00 7.00 6.80 6.50MPL 6.00 7.00 8.00 7.00 6.00 5.00

TC= 22,800.00 34,600.00 46,400.00 58,200.00 70,000.00 81,800.00

VC= 11,800.00 23,600.00 35,400.00 47,200.00 59,000.00 70,800.00

FC= 11,000.00 11,000.00 11,000.00 11,000.00 11,000.00 11,000.00

AC= 3,800.00 2,661.54 2,209.52 2,078.57 2,058.82 2,097.44

MC= 1,685.71 1,475.00 1,685.71 1,966.67 2,360.00

AVC= 1,966.67 1,815.38 1,685.71 1,685.71 1,735.29 1,815.38


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Exercise 1: TThe following table shows the relationship between hours of study and final examinationgrades in each of three classes for a particular student, who has a total of 15 hours to preparefor these tests. If the objective is to maximize the average grade in the three classes, how manyhours should this student allocate to preparation for each of these classes? Explain yourapproach to this problem.

Economics Mathematics ManagementHours Grade Hours Grade Hours Grade0.00 40.00 0.00 50.00 0.00 30.001.00 50.00 1.00 60.00 1.00 50.002.00 59.00 2.00 69.00 2.00 60.003.00 67.00 3.00 77.00 3.00 66.004.00 74.00 4.00 84.00 4.00 71.005.00 79.00 5.00 90.00 5.00 74.006.00 83.00 6.00 95.00 6.00 76.00

7.00 86.00 7.00 96.00 7.00 77.008.00 88.00 8.00 97.00 8.00 77.009.00 89.00 9.00 97.00 9.00 77.0010.00 89.00 10.00 97.00 10.00 77.00


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Economics Mathematics

Hours Grade Hours Grade0 40 0 501 50 1 602 59 2 693 67 3 774 74 4 845 79 5 906 83 6 957 86 7 968 88 8 979 89 9 9710 89 10 97

Management

Hours Grade M Eco M Math M Mana

0 301 50 10 10 202 60 9 9 103 66 8 8 64 71 7 7 55 74 5 6 36 76 4 5 27 77 3 1 18 77 2 1 0

9 77 1 0 010 77 0 0 0


46/65

Exercise 2:

Given the total cost function:

TC=1000+10Q-0.9Q^2+0.04Q^3find the rate of output that results in minimum average variable cost.

AVC=VC/Q=10-0.9Q+0.04Q^2AVCmin Q= - (-0.9)/(2*0.04) = 11.25 => AVC min = 14.05TC'= 10.00 + -1.80 *Q +

0.12 *Q^2TC''= -1.80 + 0.24 *Q= -1.56


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a. Determine the break even number of programs and the total revenue associate with this volume.

Q FC VC AFC AVC TC

0.00 23,000.00 0.00 23,000.00100.00 23,000.00 650.00 230.00 6.50 23,650.00200.00 23,000.00 1,300.00 115.00 6.50 24,300.00300.00 23,000.00 1,950.00 76.67 6.50 24,950.00400.00 23,000.00 2,600.00 57.50 6.50 25,600.00500.00 23,000.00 3,250.00 46.00 6.50 26,250.00600.00 23,000.00 3,900.00 38.33 6.50 26,900.00700.00 23,000.00 4,550.00 32.86 6.50 27,550.00800.00 23,000.00 5,200.00 28.75 6.50 28,200.00900.00 23,000.00 5,850.00 25.56 6.50 28,850.00

1,880.60 23,000.00 12,223.88 12.23 6.50 35,223.88686.57 23,000.00 4,462.69 33.50 6.50 27,462.69

MC TR MR

0.00 -23,000.006.50 4,000.00 40.00 -19,650.006.50 8,000.00 40.00 -16,300.006.50 12,000.00 40.00 -12,950.006.50 16,000.00 40.00 -9,600.006.50 20,000.00 40.00 -6,250.006.50 24,000.00 40.00 -2,900.006.50 28,000.00 40.00 450.00

6.50 32,000.00 40.00 3,800.006.50 36,000.00 40.00 7,150.006.50 75,223.88 40.00 40,000.006.50 27,462.69 40.00 0.00

TR= 0.00 + 40.00 *QTC= 23,000.00 + 6.50 *Q -23,000.00 + 33.50 *QQbep= 686.57


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b. MicroApplications has a minimum profit target of $40000 on each new program it develops.Determine the unit and dollar volume of sales required to meet this goal.= 40,000.00Q= 1,880.60TR= 75,223.88c. While this program is still in the development stage, market prices for software fall by 25 percentdue to a significant increase in the number of programs being supplied to the market. Determinethe new break even unit and dollar volumes.Qbep= 978.72TR= 29,361.70Pro=0Qbep=FC/(P-AVC)Pro=0Trbep=FC/(1-AVC/P)=P*Qbep


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A firm is considering the rental of a new copying machine. The rental terms AVC ATC Exercise 4:machines under consideration are given here:

Costs 0.03 10.03

MachineMonthly Fee

($)

Per Copy

($) 0.03 5.03A 1,000.00 0.03 0.03 3.36B 300.00 0.04 0.03 2.53C 100.00 0.05 0.03 2.03

How many copies per month would the firm have to make for B to be a lowe 0.03 1.70than C? For A to be lower cost than B? TC(B)-TC(C)

Q FC VC TC AFC 200.000.00 1,000.00 0.00 100.00

100.00 1,000.00 3.00 1,003.00 10.00 0.00200.00 1,000.00 6.00 1,006.00 5.00 -100.00300.00 1,000.00 9.00 1,009.00 3.33 -250.00

400.00 1,000.00 12.00 1,012.00 2.50 -300.00500.00 1,000.00 15.00 1,015.00 2.00 -400.00600.00 1,000.00 18.00 1,018.00 1.67 -500.00

TC(A)= 1,000.00 + 0.03 *Q -600.00TC(B)= 300.00 + 0.04 *Q -700.00TC(C)= 100.00 + 0.05 *Q -800.00

Q TC(A) TC(B) TC(C) TC(A)-TC(B) TC(A)-TC(C)0.00 1,000.00 300.00 100.00 700.00 900.00

10,000.00 1,300.00 700.00 600.00 600.00 700.00

20,000.00 1,600.00 1,100.00 1,100.00 500.00 500.0030,000.00 1,900.00 1,500.00 1,600.00 400.00 300.0045,000.00 2,350.00 2,100.00 2,350.00 250.00 0.0050,000.00 2,500.00 2,300.00 2,600.00 200.00 -100.0060,000.00 2,800.00 2,700.00 3,100.00 100.00 -300.0070,000.00 3,100.00 3,100.00 3,600.00 0.00 -500.0080,000.00 3,400.00 3,500.00 4,100.00 -100.00 -700.0090,000.00 3,700.00 3,900.00 4,600.00 -200.00 -900.00

100,000.00 4,000.00 4,300.00 5,100.00 -300.00 -1,100.00


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Exercise 5:

Suppose that the total cost equation (TC) for a monopolist is given byTC=500+20Q^2

Let the demand equation be given byP=400-20Q

What are the profit-maximizing price and quantity?What are the Revenue-maximizing price and quantity?Complete the following table.

Q TC TR MC MR Profit

0.00 500.00 0.00 0.00 400.00 -500.001.00 520.00 380.00 40.00 360.00 -140.002.00 580.00 720.00 80.00 320.00 140.003.00 680.00 1,020.00 120.00 280.00 340.004.00 820.00 1,280.00 160.00 240.00 460.005.00 1,000.00 1,500.00 200.00 200.00 500.00

6.00 1,220.00 1,680.00 240.00 160.00 460.007.00 1,480.00 1,820.00 280.00 120.00 340.008.00 1,780.00 1,920.00 320.00 80.00 140.009.00 2,120.00 1,980.00 360.00 40.00 -140.0010.00 2,500.00 2,000.00 400.00 0.00 -500.0011.00 2,920.00 1,980.00 440.00 -40.00 -940.0012.00 3,380.00 1,920.00 480.00 -80.00 -1,460.0013.00 3,880.00 1,820.00 520.00 -120.00 -2,060.0014.00 4,420.00 1,680.00 560.00 -160.00 -2,740.00


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Exercise 6:

A firm sells in two markets and has constant marginal cost of production equal to $2 per unit,FC=5. The demand equations for the two markets are as follows:Market 1: Market 2:

P1=14-2Q1 P2=10-Q2

Use third-degree price discrimination, what are the profit-maximizing price and quantitiesin each market? Show that greater profits result from price discrimination than would beobtained if a uniform price were used.MC= 2.00FC= 5.00

Solution 1

MR1= 14.00 + -4.00 Q1MR2= 10.00 + -2.00 Q2Price discriminationMR1=MC Q1= 3.00

P1= 8.00TR1= 18.00

MR2=MC Q2= 4.00P2= 6.00TR2= 16.00= 29.00

non-price discriminationP1=14-2Q1 3P=34-2QP2=20-2Q2

P=34/3-2/3QMR=34/3-4/3Q MC=2Q= 7.00 P1= 6.67TR= 46.67TC= 19.00= 27.67

Greater = 1.33


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Exercise 7:

An automobile manufacturer estimates that total variable costs will be $500 million andtotal fixed costs will be $1 billion in the next year. In setting prices, it is assumed thatsales will be 80% of the firm's 125000 vehicle per year capacity, or 100000 units. Thetarget rate of return is 10 percent, which is to be earned on an investment of $2 billion.If prices are set on a cost-plus basic, what price should be charged for each automobile?P=AC+ Pro/Unit

VC= 500.00FC= 1,000.00TC= 1,500,000,000.00Pro= 200,000,000.00Pro/Unit= 2,000.00AC= 15,000.00P 17,000.00


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54/65

Exercise 9: ging bi 6, 7Global motors sells its automobies in both the United States and Japan. Due to traderestriction, a vehicle sold in one country cannot be resold in the other. The demandfunctions for the two countries areUS P=30000-0.4Q

Japan P=20000-0.2Q

The firm's total cost function is TC=10,000,000+12,000Q. What price should Globalcharge in each country in order to maximize profit? What will be the total profit?

MR(US)= 30,000.00 + -0.80 *QMR(JP)= 20,000.00 + -0.40 *Q

MC=TC'= 12,000.00MR(US)=MC


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Exercise 10: ly o hmA firm produces two types of calculators, x and y. The revenue and cost equations areshown below with Qx and Qy measured in thousands of calculators per year.Total revenue=2Qx+3Qy

Total cost=Qx^2-2Qx*Qy-2Qy^2+6Qx+14Qy+14.72*10^6

a. To maximize profit, how many of each type of calculator should the firm produce?

b. What is the maximum profit the firm can earn?=>Pro=TR-TC=-4Qx-11Qy-Qx^2+2QxQy+2Qy^2-14.72*10^6

=>Pro maxPro x=-4-2Qx =0=>Pro y=-11+2Q=0 n v l ngn=>Qx=X= 0.50 500.00=>Qy=Y= 2.50 2,500.00=>Pro= 500.00


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Exercise 11:

Miss X is considering the rental of a new telephone. The rental terms of each of the threetelephone under consideration are given here:

Costs

TelephoneMonthly Fee

($)

Per Min

($)

A 40,000.00 1,000.00B 20,000.00 1,200.00C 50,000.00 1,250.00 and free of change per month for call: 50000

1. Find the TC function/month as TC=FC+AVC*Q for A, B and C?2. Compare beetwen A and B?3. Compare beetwen A, B and C?

TC(A)= 40,000.00 + 1,000.00 *Q

TC(B)= 20,000.00 + 1,200.00 *QTC(C)= 50,000.00 if Q 40.00

Q TC(A) TC(B) TC(C) TC(A)-TC(B) TC(A)-TC(C) TC(B)-TC(C)0.00 0.00 17,000.00 -20,000,000.00 -17,000.00 20,000,000.00 20,017,000.00

10.00 0.00 207,000.00 -30,000,000.00 -207,000.00 30,000,000.00 30,207,000.0020.00 0.00 397,000.00 -40,000,000.00 -397,000.00 40,000,000.00 40,397,000.0025.00 0.00 492,000.00 -45,000,000.00 -492,000.00 45,000,000.00 45,492,000.00

60.00 0.00 1,157,000.00 -80,000,000.00 -1,157,000.00 80,000,000.00 81,157,000.0070.00 0.00 1,347,000.00 -90,000,000.00 -1,347,000.00 90,000,000.00 91,347,000.0080.00 0.00 1,537,000.00 -100,000,000.00 -1,537,000.00 100,000,000.00 101,537,000.0090.00 0.00 1,727,000.00 -110,000,000.00 -1,727,000.00 110,000,000.00 111,727,000.00

100.00 0.00 1,917,000.00 -120,000,000.00 -1,917,000.00 120,000,000.00 121,917,000.00110.00 0.00 2,107,000.00 -130,000,000.00 -2,107,000.00 130,000,000.00 132,107,000.00120.00 0.00 2,297,000.00 -140,000,000.00 -2,297,000.00 140,000,000.00 142,297,000.00


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Compare between A and B 0100 TC(A)


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Exercise 12:

A Hotel have data:Rooms:

xed cost ($/mont =FCost ($/room/day =AVCrice ($/room/day =PMonth=30 days

1. Find the TC function/month as TC=FC+AVC*Q?2. Find the TR function/month as TR=P*Q?3. Find the function/month as =TR-TC?4. Find the break even point (BEP) (Qbe; TRbe)?5. Find Profit max/month with the data above?6. Find the , if Q=150%Qbe?7. Find Q/month, if =50*10^6? t li nhun = 50 triu tm sn lng8. Find P/room/day, if=50*10^6 and Q=200%*Qbe

TC= 200,000,000.00 + 100,000.00 *QTR= 250,000.00 *Q

= -200,000,000.00 + 150,000.00 *Q

= 1,333.33 =FC/(P-AVC) 2,666.67=>TRbep= 333,333,333.33 =FC/(1-AVC/P)=>Goal Seek=>P= 250,000.00Q= 1,333.33 2,666.67 44.44%

TR= 333,333,333.33 666,666,666.67TC= 333,333,333.33 466,666,666.67Pro= 0.00 200,000,000.00

=>Qmax= 6,000.00 =200*30Pro= 700,000,000.00 =TR-TC

700,000,000.00Pro=TR-TC=(P*Q)-(FC+AVC*Q)=(P-AVC)*Q-FC

=>P=??? 193,750.00

200.00

200,000,000.00

100,000.00

250,000.00


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Exercise 13:

A Firm have data:FC($/month)= 20,000,000.00

AVC($/Q)= 4,000.00

P($/Q)= 12,000.00

Q=Number of Q/Month1. Find the TC function/month as TC=FC+AVC*Q?2. Find the TR function/month as TR=P*Q?3. Find the function/month as =TR-TC?4. Find the break even point (BEP) (Qbe; TRbe)?5. If Q=200%*Qbe, find and /TC; /TR?6. If /TC=25%; Find , Q, /TR?7. Find the shutdown point of the firm in the short run?/TR=X% /TC=X%/(1+X%)

/TC=Y% /TR=Y%/(1-Y%)

TC= 20,000,000.00 + 4,000.00 *QTR= 12,000.00 *Q= -20,000,000.00 + 8,000.00 *QQbe= 2,500.00TRbe= 30,000,000.00

Q= 5,000.00

= 20,000,000.00

/TC= 25%Q= 3,571.26= 8,570,103.91/TR= 20%

Shutdown pointP= 4,000


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Exercise 14:

A Firm have data:FC($/month)= 20,000,000.00

AVC($/Kg)= 8,000.00

P($/Kg)= 12,000.00

Q (Kg/Month)= 20,000.00

1. Find the /month?

2. If Q(Kg/month) around 15000, 16000, 17000, 18000, 19000, 20000, 21000, 22000, 23000, 24000, 25000

and P ($/Kg) around 8000, 9000, 10000, 11000, 12000, 13000, 14000, 15000, 16000, 17000, 18000

Show the Profits of the firm? 23,000 24,000 25,000-20,000,000 -20,000,000 -20,000,000

TC= 180,000,000.00 3,000,000 4,000,000 5,000,000TR= 240000000 26,000,000 28,000,000 30,000,000Pro= 60,000,000.00 49,000,000 52,000,000 55,000,000

72,000,000 76,000,000 80,000,000

95,000,000 100,000,000 105,000,000118,000,000 124,000,000 130,000,000141,000,000 148,000,000 155,000,000164,000,000 172,000,000 180,000,000187,000,000 196,000,000 205,000,000210,000,000 220,000,000 230,000,000

16,000 17,000 18,000 19,000 20,000 21,000 22,000-20,000,000 -20,000,000 -20,000,000 -20,000,000 -20,000,000 -20,000,000 -20,000,000-4,000,000 -3,000,000 -2,000,000 -1,000,000 0 1,000,000 2,000,000

12,000,000 14,000,000 16,000,000 18,000,000 20,000,000 22,000,000 24,000,00028,000,000 31,000,000 34,000,000 37,000,000 40,000,000 43,000,000 46,000,00044,000,000 48,000,000 52,000,000 56,000,000 60,000,000 64,000,000 68,000,00060,000,000 65,000,000 70,000,000 75,000,000 80,000,000 85,000,000 90,000,00076,000,000 82,000,000 88,000,000 94,000,000 100,000,000 106,000,000 112,000,00092,000,000 99,000,000 106,000,000 113,000,000 120,000,000 127,000,000 134,000,000

108,000,000 116,000,000 124,000,000 132,000,000 140,000,000 148,000,000 156,000,000124,000,000 133,000,000 142,000,000 151,000,000 160,000,000 169,000,000 178,000,000140,000,000 150,000,000 160,000,000 170,000,000 180,000,000 190,000,000 200,000,000


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Exercise 1: TD: 100.00 =PV gi 1 s m chy ra 100

X months: 12.00 =Nperi/month: 1.00% =Rate

R: 112.68 =FV tr 1 s dng chy vo 112.68112.68 =100*(1+1%)^12

Yt=Yo*(1+i)^(X) Ya=Yb*(1+i)^(a-b)Yo=PV=Present valueYt=FV=Future valueX=Nper=The total muber of payment period in an annuityi=Rate=The interest rate per period

Exercise 2: Yt=Yo*(1+i)^(X)D: 887.45 =PV Yo=Yt/[(1+i)^(X)]

X months: 12.00 =Nper Yo=Yt*(1+i)^(-X)i/month: 1.00% =RateR: 1,000.00 =FV

Exercise 3: Yt=Yo*(1+i)^(X)D: 100.00 =PV i=[Yt/Yo]^[1/X]-1

X months: 90.00 =Nperi/month: 1.80% =Rate

R: 500.00 =FV

Exercise 4:

D: 100.00 =PV X=log(Yt/Yo)/log(1+i)X months: 161.75 =Nper 161.75i/month: 1.00% =Rate

R: 500.00 =FV


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Exercise 5: Yt=Yo*(1+i)^(X)Account A Account B YtA=YoA*(1+iA)^(XA)

D: 100.00 500.00 YtB=YoB*(1+iB)^(XB)i/month: 1.00% 0.20% YtA=K*YtB and XA=XB=XX month: 60.00 60.00 =>X=log(K*YoB/YoA)/(Log((1+iA)/(1+iB)))

R: 181.67 563.68

Nper 202.39After X months: RA RB RA-RB

R: 749.18 749.18 0.00

289.55After X months: RA RB RA/RB

R: 1,783.41 891.70 2.00Cho 1 gi nh r dng Goal Seek, set cell KQ sau khi n tnh bng cng tnh, to value: hng s, by changing sell gi nhExercise 6:

PMT: -100.00X months: 60.00

i/month: 1.00%

FV= 8,166.97

PMT=The payment made each period and cannot change over the life of the annuity.

Exercise 6:

PMT: -100.00

X months: 42.23

i/month: 0.80%

FV= 5,000.00

Account A=Account B

202.39

Account A=2 Account B

289.55

(1 ) 1*

1 (1 )*

X

X

iFV PMT

i

iPV PMT

i


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Exercise 12:

PMT: -1,055.82

X months: 10.00

i/month: 1.00%

PV= 10,000.00

Exercise 13:

Real interest rate/ 1 month= 1.00% 1.00% 0.99% 0.98% 0.97% 0.96%Real interest rate/ 2 months= 2.01% 2.00% 1.98% 1.96% 1.94% 1.92%Real interest rate/ 3 months= 3.03% 3.01% 2.99% 2.96% 2.93% 2.90%Real interest rate/ 4 months= 4.06% 4.04% 4.00% 3.96% 3.92% 3.89%Real interest rate/ 5 months= 5.10% 5.08% 5.02% 4.98% 4.93% 4.88%Real interest rate/ 6 months= 6.15% 6.12% 6.06% 6.00% 5.94% 5.89%Real interest rate/ 7 months= 7.21% 7.18% 7.10% 7.03% 6.97% 6.90%Real interest rate/ 8 months= 8.29% 8.24% 8.16% 8.08% 8.00% 7.92%

Real interest rate/ 9 months= 9.37% 9.32% 9.23% 9.13% 9.04% 8.96%Real interest rate/ 10 months= 10.46% 10.41% 10.30% 10.20% 10.10% 10.00%Real interest rate/ 11 months= 11.57% 11.51% 11.39% 11.27% 11.16% 11.05%Real interest rate/ 12 months= 12.68% 12.62% 12.49% 12.36% 12.24% 12.12%Real interest rate/ 13 months= 13.81% 13.74% 13.59% 13.46% 13.32% 13.19%Real interest rate/ 14 months= 14.95% 14.87% 14.71% 14.56% 14.42% 14.27%Real interest rate/ 15 months= 16.10% 16.01% 15.84% 15.68% 15.52% 15.37%Real interest rate/ 16 months= 17.26% 17.17% 16.99% 16.81% 16.64% 16.47%Real interest rate/ 17 months= 18.43% 18.33% 18.14% 17.95% 17.77% 17.59%

Real interest rate/ 18 months= 19.61% 19.51% 19.30% 19.10% 18.91% 18.72%Real interest rate/ 19 months= 20.81% 20.70% 20.48% 20.26% 20.06% 19.85%Real interest rate/ 20 months= 22.02% 21.90% 21.67% 21.44% 21.22% 21.00%Real interest rate/ 21 months= 23.24% 23.11% 22.86% 22.62% 22.39% 22.16%Real interest rate/ 22 months= 24.47% 24.34% 24.07% 23.82% 23.57% 23.33%Real interest rate/ 23 months= 25.72% 25.57% 25.30% 25.03% 24.77% 24.51%Real interest rate/ 24 months= 26.97% 26.82% 26.53% 26.25% 25.97% 25.70%


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0.95% 0.94% 0.93% 0.92% 0.92% 0.91% 0.90%

1.91% 1.89% 1.87% 1.86% 1.84% 1.82% 1.81%

2.87% 2.85% 2.82% 2.80% 2.77% 2.75% 2.73%

3.85% 3.81% 3.78% 3.75% 3.71% 3.68% 3.65%

4.84% 4.79% 4.75% 4.70% 4.66% 4.62% 4.58%

5.83% 5.78% 5.72% 5.67% 5.62% 5.57% 5.53%

6.83% 6.77% 6.71% 6.65% 6.59% 6.53% 6.48%

7.85% 7.77% 7.70% 7.63% 7.57% 7.50% 7.43%

8.87% 8.79% 8.71% 8.63% 8.55% 8.47% 8.40%

9.90% 9.81% 9.72% 9.63% 9.54% 9.46% 9.38%

10.95% 10.84% 10.74% 10.64% 10.55% 10.45% 10.36%

12.00% 11.89% 11.77% 11.67% 11.56% 11.46% 11.36%

13.06% 12.94% 12.82% 12.70% 12.58% 12.47% 12.36%

14.14% 14.00% 13.87% 13.74% 13.61% 13.49% 13.37%

15.22% 15.07% 14.93% 14.79% 14.65% 14.52% 14.39%

16.31% 16.15% 16.00% 15.85% 15.70% 15.56% 15.42%17.42% 17.25% 17.08% 16.92% 16.76% 16.61% 16.46%

18.53% 18.35% 18.17% 18.00% 17.83% 17.67% 17.51%

19.65% 19.46% 19.27% 19.09% 18.91% 18.74% 18.57%

20.79% 20.58% 20.39% 20.19% 20.00% 19.81% 19.63%

21.94% 21.72% 21.51% 21.30% 21.10% 20.90% 20.71%

23.09% 22.86% 22.64% 22.42% 22.21% 22.00% 21.80%

24.26% 24.02% 23.78% 23.55% 23.33% 23.11% 22.89%

25.44% 25.18% 24.94% 24.69% 24.46% 24.23% 24.00%

Documents

FTU2 - Microeconomics 2 - Trần Thông Tú - 1201017440