SOLUTIONS: MONOPOLY

 

1.        

Price

Quantity

MR

MC

4

400

4

2

3.5

800

3

2

3

1400

2.33

2

2.5

2800

2

2

2

4000

0.833

2s

 

b. Profit max Q = 2800; P= 2.5

c. VC = MC x Q (This is the case when MC is constant)

            VC (q=2800) = 2800x 2 = 5600

            FC = 1000

            TC = VC + FC = 5600+1000=6600

            Profit = TR - TC = 7000-6600 = 400.

d. Q = 2800; P= 2.5; profit = 900

Unless the firm decides to shut down, fixed costs do not affect price-output decisions.

2.                  a.

 

Price

Quantity

MR

MC

8

100

 

1

7

150

5

1

6

200

3

1

5

250

1

1

4

300

-1

1

3

350

-3

1

2

400

-5

1

 

b. P= 5; Q = 250,000

c. VC = 250,000

FC= 100,0000

TC= 350,000

TR = 5 (250,000) = 1,250,000

Profit = 900,000

d. Profit max price and quantity does not change. New  profit = 1,250,000 - 400,000 = 850,000

e. The first graph is the one that corresponds to this particular exercise where the MC is constant at one. The second graph is for the typical case where the MC is not constant.

 

 

 


Quantity

 

= Old profit

 

= New profit

 
Text Box: New ProfitText Box: Old Profit

Price

 

New ATC

 

Demand

 

MR

 

MC = AVC =1

 

Old ATC

 

New ATC

 

Old ATC

 

= Old profit

 

MC

 

Quantity

 

= New profit

 

New ATC

 

New ATC

 

Old ATC

 

Old ATC

 

Price

 

MR

 

Demand

 

 

 

3.                  a. See table

 

Price

Quantity

Mg Revenue

MC

10

1

-

8

9

2

8

8

8

3

6

8

7

4

4

8

6

5

2

8

5

6

0

8

4

7

-2

8

 

 

Profit max price = 9; quantity = 2; profit = TR (18) - TC  (16) = 2

 

b. See table

 

Price

Quantity

Mg Revenue

MC

0.5

500,000

-

0.1

0.45

600,000

0.2

0.1

0.4

700,000

0.1

0.1

0.35

800,000

0

0.1

0.3

900,000

0.1

0.1

 

Profit max price = 0.4 ; quantity = 700,000 ; profit = TR (280,000) - TC  (120,000) = 160,000

 

c. See Table

 

Price

Quantity

Mg Revenue

MC

20

400

-

-

18

800

16

5

16

1200

12

6

14

1600

8

8

12

2000

4

9

10

2400

0

12

 

Profit max price = 14; quantity = 1,600; profit = TR (22,400) - TC  (12,600) = 9,800

 

d. See Table

 

Price

Quantity

Mg Revenue

MC

1

1000

 

 

0.9

2000

0.8

0.1

0.8

3500

0.667

0.1

0.7

5500

0.525

0.1

0.6

8000

0.380

0.1

0.5

11000

0.233

0.110

0.4

15000

0.125

0.125

0.3

20000

0

0.125

 

Profit max price = 0.4; quantity = 15,000; profit = TR (6,000) - TC  (1,730) = 4,270

 

PRICE DISCRIMINATION

 

4.

Nonaddicts

Price

Quantity

Revenues

Mg Revenue

MC

50

100

5000

50

10

40

300

12000

35

10

30

500

15000

15

10

20

1000

20000

10

10

 

 

Profit max price = 20; quantity = 1000

 

                                                            Addicts

Price

Quantity

Revenues

Mg Revenue

MC

50

500

25000

50

10

40

700

28000

15

10

30

1050

31500

10

10

20

1650

33000

2.5

10

 

      Profit max price = 30; quantity = 1050

 

 

a.      See tables.

b.      See below each table

c.       Total profit= TR [(1050x30)+(1000x20)]- TC [(1050+1000=2050)x10] = 51,500 - 20,500 = 31,000

 

5. a. See Table

 

Home Market

Price

Quantity

Revenues

Mg Revenue

MC

10

2,000

$20,000.00

 

1

9

2,500

$22,500.00

5

1

8

3,000

$24,000.00

3

1

7

3,500

$24,500.00

1

1

6

4,000

$24,000.00

-1

1

5

4,500

$22,500.00

-3

1

4

5,000

$20,000.00

-5

1

 

      Profit max price = 7; quantity = 3,500

 

                        Foreign Market

Price

Quantity

Revenues

Mg Revenue

MC

10

2,000

20000

 

1

9

3,000

27000

7

1

8

4,000

32000

5

1

7

5,000

35000

3

1

6

6,000

36000

1

1

5

7,000

35000

-1

1

4

8,000

32000

-3

1

 

 

b. Profit max price = 6; quantity = 6,000

 

d.      Total profit = (7x3,500) + (6x6,000) - 5,000 - (3,500+6,000)x 1

 

6. a. See table.

Suburbs

           

Price

Quantity

Revenues

MR

MC

4

200

800

 

1

3.5

400

1400

3

1

3

600

1800

2

1

2.5

800

2000

1

1

2

1000

2000

0

1

1.5

1200

1800

-1

1

 

b. Profit max price = 2.5; quantity = 800

 

                                                Inner City

                       

Price

Quantity

Revenues

MR

MC

4

100

400

 

1

3.5

120

420

1

1

3

140

420

0

1

2.5

160

400

-1

1

2

180

360

-2

1

1.5

200

300

-3

1

 

b. Profit max price = 3.5; quantity = 120

 

a.      Total Profit = 2,420 - 100 - 920

 

APPLICATIONS

 

7. See Table

 

Price

Quantity

Revenues

Imelda's TR

MR

MC

40

10,000

400000

80000

 

20

35

20,000

700000

140000

30

20

30

30,000

900000

180000

20

20

25

40,000

1000000

200000

10

20

20

50,000

1000000

200000

0

20

 

a.      See table.

b.      Profit Max Price = 30; quantity = 30,000.

c.      Imelda's total revenue for each price: see table.

d.      Price maximizes Imelda's revenues = 25 or 20.

 

8.

 

           

Price

Quantity

Revenues

Magdal's TR

MR

MC

20

20,000

400000

100000

 

6

18

25,000

450000

112500

10

6

16

30,000

480000

120000

6

6

14

35,000

490000

122500

2

6

12

40,000

480000

120000

-2

6

10

45,000

450000

112500

-6

6

 

a.      See table

b.      P = 16; Q = 30,000

c.      See table

d.      P=14 Magdalena's revenues = 122,500

 

9.

 

           

Price

Quantity

Revenues

MR

MC

MC + tax

 

1

30,000

30000

 

 

 

 

0.95

40,000

38000

0.8

0.1

0.2

 

0.9

50,000

45000

0.7

0.1

0.2

 

0.85

60,000

51000

0.6

0.1

0.2

 

0.8

70,000

56000

0.5

0.1

0.2

 

0.75

80,000

60000

0.4

0.1

0.2

 

0.7

90,000

63000

0.3

0.1

0.2

 

0.65

100,000

65000

0.2

0.1

0.2

Profit max with tax

0.6

110,000

66000

0.1

0.1

0.2

Profit max without tax

0.55

120,000

66000

0

0.1

0.2

 

 

 

a.      See table

b.      P= 0.6; Q= 110,000

c.      Tax adds to MC. New P = 0.65; new Q=100,000.

d.      Consumers pay five cents more.

 

MC without tax

 

MR

 

0.65

 

0.6

 

0.2

 

0.1

 

100,000

 

110,000

 

MC plus tax

 

Demand

 

 

 

10.

 

                       

Price

Quantity

Revenues

MR

MC

45

60,000

2700000

 

15

40

80,000

3200000

25

15

35

100,000

3500000

15

15

30

120,000

3600000

5

15

25

140,000

3500000

-5

15

 

a.      See table

b.      P=35; q= 100,000

c.      Company must charge the highest possible price = $25. At this price the company can sell 140,000 units.

 

11.

 

                       

Price

Quantity

Revenues

MR

MC

Elasticity

 

10

1

10

 

8

 

 

9

2

18

8

8

6.33

Elastic

8

3

24

6

8

3.40

Elastic

7

4

28

4

8

2.14

Elastic

6

5

30

2

8

1.44

Elastic

5

6

30

0

8

1.00

Unitary elastic

4

7

28

-2

8

0.69

Inelastic