MBA 500 Managerial Economics-Assignment

7/30/2019 MBA 500 Managerial Economics-Assignment

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MBA 500 Managerial Economics

1st Unit

Case 11. Tickets were sold last year = $100 million $1 = 100 million.

2. Price elasticity of demand is 0.4,

So,P

Q

dP

dQ4.0= = 0.4 100 million = 40,000,000

i.e. Slope =000,000,40

1=

dQ

dP

Demand function: P = a bQ,

When P = $1, Q = 100 million, b = 000,000,40

1=

dQ

dP

1 = a ( )000,000,100000,000,40

1

a = 3.5

Demand function: P = 3.5 Q000,000,40

1

Demand Table:

P $1 $1.1 $1.2 $1.3 $1.4 $1.5

Q 100m 96m 92m 88m 84m 80m

3. When both ends meet, total revenue = total cost,

We know that:P

dPP=0

,Q

dQQ =0

,

then0

0

P

Q

P

dP

Q

dQ

Ed

== , 00

4.0 PQ =

100,000,000(1 +0

P)(1 +0

Q ) = 120,000,000

=> 100,000,000((1 +0

P )(1 0.40

P) = 120,000,000

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Case 2

A.

B

B

A

A

AB

P

dP

Q

dQ

E =

1667.02/)5565(

6555

2/)('

'

=

+

=

+

BB

BB

PP

PP

2222.0

2/)000,10000,8(

000,10000,8

2/)('

'

=

+

=

+

AA

AA

QQ

QQ

3329.11667.0

2222.0=

=ABE

B. Shoes produced by these two firms are substitutes because 0>ABE .

C. They are close substitutes because )1(3329.1 >=ABE .

D. If the Arc price elasticity of demand for As shoes is 2,

The change rate of quantity = 2222.02/)000,8000,10(

000,8000,10 =+

=>2

2/)60(

60

2222.0

'

'=

+

A

A

P

P

685.53' =AP

The price should be set at $53.685.

P. 3


4/23

Case 3

US British

Export 1,000 computers 150 autosUS$3,000 each 10,000 each

1. Original exchange rate: US$2/, or US$1 =0.5

If dollars exchange value depreciates by 10%, i.e. US$1 =0.45 (= 0.5 x

90%).

2. The computer price in pound = 3,000 x0.45 =1,350

P

QE dd

=%

%

%30%

%10

%3

=

=

d

d

Q

Q

300,13.1000,1 ==dQ computers

3. The auto price in US$ = 22.222,22$45.0

1000,10 US=

P

QE dd

=

%

%

%22.22%

%11.11

%2

=

=

d

d

Q

Q

117%)22.221(150 ==dQ autos

4. After the dollars 10% depreciation,

For US export revenue will increase and import spending will decreasebecause the US goods are cheaper but British goods are more expensive.

For British it will be opposite, export revenue will decrease and import

spending will increase, the reason is that US goods are cheaper, British is

willing to spend more.

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2nd Unit

Case 1

a) From the graph, we can find out:

Breakeven point: TR = TC (profit = 0), Output = 10,000, TR = $300,000

The CVP graph already drew in the question.

b) Complete the table below

Total Sales Total Cost Average Cost Profit Function

TR = 3Q TC = 100,000 +

2Q

AC =

2

000,100+Q

= Q 100,000

Let TR = a + bQ

From the graph, it is obvious that a = 0.

From the graph, when Q = 100, TR = 300, substitute into TR = a + bQ

300 = 0 + 100b, => b = 3

TR = 3Q

Let TC = a + bQ

From the graph, when Q = 0, TC = 100, so a = 100,000

When Q = 100, TC = 300, substitute into TC = a + bQ

300,000 = 100,000 + 100,000b, => b = 2

TC = 100,000 + 2Q

AC = TC Q = 21002100

+=+

QQ

Q

Profit = TR TC = 3Q (100,000 + 2Q) = Q 100,000

c) Operating leverage = TFC/TVC

Output 2,500 5,000 7,500 10,000 12,500 15,000 17,500

Leverage 2 1 0.6667 0.5 0.4 0.3333 0.2857

When output = 2,500, operating leverage = 2500,220

000,100=

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When output = 5,000, operating leverage = 1000,520

000,100=

When output = 7,500, operating leverage = 6667.0500,720

000,100=


000,100=


000,100=


000,100=


000,100=

d) Let Q be the output, when profit = 60,000:

60,000 = Q 100,000

Q = 160,000

Total sales = 3Q = 3 x 160,000 = $480,000

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Case 2

TR function (TR) = Price (P) x Quantity (Q) = 2Q (P = $2 from the question

provided).

Cost function (TC) = Fixed cost + Variable cost = 20,000 + 1.5Q (from question

provided).

Average cost (AC) = Cost function Quantity =Q

Q5.1000,20 +

Profit function = TR TC = 2Q (20,000 + 1.5Q) = 0.5Q 20,000

DOL =

Q

dQ

d

=Q

dQ

TFCAVCPQAVCPdQ ])(/[)(

=dQ

Q

TFCAVCPQ

AVCPdQ

)(

)(

=TFCAVCPQ

AVCPQ

)(

)(

=

+

Q

TFCTVCP

AVCP

=

ACP

AVCP

=

+

Q

Q5.1000,202

5.12

Figure out degree of operational leverage at each output

Output 60,000 80,000 100,000 120,000

Leverage 3 2 1.66 1.5

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For Company B

TR function Cost

function

Average cost Profit

function

DOL

2Q 40,000 +1.5Q Q

Q2.1000,40+

0.8Q 40,000 QQ /)000,402.1(2

2.12+

Output 60,000 80,000 100,000 120,000

Leverage 6.15 2.66 2 1.73

For Company C

TR function Cost function Average cost Profit

function

DOL

2Q 60,000 + Q

Q

Q+000,60 Q 60,000

QQ /)000,60(2

12

+

Output 60,000 80,000 100,000 120,000

Leverage 0 4 2.5 2

Conclusion:

Yes, the three conclusions are valid. It can be seen from Company C, it has the highest

fixed costs and the lower rate of change in variable costs, so the breakeven point is

higher than Company A and Company B. However, after the breakeven point, the

increase in profit of Company C will also be higher than the other two companies.

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Case 3

1) The isocost curve can be found from the graph in the question.

K = 750 75 = 10

S = 750 50 = 15

2) Process 1 = 6 x 75 + 2 x 50 = 550

Process 2 = 3 x 75 + 3 x 50 = 375

Process 3 = 2 x 75 + 6 x 50 = 450

So Mr Wang should use process 2 because it has lowest cost incurred.

The maximum number of garments could dry = 100 garments. Mr Wang can

incur expenses up to $750. For process 2, the cost is $375, so he can double thenumber of garments under process 2 ($750/$375 = 2), so the maximum number

of garments being dried = 50 x 2 = 100.

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15

10

K

S


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3) Complete the table below

Process 1 Process 2 Process 3

TC per day $750 $750 $750

Labor hired 72.22550750 = 63

375750 = 106

450750 =

Machine rented18.86

550

750= 63

375

750= 33.32

450

750=

Garments dry

cleaned18.6850

550

750= 10050

375

750= 33.8350

450

750=

4) Process 1 = 6 x 62.5 + 2 x 62.5 = 500

Process 2 = 3 x 62.5 + 3 x 62.5 = 375

Process 3 = 2 x 62.5 + 6 x 62.5 = 500

Again, Process 2 should be used due to its lowest cost among three processes.

The maximum number of garments to be dry-clean still remains at 100. The

calculation is same as part (2) above (50 x 2 = 100).

5) The new isocost curve is as below:

K = 750 62.5 = 12

S = 750 62.5 = 12

P. 10

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12

K

S


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3rd Unit

Case 1

1. Let H be the output of heating oil and G be the output of gasoline.

Target function (P) is to maximize the profit of the company.

P: 20H + 30G

Subject to:

1H + 1G 10 (Labor constraint)

0.5H + 1G 7 (Capital constraint)

1/3H + 1G 6.5 (Crude oil constraint)

H, G 0

Answer 2, 3 and 4

There are three combination to solve the H and G, also it can also be found the

optimal point by graph.

(a) Solve the equation of labor constraint and crude oil constraint:

H + G = 10 (1)

1/3H + G = 6.5 (2)

(1) (2)

2/3H = 3.5

H = 5.25

G = 10 5.25 = 4.75

Profit = 20 x 5.25 + 30 x 4.75 = 247.5

(b) Solve the equation of labor constraint and capital constraint:H + G = 10 (1)

0.5H + G = 7 (2)

(1) (2)

0.5H = 3, H = 6

G = 10 6 = 4

Profit = 20 x 6 + 30 x 4 = 240

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(c) Solve the equation of capital constraint and crude oil constraint:

0.5H + G = 7 (1)

1/3H + G = 6.5 (2)

(1) (2)

0.1667H = 0.5, H = 3

G = 7 0.5 x 3 = 5.5

Profit = 20 x 3 + 30 x 5.5 = 225

Therefore, the company should produce 5.25 barrel of heating oil and 4.75

barrel of gasoline in order to maximize the profit.

Of course, if the company must produce exact number of barrels, then the

company should produce 6 barrel of heating oil and 4 barrel of gasoline, and the

maximized profit is $240.

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4th Unit

Case 1

1.

USA China

$ Y $ Y

Gun 20 1,000 16 800

Butter 6.67 333.5 8 400

2. According to the law of comparative advantages, USA should export butter

because it has lower opportunity cost than China ($6.67 in USA < $8 in China),

and China should export Gun with the same reason ($16 in China < $20 in

USA).

3. To reduce the US imports from China to zero, the production cost between the

two countries should be the same.

Let y be the new exchange rate

20y = 1,600 2

y = 40

So, the US$ should be depreciated by (40 50)/50 x 100% = 20%

4. Same principle as part (3).

Let X be the new wage rate

50X = 1,600 2

X = 16

So, the wage rate should reduced by 20% [(16 20) / 20 = -20%], and the newproductivity of US labor should be $20/$16 = 1.25 gun per unit of labor, i.e. the

productivity increases by (1.25 1)/1 x 100% = 25%

5. If the products are homogenous, the price between two countries will finally be

the same by exchange rate movement or the domestic wage rate.

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15/23

Case 2

1. 1st demand curve less elastic, observed from the slope of demand curve. (In

fact, not really understand what the question asks.)

2. 2nd demand curve more elastic.

3. and 4.

Solve the following two equations of 1st demand curve and 2nd demand curve.

P1 = 7 0.025Q1 (1)

P2 = 10 0.1Q2 (2)

If two demand curves cross each other, P1 = P2 and Q1 = Q2

(2) (1)

0 = 3 0.075Q

Q = 40

P = 7 0.025 x 40 = 6

So, quantity is 40 and price is 6.

5. Upper limit: MR1 = 7 0.05 x 40 = 5

Lower limit: MR2 = 10 0.2 x 40 = 2

6. Yes, MC fall into the MR gap.

TC = 2Q + 0.025Q2

By differentiation: MCdQ

dTC=

MC = 2 + 0.05Q

MC = 2 + 0.05 x 40 = 4, it is between 2 and 5, so MC falls into MR gap.

7. It implies that price is stable because they are not willing to change price. This

often finds in oligopolistic markets

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16/23

Case 3

1. From the information of the question, the satisfaction can be quantified, so:

A = 20

B = 5

D = 0

2. Cost of sufficient preparation = 10

Cost of insufficient preparation = 6

The answers for 3, 4, 6, and 7 (5 is missing from the question) can be shown in the

following payoff matrix.

Bob

Time (Cost = 10) Time (Cost = 6)

Others Time (Cost = 10) B(-5), B(-5) A(14), D(-6)

Time (Cost = 6) D(-6), A(14) B(-1), B(-1)

For top right cell, the Bob and others spend same effort, so all can get B grade, and

the payoff is satisfaction less cost, i.e.5 10 = 5.

Same principle applies to other three cells. For example, at the bottom left cell, Bob

spends sufficient time but others not, so others only get D grade but Bob can get A

grade. The payoff of others = 0 6 = 6 and the payoff of Bob = 20 6 = 14

It has dominant strategy at the top left cell, i.e. B(-5), B(-5).

8. The cooperation is difficult to achieve because others will think that if Bob

really spends less time, they will get A grade if they spend much time instudying. At the same time, Bob will worry about others if they study hard, so

for safety, Bob will study hard too.

9. It clearly illustrates Nash equilibrium.

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5th Unit

Case 1

1.

2. Before tax:

P = 1,400 0.2Qd

P = 200 + 0.1 Qs

P* = 600, Q* = 4,000

After tax:

P = 1,400 0.2Qd

P = 200 + 0.1 Qs + 0.1 = 200.1 + 0.1 Qs

P* = 600.07, Q* = 3,999.7

3. From part (1) and (2), we solve thatEquilibrium output = 3,999.7

Equilibrium price = $600.07

4.

Total consumer spending = 600.07 x 3,999.7 = 2,400,099.98

Price charged after tax = 600.07

The total net sales = 599.97 x 3,999.7 = 2,399,700

Total taxes paid or charged = 0.1 x 3,999.97 = 399.97

P. 17

0.1

A

A

D

S

S

600.07

600

599.97

4,0003,999.7Q

P


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= (600.07 600) x 3,999.7 = 279.979

= (0.1 0.07) x 3,999.7 = 119.99

5. True cost of this tax for the society= 0.1 x (4,000 3,999.7) 2 = 0.015

P. 18


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Case 2

Items Home Foreign

1. Demand D = 100 20P,P = 5 0.05D

D* = 80 20P,P = 4 0.05D

2. Supply S = 20 + 20P,

P = -1 + 0.05S

S* = 40 + 20P,

P = -2 + 0.05S*

3 Equilibrium price before trade 2 1

4 Equilibrium quantity before trade 60 60

5 Import or export function I E

6 Consumer surplus before trade 90 90

7 Producer surplus before trade 90 90

8 Total surplus before trade 180 180

9 Price per trade 1.5 1.5

10 Import or export volume 10 10

11 Consumer surplus after trade 122.5 62.5

12 Producer surplus after trade 87.5 87.5

13 Total surplus after trade 210 150

14 Price when $0.5 tariff is levied 1.75 1.25

15 Trade volume when $0.5 tariff is

levied 10 10

16 Consumption after tariff 65 55

17 Domestic production after tariff 55 65

18 Consumer surplus after tariff 105.625 75.625

19 Producer surplus after tariff 89.375 89.375

20 Tariff revenue 10 x 0.5 = 5 10 x 0.25 = 2.5

21 Tariff burden +0.25 -0.25

22 Total surplus after tariff 195 165

Item 3

Home: 100 20P = 20 + 20P, P = 2

Foreign: 80 20P = 40 + 20P, P = 1

Item 4

Home: 5 0.05Q = -1 + 0.05Q, Q = 60

Foreign: 4 0.05Q = -2 + 0.05Q, Q = 60

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Item 6 From the graph at the end

Home: Area of triangle = [60 x (5 2) 2] = 90

Foreign: Area of triangle = [60 x (4 1) 2] = 90

Item 7 From the graph

Home: Producer surplus = [60 x (2 + 1) 2] = 90

Foreign: Producer surplus = [60 x (1 + 2) 2] = 90

Item 8 = Item 6 + Item 7

Home: Total surplus before trade = 90 + 90 = 180

Foreign: Total surplus before trade = 90 + 90 = 180

Item 9

D = 100 20P

S = 40 + 20P

In equilibrium, D = S, then solve the above equation:

100 40 = 20P + 20P

40P = 60

P = 1.5

Item 10

From the graph, after trade at price = 1.5:

Home import = 60 (home demand) 50 (home supply) = 10 units

Foreign export = home import = 10 units

Item 11

Home = [70 x (5 1.5) 2] = 122.5Foreign = [50 x (4 1.5) 2] = 62.5

Item 12

Home = [70 x (1.5 + 1) 2] = 87.5

Foreign = Same as Home = 87.5


Home = 122.5 + 87.5 = 210

Foreign = 62.5 + 87.5 = 150

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Item 14

From the graph, Home = 1.75 and Foreign = 1.25.

Item 15

From graph, it can be found the trade volume of Home and Foreign is 10.

Item 16

From graph, it can be found that consumption after tariff:

Home = 65

Foreign = 55

Item 17

From graph, it can be found that domestic production after tariff:

Home = 55

Foreign = 65

Item 18

Consumer surplus after tariff (from graph):

Home (area of triangle) = [(5 1.75) x 65 2] = 105.625

Foreign = [(4 1.25) x 55 2] = 75.625

Item 19

Producer surplus after tariff (from graph):

Home = [(1.75 + 1) x 65 2] = 89.375

Foreign = [(1.25 + 2) x 55 2] = 89.375


Home = 105.625 + 89.375 = 195Foreign = 75.625 + 89.375 = 165

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MBA 500 Managerial Economics-Assignment

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