emba induction session 1

8/10/2019 EMBA Induction Session 1

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Induction on

Preliminary Econometrics

Basics on the Use of Mathematics on Economics)Ace Institute of Management

Executive MBA Program

Session 1: Basic Economic Relations

InstructorSandeep Basnyat

[email protected]

9841 892281
mailto:[email protected]:[email protected]


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Course Structure

To understand basic tools needed to solvemathematical problems related to managerial

economics and macroeconomics

4 Sessions Session 1: Basic Economic Relations

Session 2: Use of basic calculus

Session 3: Economic application: Microeconomics Session 4: Economic Application: Macroeconomics


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Objectives of the firms

Varieties of objectives:

1. Profit maximization

2. Sales Revenue maximization3. Utility maximization

4. Corporate growth maximization

5. Etc


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Most Important economic objective-

Profit Maximization

Profit = Total revenue Total cost

the amount afirm receives

from the sale

of its output

the marketvalue of the

inputs a firm

uses in

production

The most important role played is by the Total Product

(Quantity)


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Total Product (Quantity): TP

Q =f(K, L)

Where,

Q = Total Product or Total Quantityf= function of

K = capital

L = LabourBasic Relations:Q is the output resultedfrom the inputs K and L


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The Production Function: The

relationship between Input and Output

A production functionshows the relationship

between the quantity of inputs used to

produce a good, and the quantity of output ofthat good.

It can be represented by a table, equation, or

graph.


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0

500

1,000

1,500

2,000

2,500

3,000

0 1 2 3 4 5

No. of workers

Quantity

ofoutput

Simple Example: Production Function

(Assume capital is fixed)

30005

28004

24003

18002

10001

00

TPL or Q

(bushelsof wheat)

L

(no. ofworkers)

(i) Q = 3L (ii) Q = L0.5

(iii) Q = L2


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Marginal Product

The marginal productof any input is the increase in

output arising from an additional unit of that input,holding all other inputs constant.

Marginal product of labor (MPL) =

Q= change in output, L= change in labor

Q

L


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30005

28004

24003

18002

10001

00

Q (bushelsof wheat)

L

(no. of

workers)

EXAMPLE :Marginal Product

200

400

600

800

1000

MPL

Q= 1000L= 1

Q= 800L= 1

Q= 600L= 1

Q= 400L= 1

Q= 200L= 1


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0

500

1,000

1,500

2,000

2,500

3,000

0 1 2 3 4 5No. of workers

Quantityof

output

Relationship between Production Function and MPL

30005200

2800440024003

60018002

80010001 1000

00

MPL

Q

(bushels

of wheat)

L

(no. of

workers)

Diminishing MPL:This property explains why Production Function flatters as

output increases.


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Average Product of the Labour (APL)

APL =TP or Q

L

30005

28004

24003

18002

10001

00

MPL

Q

(bushels

of wheat)

L

(no. of

workers)

1000

1000

1000

1000

1000

APL

0

1000

900

800

700

600


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Total Revenue

Total Revenue = Price x Quantity

TR = P x Q

Incase, P remains constant (eg. Perfectly

competitive market):

TR =f(Q)


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Total Revenue and Output

Price ($) OutputTotal

Revenue

1.5 1 1.5

1.5 2 3.0

1.5 3 4.5

1.5 4 6.0

1.5 5 7.5

1.5 6 9.0


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Marginal and Average Revenue

The Marginal Revenueis the increase in revenue

arising from an additional unit of output.

Marginal Revenue (MR) =

TR= change in Total Revenue, Q= change in Output

TR

Q

Average Revenue (AR) =TR

Q


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Sample Data for Perfectly Competitive Market

15

$50$105

$40$104

$103

$10

$10

$10

$10$102

$10$101

n.a.

$30

$20

$10

$0$100

TR= Px QPQ

TRQ

MR=TRQ

AR=

$10

$10

$10

$10

$10

Notice that

MR= P


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A Sample Data for Monopoly Market

16

1.506

2.005

2.504

3.003

3.502

1.50

2.00

2.50

3.00

3.50

$4.004.001

n.a.

9

10

10

9

7

4

$ 0$4.500

MRARTRPQ

1

0

1

2

3

$4


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Learning Exercise-RevenueFill in the missing data

Q P ($) TR MR AR0 10.0

1 9.0

2 8.0

3 7.04 6.0

5 5.0

6 4.0

7 3.0

8 2.0

9 1.0

10 0.0


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Q P ($) TR MR AR

0 10 0 0

1 9.0 9 9 9

2 8.0 16 7 8

3 7.0 21 5 7

4 6.0 24 3 6

5 5.0 25 1 5

6 4.0 24 -1 4

7 3.0 21 -3 38 2.0 16 -5 2

9 1.0 9 -7 1

10 0.0 0 -9 0

Learning Exercise-Revenue


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Deriving Costs: FC, VC and TC

7

6

5

4

3

2

1

620

480

380

310

260

220

170

$100

520

380

280

210

160

120

70

$0

100

100

100

100

100

100

100

$1000

TCVCFCQ


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Marginal Cost (MC)

is the change in total cost from

producing one more unit:

Marginal Cost

6207

4806

3805

3104

26032202

1701

$1000

MCTCQ

140

100

70

50

40

50

$70

TC

Q

MC=


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Average Fixed Cost

1007

1006

1005

1004

1003

1002

1001

14.29

16.67

20

25

33.33

50

$100

n.a.$1000

AFCFCQ Average fixed cost (AFC)

is fixed cost divided by thequantity of output:

AFC= FC/Q


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Average Variable Cost

5207

38062805

2104

1603

1202

701

74.29

63.3356.00

52.50

53.33

60

$70

n.a.$00

AVCVCQ Average variable cost (AVC)

is variable cost divided by thequantity of output:

AVC= VC/Q


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Average Total Cost

88.57

8076

77.50

86.67

110

$170

n.a.

ATC

6207

48063805

3104

2603

2202

1701

$1000

TCQ


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ACTIVE LEARNING:

Costs

Fill in the blank spaces of this table.

24

210

150

100

30

10

VC

43.33358.332606

305

37.5012.501504

36.672016.673

802

$60.00$101

n.a.n.a.n.a.$500

MCATCAVCAFCTCQ

60

30

$10


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ACTIVE LEARNING:

Answers

25

210

150

100

60

30

10

$0

VC

43.33358.332606

40.003010.002005

37.502512.501504

36.672016.671103

40.001525.00802

$60.00$10$50.00601

n.a.n.a.n.a.$500

MCATCAVCAFCTCQ

60

50

40

30

20

$10


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Profit Function

Marginal profit (M) =

= change in Total Profit, Q= change in Output

Q

Average Profit (A) = Q

Profit () = TR - TC


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Learning Exercise (Revenue, Cost and Profit)

Q P TR MR TC MC M

0 160 0 0 0

1 150 150 150 25 25 125 125

2 140 55 30 100

3 390 35 300 75

4 90 130 350

5 110 550 175

6 600 50 55 370

7 630 290 60 -308 80 640 355 285

9 75 -85

10 600 525


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Learning Exercise (Revenue, Cost and Profit)

Q P TR MR TC MC M

0 160 0 0 01 150 150 150 25 25 125 125

2 140 280 130 55 30 225 100

3 130 390 110 90 35 300 75

4 120 480 90 130 40 350 50

5 110 550 70 175 45 375 25

6 100 600 50 230 55 370 - 5

7 90 630 30 290 60 340 -308 80 640 10 355 65 285 -55

9 70 630 -10 430 75 200 -85

10 60 600 -30 525 95 75 -125


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Numerical Exercise Given the Total Cost function:

TC = 150Q

3Q

2

+ 0.25Q

3

a) Find the Average Total cost function for the above

b) Compute Total, Average and Marginal costs when thequantity produced are 5,6 and 7.

Ans.:

a) TC = 150 3Q + 0.25Q2

b) Computation

Q Total Cost Average Cost Marginal Cost

5 706.25 141.25 -

6 846 141 139.75

7 898.75 128.39 52.75


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Numerical Exercise

Given the following TR and TC functions,determine the output (Q) that would result in

break-even (zero profit).

TR = 51Q Q2

TC = 625 + Q

Ans:Q = 25


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Market Mechanism

Two forces of market: Demand and Supply

Demand: willingness and ability to pay

Law of demand: Qd = f (P) (Inverse)

Supply: Willingness and ability to sell

Law of Supply: Qs = f (P) (Positive)

Equilibrium at the point where:

Demand = Supply

Qd = Qs


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$0.00

$1.00

$2.00

$3.00

$4.00

$5.00

$6.00

0 5 10 15 20 25 30 35

P

Q

Supply and Demand Together

D S Equilibrium

Price and

Quantity


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Numerical Problem on Demand and Supply

1) Suppose:

Demand eqn. for a product: Qd= 286 20p

Supply eqn. For a product: Qs= 88 + 40p

Find Equilibrium Quantity and Price:

Solution:Qd= Qs

286 20p = 88 + 40p

60p = 198

P = $3.30

Q = 28620(3.3) = 220


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Disequilibrium in Automobile market- Surplus

Market demand curve: Qd = 20,500,000500P

Market supply curve:Qs = - 42000000 +2000P

Suppose a seller is trying to sell the car at $27000.

How many cars will be bought and sold?

Answer:

Qd = 20,500,000500(27000)= 7,000,000

Qs = - 42000000 +2000(27000) = 12,000,000

Surplus = 5 million cars.


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Disequilibrium in Automobile market- Shortage

Market demand curve: Qd = 20,500,000500P

Market supply curve:Qs = - 42000000 +2000P

Suppose a car is being sold at $23000.

How many cars will be bought and sold?

Answer:

Qd = 20,500,000500(23000)= 9,000,000

Qs = - 42000000 +2000(23000) = 4,000,000Shortage = 5 million cars.


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Thank You

emba induction session 1

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