Managerial Economics 10 - 10

8/14/2019 Managerial Economics 10 - 10

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Production Function

Single FactorTwo Factors

Returns to Scale

Managerial EconomicsMicroeconomics


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Production Function

All inputs for production are referred as Factors of Production and classified

as Land Rent

Labour Wages

Kapital Interest

Entrepreneur skill Profits

Production function functional relationship between quantities of factors of

production and the resultant quantity of output. Thus the quantity of Output (Q) from the process of Production can thus be

expressed as a functional relationshipQ =f(L, Lb, K, E)

Implying that

A change in the proportion of factors may vary the level of output

Same level of output can be achieved using different proportions of factors For the sake of simplicity we further assume that there are only 2 factors of

production i.e. Kapital and Labour

The Production Function can thus be written asQ =f(K, L)


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Single Factor Model


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Single Factor Model

Production can further be thought of as a function of a single factor eg. Labour

by keeping the other factors constant.

Eg. Say a certain amount of investment is done in Plant & machinery which

remains fixed over a period i.e. Does not change with additions to Labour.

Then

Total Product can be defined as the total quantity of output produced on employing

certain units of Labour Marginal Product of Labour (MPL) can be defined as addition to total product due to an

addition of one unit of labour

Thus MPL = dTP/dL

In such situation

Marginal Product will

Increase initially

Then decrease after certain level

Will reach Zero

Then becomes negative

Total Product will

Increase at increasing rate

Increase at decreasing rate

Reach a maximum

Start declining


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Total and Marginal Product

Marginal Product will

Increase initially (OA)

Then decrease after certain level (AB)

Will reach Zero (B)

Then becomes negative (BC)

Total Product will

Increase at increasing rate (OD)

Increase at decreasing rate (DE)

Reach a maximum (E)

Start declining (EF)

Kapital Labour MP TP AP

100 1 10 10 10

100 2 20 30 15

100 3 30 60 20

100 4 20 80 20

100 5 15 95 19

100 6 7 102 17

100 7 0 102 15

100 8 -10 92 12

Output

O

utput

Labour Units

Labour Units

A

B

E

F

D

O

O

30

102

C

3 7

3 7

Marginal Product

Total Product


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Average and Marginal Product

When Marginal Product (MP) increases Average Product (AP) also increases MP

curve is above AP (OA OF)

When MP starts to decline AP keeps increasing MP curve is above AP (AD FD)

Till such point where AP is equal to MP MP and AP intersect (D)

Thereafter, AP also starts declining AP curve is above MP (DB DC)

Kapital Labour MP TP AP

100 1 10 10 10

100 2 20 30 15

100 3 30 60 20

100 4 20 80 20

100 5 15 95 19

100 6 7 102 17

100 7 0 102 15

100 8 -10 92 12

Output

Labour Units

A

BO

30

C

3 7

20

4

D

EF


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Total Product, Marginal Product and Average Product

MP = dTP/dL = Slope of TP curve

AP = TP/L = Slope of line joining point on TPcurve and Origin

At point H on the TP curve

AP is the slope of line OH

MP is the slope of line PQ

PQ is steeper than OH thus MP is higherthan AP

At point G on the TP curve

Slope of OG = AP = MP

Point G corresponds to Point D where MPintersects AP

Beyond point G on the TP curve

Slope of TP Curve < Slope of Line from Originto point on Curve

MP < AP

Output

O

utput

Labour Units

Labour Units

A

B

E

F

O

O

30

102

C

3 7

3 7

D

G

H

P

Q


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Two Factor Model


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Two Factor Model

Given Production Function Q =f(K,L) let us now

assume that both factors are variable. Thus

Increasing quantity of K or L or both K and L will increaseOutput

Decreasing quantity of K or L or both K and L will decreaseOutput

ALSO, Increasing K and decreasing L in some proportion will

keep the Output constant

The last proposition above gives us iso-output curve i.e.A curve joining different combinations of K and L suchthat Output remains constant referred to as ISOQUANTcurves.

Properties similar to indifference curves

Negative sloping Convex to origin

Higher Isoquant represent higher levels of Output

Slope of the curve here referred to as Marginal Rate ofTechnical Substitution (MRTS) gives the MRS betweenKapital and Labour = dK/dL for a given level of Output.

Labour

Kapital

IQ1IQ2

IQ3


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Properties of Isoquants

Substitution

The 2 inputs K and L are substitutable

A rate of substitution exists between K and L such that

the resultant Output remains constant

Diminishing MRTS

The convexity of the curve implies a diminishing MRTS

Thus every additional units of K can be substituted bylesser and lesser units of L

Implying Law of Diminishing Marginal Returns

L K K/Y

A 1 4 -

B 2 1.75 2.25/1

C 3 1.25 0.5/1

D 4 1 0.25/1

Labour

Kapital

1

2

3

4

1 2 3 4 5

A

B

DC

Marginal Rate of Technical Substitution

Q =f(K, L)

dQ = dL . (Q/L) + dK . (Q/K) . . . Total differentiation

[Marginal addition to total Output] = [additional units if L] x

[MPL] + [additional units of K] + [MPK]

dQ = dL . (MPL) + dK . (MPK)

But along an Isoquant Curve marginal addition to Output is 0.

So, dQ = dL . (MPL) + dK . (MPK) = 0

- dK/dL = MPL/MPK = MRTSKL


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Special Cases

Perfect Substitutes

In fig 1 the Isoquant is linear

Constant MRTS

Constant MP of factors (not diminishing)

Factors perfectly substitutable at all stagesof production

Entire production possible only by K

Entire Production possible only by L

Fixed Factor Proportions

In fig 2 Isoquants are rt. angled

A certain level of Output possible onlywith a unique combination of K and L

Quantity of K and L along line OP For any IQ increase in K or L more than the

combination given by OP results in ZeroMP of factors

Typically modular expansion of production

IQ1

IQ2

IQ3

IQ1

IQ2

IQ3

Labour

Kapital

Labour

Kapital

O

O

P


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Choice of Inputs

The Choice of optimum combination of Factors is

determined by the Relative Prices of Factors The logic is similar to that used in the Indifference

Curve analysis

In fig, - IQ1, IQ2 and IQ3 are various Output levels possible by

combinations of K and L

AB is the Iso-cost Line (similar to the Budget line)

If all resources are used in buying K OA is themaximum K that can be employed

OA i.e. Total units of K affordable is determined bycost of K i.e interest rate (r)

If all resources are used in buying L OB is themaximum L that can be employed

OB i.e. Total units of L affordable is determined bycost of L i.e. Wages (w)

Slope of AB = w/r

Optimum Choice of Inputs would be point whereIsocost line is tangential to the Isoquant

At equilibrium

Slope of Isoquant = Slope of Isocost

MRTS = w/r

MPL/MPK = w/r

Labour

Kapital

IQ1IQ2

IQ3

RS

Q

P

T

B

A

O


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Returns To Scale


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Returns to Scale

A unit increase in inputs how much change in output will it result in ?

Double the InputsMore than double change in Output Increasing Returns

Double the Inputs Less than double change in Output Decreasing Returns

Double the Inputs Double the Output Constant returns

Labour

Kapital

1

2

3

4

1 2 3 4 5

55

50

30

10O

A

B

D

C

In the fig.

From OA to AB Inputs have doubled but

output has more than doubled Increasing

returns

From AB to BC Inputs have grown by 50% -

Output has grown by more than 50% -

Increasing returns

From BC to CD Inputs have grown by 33% -Output has increased by 10% - Decreasing

returns


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Returns to Scale

Managerial Efficiency

Benefits of specialization

Benefits of R&D

Technology

Business too big to manage

Specialised Units Common Infrastructure

Emergence of Market Place

Over utilisation of infrastructure Competition takes business

share

Internal Factors Resulting from Expansion of the Firm

External Factors Resulting from Expansion of the Industry

Dis-economies

Dis-economiesEconomies

Economies


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Documents

Managerial Economics 10 - 10