LONG RUN PRODUCTION FUNCTION

MBA (PM) IInd SEM

What Is Production FunctionProduction function deals with

the maximum output that can be produced with a limited and given quantity of inputs.

PRODUCTION FUNCTION

1. The tool of analysis used to explain the input-output relationship

2. Describes the technological relationship between inputs and outputs in physical terms

3. It tells that the production of a commodity depends on specific inputs

4. It represents quantitative relationship between inputs and output

5. It represents the technology of a firm, of an industry, or of the economy as a whole

Production FunctionMathematical representation

of the relationship:Q = f (K, L, La)

Output (Q) is dependent upon the amount of capital (K), Land (L) and Labour (La) used

ASSUMPTIONS

THE PRODUCTION FUNCTIONS ARE BASED ON CERTAIN ASSUMPTIONS

1. Perfect divisibility of both inputs and outputs

2. Limited substitution of one factor for another

3. Constant technology

4. Inelastic supply of fixed factors in the short run

THE LAWS OF PRODUCTION

LAWS OF VARIABLEPROPORTIONS

LAWS OF RETURNSTO SCALE

Relates to the study of input output relationship in the short run with one variable input while other inputs are held constant

Relates to the study of input output relationship in the long run assuming all inputs to be variable

What is long run production function ?

Long run refers to that time in the future when all inputs are variable inputs.

In the long run both capital and labour are included

Output can be varied by changing the levels of both L & K and the long run production function is expressed as:

Q = f (L, K)

THE LAW OF RETURNS TO SCALE

EXPLAINED BY

ISOQUANT CURVE

TECHNIQUE

PRODUCTIONFUNCTION

LONG RUN TOTAL PRODUCTION-Returns to scale

During the short period, some factors of production are relatively scarce, therefore , the proportion of the factors may be changed but not their scale. But in the long run, all factors are variable, therefore, the scale of production can be changed in the long run

Returns to scale is a factor that is studied in the long run.

Returns to scale show the responsiveness of total product when all the inputs are increased proportionately.

Returns to ScaleWhen all inputs are changed in

the same proportion (or scale of production is changed),the total product may respond in three possible ways:

1) Increasing returns to scale2) Constant returns to scale, and 3) Diminishing returns to scale

INCREASING RETURNS TO SCALEThe law of increasing

returns to scale operates when the percentage increase in the total product is more than the percentage increase in all the factor inputs employed in the same proportion.

Many economies set in and increase in return is more than increase in factors.

For e.g 10 percent increase in labour and capital causes 20 percent increase in total output. Similarly, 20 percent increase in labour and capital causes 45 percent increase in total output.

CONSTANT RETURNS TO SCALE

Law of constant returns to scale operates when a given percentage increase in the factor inputs in the same proportion causes equal percentage increase in total output.

Economies of scale are counter balanced by diseconomies of scale.

DIMINISHING RETURNS TO SCALE The law of diminishing

returns to scale occurs when a given percentage increase in all factor inputs in equal proportion causes less than percentage increase in output.

Output increases in a smaller proportion.

Diseconomies outweigh economies of scale

Q

X,Y

IRTS Q

X,Y

DRTSQ

X,Y

CRTS

Graphically, the returns to scale concept can be illustrated using the following graphs

ADVANTAGES AND DISADVANTAGES OF LARGE SCALE PRODUCTION

Specialization

Economy of labour

Economics of buying and

selling

Overhead charges

Rent

ECONOMIES OF SCALE

INTERNAL ECONOMIES

EXTERNAL ECONOMIES

Reduction in costs when the scale of production increases

is called

INTERNAL ECONOMIES

Economies in Production

Economies in

Marketing

Technological Advantages

Advantages of divisions of labour & Specialization

Large scale production provides opportunities for technological advances

Large scale production workers of varying skills & qualifications are employed which facilitates division of labour as per specialization

.. Large scale selling of firms own products

.. Advertising cost .. Large scale distribution

.. Large scale purchase of raw materials & other inputs

Improves the overall performance of the firm

Managerial Economies

Transport & Storage Economies

.. Specialization in managerial activities

.. Mechanization of managerial functions

.. Improves managerial efficiency

.. Efficient management of the transport function

.. Proper utilization of storage facilities

.. Helps in reducing transportation and storage costs

CAUSES OF INTERNAL ECONOMIES

SIZE Big Machine

Bigger capacity lower Energy less labour

LIMITING PROCESS

MergersSpreading of

costs

TECHNIQUE

Superior Technique

Shorter period of time

SPECIALI - ZATION

Division of Labour

Increase in efficiency

MANAGERIAL ECONOMICS

COMMERCIAL ECONOMIES

Aggregation

Financial economies

Wide Market

Credit facilities

Encourages investment

Managerial economies

RISK BEARING ECONOMIES Spreading

RisksDiversification

CAUSES OF EXTERNAL ECONOMIES

CONCENTRATION

Advantages of locality

Common Pool of Knowledge of localityReduced transportation cost

INFORMATION

DISINTEGRATION

Breaking up processes

The benefits which companies derive from trade publications and technical journalsBy virtue of location, common pool of research can be created and benefits can be shared

Knowledge sharing

Breaking up of processes which can be handled by specialist firms

22

Production Isoquants/ isoquant curve/iso-product

curve• In the long run, all inputs are

variable & isoquants are used to study production decisions– An isoquant or iso-product curve is a

curve showing all possible input combinations capable of producing a given level of output

– Isoquants are downward sloping; if greater amounts of labor are used, less capital is required to produce a given output

ASSUMPTIONS

1. THERE ARE ONLY TWO FACTORS OF PRODUCTION…CAPITAL (K) AND LABOUR (L) TO PRODUCE A COMMODITY X

2. THE TWO FACTORS CAN SUBSTITUTE EACH OTHER UP TO A CERTAIN LIMIT

3. THE TECHNOLOGY IS GIVEN OVER A PERIOD

Example Isoquant Curve

01

2345

67

0 2 4 6 8 10

Units of X

Units

of Y

Isoquant; TP = 100 units

The following combinations of inputs X and Y produce 100 units of output:

º 2,6º 3,4º 4,3º 6,2º 8,2 Units of Labour

Unit

s of

cap

ital

Iq1 = 100

A

B

C

D

K4

K3

K2

K1

0L1

Units of L

Unit

s of

K

L2

L3

L4

Isoquant curve for 100 units of output PROPERTIES:-

1. Slopes downward towards right

2. Convex to the origin point because of diminishing

marginal rate of technical substitution (MRTS)

3. Two iso-product curves do not cut each other

labourin change

capitalin changeMRTS

Iq4

Iq3

Iq2

Iq1 = 100

A

B

C

D

K4

K3

K2

K1

0L1 L2 L3 L4

Units of L

Unit

s of

K

= 200

= 300

= 400

ISOQUANT MAP- A family or a group of isoquants is called an ISOQUANT MAP

27

The Isocost Line

0 1 2 3 4 5 6 7 8 9 10 Labor, L (worker-hours employed)

Cap

ital,

K (

mac

hine

s re

nted

)

Cost = Rs50Per unit price of labor input = Rs10/hourPer unit price of capital input = Rs5/machine

2

4

8

10

a

b

c

d

e

f

6

A

B

M=PL.QL+PK.QK

Where, M=total outlay PL= price per unit of labor QK= price per unit of capital QL= units of labor QK= units of capital

Slope of isocost line= OA/OF

Slope of isocost line can be change in two ways:1) Change in the factor price, and2) Change in total outlay or total cost

Slope of isocost line

input capital ofunit per price

inputlabour ofunit per price

29

Changes in One factor Price

Decrease in the factor price causes rightward shift and increase in factor price causes leftward

shift in iso-cost line.

0 1 2 3 4 5 6 7 8 9 10

Cap

ital,

K (

mac

hine

s re

nted

)

2

4

6

8

10

Labor, L (worker-hours employed)

a

f

Cost = 500; labor,R = 16.5 or 10or 1/ hourThe money wage, W = Rs5/machine

…Rs10

…Rs1

A Change in unit price of labor

hRs16.5

30

L

K

Units of labour(w)

Slope = -w/r

Direction of increasein total cost

Change in total outlay or total cost

Un

its o

f

cap

ital (r

)

TC=Rs. 50

TC= Rs. 75

TC= Rs. 100

31

L

K

Units of Labour

•

Isoquants and Cost Minimization

•

Q=200

Q=300

Q=100

IQ

1IQ 2

IQ 3

TC=Rs50

•

•

0 2 4 6 8 10 12 14 16 18 20

Unit

s of

Cap[i

tal

0

2

4

6

8

10

TC=Rs=75

TC=Rs100

P

P”

P’

•N

M

32

Optimization & Cost• Expansion path gives the efficient

(least-cost) input combinations of labor and capital needed foe every levels of output.Derived for a specific set of input pricesAlong expansion path, input-price ratio

is constant & equal to the marginal rate of technical substitution

• It is defined as the locus of tangency points between iso-cost lines and isoquants.

•It implies to Long run because: No input is fixed.Path starts from origin indicating that if output is zero costs are zero.•Expansion path gives us thelevel of output & one leastcombination that canproduce this level of output.•Movement along the line givesthe costs at which output canbe expanded•So called Expansion Path.

EXPANSION PATH

Labor input

Capita

l input

ISOQUANTS AND RETURNS TOSCALE

INCREASING RETURNS TO SCALE

0E>EE1>EE2

CONSTANT RETURNS TO SCALE

EE1=EE2=EE3

DIMINISHNING RETURNS TO SCALE

0E<EE1<EE2

The LR Relationship Between Production and Cost

In the long run, all inputs are variable.◦ What makes up LRAC?

Long run average cost

•LRAC refers to minimum possible per unit costof producing different quantities of output ofa good in the long period.

•SRAC curves represent various plant sizes

•Once a plant size is chosen, per-unit production costs are found by moving along that particular SRAC curve

• LRAC is made up of SRACs. Since LRAC envelopes all short run curves, hence Called ENVELOPE CURVE

Envelope curve

• LRAC can never cut SRAC but it will be tangential to each SRAC at some point.

• Average cost can not be higher in the long run than in the short run;

•Explanation;1.Any adjustment which will reduce costs

possible to be made in the short run must also be possible in the long run

2.It is not always possible in the short run to produce a given output in the cheapest possible way as all the factors are not variable.

properties U-shaped curve.Based on assumption of unchanging technology.LRAC is flatter curve than the SRAC. In economics ,we define long period as that during which size of the organization can be altered to meet changed conditions.Normally; Output increases and average costs also increases But in long run, size of the firm Can be increased therefore Variable costs are likely to rise less sharply. Hence a flatter curve.

Long run average cost curve Minimum

efficient scale is the lowest output level for which LRAC is minimized

The Long-Run Cost Function

• Reasons for Economies of Scale…Increasing returns to scaleSpecialization in the use of labor and

capital• Economies in maintaining inventory• Discounts from bulk purchases• Lower cost of raising capital funds• Spreading promotional and R&D costs

Management efficiencies

The Long-Run Cost Function

• Reasons for Diseconomies of Scale…Decreasing returns to scaleInput market imperfections e.g. wage rate driven

upManagement coordination and controlproblemsDisproportionate rise in transportation costsDisproportionate rise in staff and indirect labour

Application of the conceptIn the long run, a firm exercises its choicewith regard to the size of the plant andscale of production, on the basis of long runaverage cost.Selection of the optimal plant size

accordingto the expected demand.Avoid unnecessary costs due to

inappropriateplant size.