Session 5b. production_function_and_returns_to_scale

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Production Function

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Production Function

Production: Any activity leading to value addition –

Transformation of inputs into output

Q= f (L,K)

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Production Function

Short term : Time when one input (say, capital) remains constant and an addition to output can be obtained only by using more labour.

Long run: Both inputs become variable.

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Production Function

Production process is subject to various phases-

Laws of production state the relationship between output and input.

.

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Laws of production

Short run :

Relationship between input and output are studied by varying one input , others being held constant.

Law of Variable Proportions brings out relationship between varying proportions of factor inputs and output

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Laws of production

Long run:

Production function is subject to different phases described under the Law of Returns to Scale

– Studied assuming that all factor inputs are variable.

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Law of Variable Proportions

Law of Variable Proportions (Short run Law of Production)

Assumptions:

• One factor (say, L) is variable and the other factor (say, K) is constant

• Labour is homogeneous

• Technology remains constant

• Input prices are given

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Law of Variable ProportionsNo of Workers

LTotal Product

(TPl)

Marginal

Product (MPl )

Average

Product (APl )

Stages of Returns

1 24 24 24 I)Increasing Returns

2 72 48 36

3 138 66 46

4 216 78 54

5 300 84 60

6 384 84 64

7 462 78 66 II)Diminishing Returns

8 528 66 66

9 576 48 64

10 600 24 60

11 594 -6 54 III) Negative Returns12 552 -42 46

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Panel A

Labour

Total product

Total Product

Tot

al P

rodu

ct

TPl

TP rises at an increasing rate till the employment of the 5th worker.

Beyond the 6th worker until 10th worker TP increases but rate of increase begins to fall

TP turns negative from 11th worker onwards.

This shows Law of Diminishing Marginal returns

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Panel B

labour

APL

MPL

MPL

Panel B represents Marginal and average productivity curves of labour

AP

/MP

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Increasing Returns- Stage I:

TPl increases at an increasing rate.

Fixed factor (K) is abundant and variable factor is inadequate. Hence K gets utilised better with every additional unit of labour

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Stage II- TPl continues to increase but at a diminishing rate.

stage III- TPl begins to decline –Capital becomes scarce as compared to variable factor. Hence over utilisation of capital and setting in of diminishing returns

Causes of 3 stages: Indivisibility and inelasticity of fixed factor and imperfect substitutability between K and L

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Significance of Law of Diminishing Marginal Returns:

- Empirical law, frequently observed in various production activities

- Particularly in agriculture where natural factors (say land), which play an important role, are limited.

- Helps manager in identifying rational and irrational stages of operation

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- It provides answers to questions such as:

a) How much to produce?

b) What number of workers (and other variable factors) to employ in order to maximize output

In our example, firm should employ a minimum of 7 workers and maximum of 10 workers (where TP is still rising)

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- Stage III has very high L-K ratio- as a result, additional workers not only prove unproductive but also cause a decline in TPl.

- In Stage I capital is presumably under-utilised.

- So a firm operating in Stage I has to increase L and that in Stage III has to decrease labour.

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Law of Returns to Scale

In the long run, all factors are variable.

• Production can be increased by adding both L and K.

• Relationship between inputs and output is depicted in the form of isoquant curves.

• Isoquant curves represent different combinations of K and L that lead to the same level of output.

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ISOQUANT CURVES

Units of L

Uni

ts o

f K

o X

Y

IQ100

IQ200

IQ300

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Isocost line: • Assume that labour costs Rs.10 per unit and

capital, Rs. 7 per unit.• Suppose the company has a budget of Rs. 70.• It can buy 7 units of labour (with no capital), or

10 units of K (with no labour), or some in-between combination.

• By joining the two extreme points we get an isocost line

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7

10

X

Isocost

o

Uni

ts

of K

Units of L

Y

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10019

Q1=100

Q2=200B

Labour

Cap

ital

Y

XO

Y Producer has a constraint-namely, budget.

Producer attains equilibrium when he reaches highest attainable level of output.

Q3=300

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• Point of tangency between isoquant and isocost is the point of least cost combination of inputs.

• At point B, labour and capital are combined in a proportion that maximises the output for a given budget.

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ε = Δq/ q ÷ Δn /n whereΔq/ q indicates proportionate change in outputΔn /n indicates proportionate change in input

If ε >1, then we have increasing returns to scale ε =1, then we have constant returns to scale

ε <1, then we have decreasing returns to scale

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Firm is subject to increasing, Constant and Decreasing returns to scale.Explanation for these phases is providedThrough conceptsCalled economiesAnd diseconomiesOf scale.

L

K

Expan

sion

Path

AB

C

B

DE

F

Q 20

Q40Q60

Q80Q100

Q120

X

Y

o

Q140

G

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ECONOMIES OF SCALE

• ECONOMIES OF SCALE are advantages enjoyed by a firm from large scale production.

Causes of increasing returns to scale

• Internal and external

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INTERNAL ECONOMIES

INTERNAL: Those advantages and disadvantages that accrue to the firm as a result of its scale of operation

Indivisibilities- if some of the factors are indivisible, then it would be technically and economically undesirable to use the indivisible factor for a smaller scale of production e.g., Can’t use a conveyor belt to unload a small truck, but need one for unloading a train or ship

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INTERNAL ECONOMIES

Dimensional economies• A mere change in the size of capital can

lead to a change in output which is proportionately more than the cost of enlarged input. e.g., Doubling the diameter of a pipeline more than doubles the water flow without doubling the cost; doubling the dimensions of a ship more than doubles its capacity without doubling costs

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INTERNAL ECONOMIES

• Specialisation- In large scale production, a process can be broken into sub processes - specialised labour and specialised machines lead to increase in productivity and decrease in average cost of production.

• Managerial economies

• Commercial economies-bulk purchases

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INTERNAL ECONOMIES

• Financial economies -Lower rate of interest, liberal terms and conditions because of reputation individual investors also like to invest money.

• Risk bearing economies:

• Diversification of output, markets and

sources of supply

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INTERNAL DISECONOMIES

Internal Diseconomies

• Effective supervision no longer possible

• Unwieldy administration and ego clashes

• Industrial unrest

• Problems of re-conversion, storage and standing costs in case of stoppage of work or lack of demand

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External Economies of Scale


Arise out of sharing and cooperation received from other firms in a given industry.

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Economies of concentration

• Supply of skilled labour in a region

• Common services

• Specialised institutions like training schools and research centres (Indian School of mines in Dhanbad),

• Reputation of a region

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Economies of Information• Trade associations, journals, seminars

• Economies of disintegration • An ancillary firm may specialise in the

production of only one part • Waste and byproducts of all firms in the

industry may be dealt with by a specialised firm.

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External Diseconomies of Scale

• As firms expand along with expansion of the industry, after a point economies turn into diseconomies

• Excessive concentration leads to bottlenecks and diseconomies

• Most firms experience these phases but some continue to defy these laws due to innovations and technological progress.

Economies of Scope

• Lowering of costs that a firm experiences when it produces more than one product together rather than each alone

• A smaller airline can profitably extend into cargo services, thereby lowering the cost of each service

• Using bye products to make something instead of throwing it away.

• Management should be alert to such possibilities.

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Learning Curve

• As a firm gains experience in the production of a commodity or service, AC often declines.

• Learning Curve shows the decline in the average input cost of production with the rising cumulative total output over time.

• Eg, 1000 hours to assemble 100th aircraft, but only 700 hours to assemble the 200th .as managers and workers become more efficient as they gain production experience.

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Case study: Masterji’s Grocery Shop

Masterji’s shop is very popular and stocks all kinds of goods- from rice and wheat to processed food, imported chocolates and cheese. There is a small section which has a photocopying machine and a STD booth. Masterji runs the shop with the help of his children.

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• The family noticed that the number of shoppers varied between times and days (See table)

• During weekdays, masterji could manage with his children, but not in week ends.

Morn Afternoon

Even

Mon-Fri

50 40 65

Sat/Sun

165 85 30

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• Sunday morning buyers were ‘ value crowd’- bulk buyers, spent extra on something new and attractive but wanted a pleasant experience and were upset at the overcrowded shop

• At certain times there were not many shoppers

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• Masterji employed 3 assistants during week ends, but that did not solve the problem as the shop had a small floor area and only one billing machine

1.Can you explain masterji’s problem in terms of law of variable proportions?

2. Pl. suggest in detail how masterji can improve the functioning of the shop.

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Measuring Productivity

• US Bureau of Labor Statistics has been conducting studies of output per hour in individual industries as well as overall economy since 1800s- earlier because of apprehensions of human labor being displaced- this fear of unemployment was replaced by concern for making the most efficient use of labour in 1920s and 30s- In recent years interest in productivity measurement and enhancement has grown because it is recognised as an important indicator of economic growth.

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• Labor productivity: Ratio of output per worker hour. Improvements in worker productivity

• Multifactor productivity: Output is related to combined inputs of labor, capital and intermediate purchases.

• Advances in productivity reflect the ability to produce more output per input

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Date post:	15-Jul-2015
Category:	Economy & Finance
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Session 5b. production_function_and_returns_to_scale

Economy & Finance