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(UNIT 3)

PRODUCTION & COST ANALYSIS

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PRODUCTION FUNCTION

It refers to the technological or engineering

relationship between the inputs of a

commodity & the output produced by them

The 4 factors of production are

1.Land

2.Labour3.Capital

4.Organisation or management

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Production function (schedule)

Labour (L)

(No.of workers)

Output quantity

(Q)

1 5 20

2 15 30

3 35 42

250 500Units of capital(K)

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Production function (Equation)

Q = f (L, K, Ld, M, T, etc.)

Where

Q -- Output of commodity X

L -- Labour employed in the production of XK Capital employed in the production of X

Ld Land employed in the production of X

M Managerial function employed in theproduction of X

T Technology employed in the production of X

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Two time frames of production

function1.Short run :

--Here at least one of the inputs remain constant, whileother inputs vary

--Different output & capital for a constant input pattern of

production function is referred as return to a factor&

2.Long Run

--A pattern of input combinations wherein both the inputs

increase or decrease relates to long run changes inproduction function

--If input change in the same proportion, then the pattern ofproduction function is referred as return to scale

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3 types of production function

1.production function with one variable input

2.production function with 2 variable input

3.Production function with all variable input

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1.production function with one variable inputfactor/short run analysis of production functio

**It is explained with Law of variable Proportions/Law of Diminishing Marginal Returns/Law of Diminishing

Marginal Productivity

Law of Variable Proportions:

It states that as more & more of one factor input is employed & if

all other input quantities are held constant, a point willeventually be reached where additional quantities of varyinginput will yield diminishing marginal contributions to totalproduct

Terms used in law of variable proportions:

1.Total Product (TP or Q)2.Marginal Product (MP)

3.Average Product (AP)

If variable Labour is L, then

Marginal Product of Labour MPL= Q/ LAverage Product of Labour APL=Q/L

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Example:Capital is Fixed

Varinput(L)

TP MP(Q/ L) AP(Q/L)

1 5 - (5/1)5

2 15 (15-5)/(2-1)=10 (15/2)7.5

3 35 (35-15)/(3-2)=20 (35/3)11.7

4 45 (45-35)/(4-3)=10 (45/4)11.25

5 50 (50-45)/(5-4)=5 (50/5)10

6 45 (45-50)/(6-5)=-5 (45/6)7.5

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Output (Q)

Var input Labour (L)

x1 x2 x3

TPL

APL

MPL

X

Y

MP>10

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3 stages of production function

from the graph1.STAGE 1: starts from 0 units of variable input (L) to AP of

at maximum (till X2)

2.STAGE 2:It follows stage I & then proceeds to a pointwhere MPL of (L) is 0(point X3).Here TPL is maximum

3.STAGE 3:It continues from Previous pointInterpretation:

-At stage I/stage III: No rational firm will operate.

-At stage I : The firm is grossly under utilizing its

fixed capacity. So in this MPL increases-At stage III: The firm grossly over utilizes its fixed

capacity

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.pro uc on unc on w wo var a einput factor/short run (only 2 var)or Long

run (more than 2 var) analysis of

production function

Example: 2 var input : Labour (L),capital (K)

Labour(L) Output Quantity (Q)

1 5 20 42

2 15 30 50

3 35 42 70

4 42 50 80

5 50 65 83

6 46 61 80

Units ofca ital K

250 500 750

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From the above table ,

If a firm want to produce 42 units ofoutput, then the possible combinations are

(4,250) (3,500) (1,750)Plotting these points on graph & line

joining these combinations of labour &

capital is called as isoquant/iso-productcurve/Equal product curve/Productionindifference curve

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Isoquant

It is defined as the locus of all those

combinations of 2 inputs that produce the

same amount of output

Unit of

Capital (K)

Units of labour (L)

0

y

xQ = 42

Q=50

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Characteristics of isoquant map

1.They are falling (reducing)

2.The higher the isoquant is, the higher is

the output

3.No 2 isoquant intersect with each other

4.They are convex towards the origin

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Types of Isoquant:

1.Linear Isoquant

2.Input-Output Isoquant / Right angled

Isoquant / Leontief Isoquant

3.Kinked Isoquant /Convex Isoquant /Activity

analysis isoquant / Linear Programming

Isoquant

4.Smooth Convex Isoquant

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1.Linear Isoquant

Natural Gas

Diesel Oil

x

y

Q1 Q2 Q3

Electric Power

It is assumed that perfect substitutability between Factors of

production is possible.

Example: Gas or oil to generate power

npu u pu soquan g ang e

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. npu - u pu soquan g ang eIsoquant / Leontief Isoquant

We assume strict Complementary /Zero substitutabilitybetween the inputs

When there is only one method of production of anycommodity

Example: Wheels cannot be replaced by carts & vice versa

y

x

carts

wheels

Q1=1 vehicle

Q2=2 vehicle

Q3=3 vehicle

3 Ki k d I t /C I t /A ti it

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3.Kinked Isoquant /Convex Isoquant /Activityanalysis isoquant / Linear Programming

Isoquant

It is assumed limited substitutability of capital & Labour

Only few process is used for production.

substitutability of input factors is possible only at kinks

K3

K2

K1

L1 L2 L3

X

Y

Q1Q2

Units of labour

Units of

leather

shoe

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Example: labour(L1) & leather(K1)

or

labour(L2) & leather(K2)(by reducing wastages)

or

more labour(L3) & more leather(k3)

(more carefully reducing wastages)

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4.Smooth Convex Isoquant

It is assumes continuous substitutability of

capital & labour only over a certain range

beyond which input cannot be substituted

Units of

Capital(K)

Units of labour(L)

Q

x

Y

Least cost combination of inputs

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Least cost combination of inputs

To get least cost of production, optimalcombination of inputs(resources) will beconsidered

Example:

Price of Labour (PL) : Rs 10 / unit

Price of capital (PK) : Rs 5 / unit

Production table

Q=2units Q=4 units Q=6 units

L k L K L K1 17 2 17 3 15

2 10 3 12 4 11

3 9 4 11 5 10

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If one needs to get 6 units of output , then

the possible combinations are (3,17)

(4,11) (5,10)

Calculation of least cost combination of

output

Method 1:Finding each output cost &

choosing the minimal one

Method 2:Finding by Geometrically

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Method 1:Finding each output cost

For 6 units Here 95 is minimal & (4,11) is chosen the best

L K Cost of production

3 15 (3x10)+(15x5)=105

4 11 (4x10)+(11x5)=95

5 10 (5x10)+(10x5)=100

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Method 2:Finding by Geometrically

M = (L x PL)+ (K x PK)

Where

M sum of money available

L units of labour

PL Price of labour for each unit of labour

K units of capital needed to produce a

given quantity of output

PK Price of capital for each unit of capital

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If the entrepreneur has Rs.95 then he can go for(4,11)

Also he can buy 9.5 units of labour (L) with no

capita (K)i.e., (L*10) + 0 = 95, Therefore L = 9.5

And he can buy 19 units of capital (K) with nolabour (L)

i.e., 0 + (K*5) = 95, Therefore K = 19 Under various combination of L & K represented

graphically called Isocost line for M=95

I t

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IsocostDefinition: An isocost (isocost line) is the locus

of all those combinations of input factors

(factors of production) that can be bought witha given sum of money here Rs.95)

Units of

Capital (K)

x

M=95

y

Units of labour (L)

M=90

M=85

D t i ti f l t t i t

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Determination of least cost input

combinations Here isocost map is superimpose on isoquant map

It is possible because the axes in both maps representthe same input variable

Units of

Capital (K)

x

y

Units of labour (L)

AB

C

Scale line

3 Production function with all variable input

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3.Production function with all variable input

factors/long run production function/return to

scale

Two ways:

1. Both L & K change in same proportion i.e.,

K/L ratio of production remains same for any

output

2. L & K change in different proportion i.e.,

K/L ratio of production varies with change in

output

Therefore increase in output when all inputs vary

in same proportion is known as return to scale

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3 alternative situation arise in

return to scale

1.Increasing return to scale

2.Constant return to scale

3.Decreasing return to scale

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3 alternative situation arise in

return to scale1.Increasing return to scale: If output increases more than proportionate to increase in all inputs

Causes: In large scale production work is divided to small parts & each individual can attain

specialization by handling only one part of the work

Some industries are not able to undertake production at small scale

Example: aircraft & shipping industry Some industries increased single operation which gives some dimensional

advantages

Example: industries where storage is important such as chemical

2.Constant return to scale:

if output increases by same percentage as all inputs

3.Decreasing return to scale: If increase in output is less than proportionate to increase in all inputs

Causes: Coordination & control becomes increasingly difficult

Information in organisation is lost when transmitted down from top level managers &vice versa when transmitted to top from down

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Statistical production function

(charles & paul H.Douglas)

Q = A Lb K1-b (or) Q = 1.01 L0.75 K0.25

Where

Q - total output

A - constant

L - units of labourK - units of capital

b - parameters

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Properties of Charles & Paul

H.Douglas production function

1.Both L & K should be positive for Q to

exist

2. Sum of the parameters (b , 1-b) = 1 which

is constant return to scale

Latest version is : Q = A LK

when + = 1; return to scale is constant

when + > 1; return to scale is increasing

when + < 1; return to scale is decreasing

3 Parameter represents input factors shares

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3.Parameter represents input factors - shares

in output

Example: =wage share & =rental share

total share total income

4.It is used to find short run relationship of

inputs & outputMarginal physical product of labour (MPPL)= (Q/L)

Marginal physical product of labour (MPPL)= (Q/K)

5.It has elasticity of substitution as unity ,

which is used in formulation of an incomepolicy

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Managerial uses of ProductionFunction

Used to Compute least cost Input combination forgiven output

Used to Compute maximum input output combinationfor a given cost

It is useful in deciding on the value of employing avariable input factor

It aids in long run decision making (increasing return

to scale implies increasing production) decreasing return to scale implies decreasing

production

Producer is indifferent about increasing / decreasing

return to scale provided the demand is of no constraint

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COST

It is the money spent (directly/indirectly) onproducing & selling a product to thecustomers

It refers to the outlay of funds forproductive producing a good or service

It states from raw materials (procuring,transporting, preparing) through

production costs (labour, power,machinery) till selling (maintenance,advertisement, salary, incentive) theproduct to customer.

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COST TYPES/COST CONCEPT

1.Actual Cost & opportunity cost

2.Incremental cost & sunk cost

3.Explicit cost & Implicit cost

4.Past cost & Future cost

5.Accounting & economic

6.Private & social

7.Direct & Indirect Cost8.Controllable & Non Controllable costs

9.Replacement & Original Costs

10.Shut down & abandonment cost

11.Urgent & Postponable Cost

12.Business cost & full cost13.Fixed & Variable Cost

14.Short run & Long run cost

15.Incremental & Marginal cost

16.Average cost, Marginal costs & total cost

1 (a) Actual Cost /acquisition

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1.(a) Actual Cost /acquisitioncosts/outlay cost/absolute cost &

(b) opportunity cost/alternate cost(a) Costs which a firm incurs for producing

/acquiring a product /service

Ex: raw material cost, labour cost

(b) * It is measured in terms of revenue / benefit,which could have been generated / earned by

employing that good or service in some other

alternative use.

* Difference between actual & opportunity cost

is called as economic profit / economic rent

2 (a) Incremental cost/Differential

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2.(a) Incremental cost/Differentialcost &

(b) sunk cost(a) It is the additional cost due to a changein the level / nature of business activity

Ex: adding new product line , changing

distribution channel

(b) Costs that are not altered by a change in

quantity produced & cannot be recovered

Ex: depreciation of Equipments

3 (a)Explicit /out of pocket/ paid

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3. (a)Explicit /out of pocket/ paidout cost & (b)Implicit /book/

imputed cost(a) Those expenses which are actually paidby the firm

It is recorded in profit & loss account

Ex: rent, wage paid

(b) These are theoretical costs that they go

unrecognized by the accounting system

Ex: for owner the cost spend is ignored

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4.(a) Past cost & (b) Future cost

(a) They are actual costs incurred in the past

& are generally contained in financial

accounts

Ex:It helps for future

(b) Costs that are expected to occur in some

future period

It is concerned for the managerial

decision makers

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5.(a) Accounting cost & (b)

economic cost

(a) It points how much expenditure has

already been incurred on a particular

process/ on production

It is used for tax planning purposes

(b) It is in nature of incremental costs both

imputed & explicit costs as well as the

opportunity costs

It is used in managerial decision making

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6.(a) Private cost & (b) social cost

(a) Those costs which are actually incurred/

provided for the business activity by an

individual / business firm

(b) Total costs to society on account of

production of a good

Ex: Polluting land/water

7 ( ) Di t /t bl / i bl t& (b)

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7.(a) Direct /traceable/assignable cost& (b)Indirect /non traceable/common/non

assignable Cost

(a) Which have direct relationship with a unitof operation like a product , a process ora department of a firm

(b) Costs whose course cannot be easily &definitely traced to the plant , a product ,a process or department

Ex: land cost, building cost cannot bedirectly attributed to cost of per unit ofproduct

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8.Controllable & Non Controllable

costs

(a) Costs which are capable of being

controlled/regulated by the managers

(b) Costs which are not capable of

controlling

Costs which are involved in

obsolescence & depreciation

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9.Replacement & Original Costs

(a) Costs that the firm incurs if it wants to

replace/acquire the same assets now

(b) Costs paid for assets such as land ,

building, cost of plant, equipment &

materials at price paid originally for them

10 Sh t d & b d t t

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10.Shut down & abandonment cost

(a) Cost which the firm incurs if it temporarily

stops its operation

Example: fixed costs, sheltering cost of

equipment

(b) Costs of retiring altogether a fixed asset

from use

Example: war time use machines

11 Urgent & Postponable Cost

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11.Urgent & Postponable Cost

(a) The cost the firm must incur so that the

operations of the firm continue

Example: Cost of material , labour, fuel

(b) Cost where postponement does not

affect the operational efficiency of firm

Example: maintenance cost

12 B i t & f ll t

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12.Business cost & full cost

(a) Costs which are known in profit & loss

account for legal & tax purposes

(b) It is the sum of Opportunity costs &

normal profits

13 Fixed & Variable Cost

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13.Fixed & Variable Cost

(a) Costs of firm which is part of total cost &

which does not vary with output

(b) The cost which vary with the output

TFC

output

output

TVC

FC

VC

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14.Short run & Long run cost

(a) A period in which supply of at least one

of inputs cannot be changed by firm

Example: building, machinery

(b) A period in which inputs can be varied as

desired

15 I t l & M i l t

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15.Incremental & Marginal cost

(a) It is important when dealing with decision

where discrete alternatives are

compared

It is change in any number of units of

output or even a change in quality of

output

(b) It is the amount added to TC by a unitincrease in output

16 A t M i l t &

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16.Average cost, Marginal costs &

total cost

Average cost = total cost

units produced

Marginal cost=extra cost of producing one

additional unit

Total cost = fixed cost + variable cost

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DETERMINANTS OF COST Level of Output

Prices of input factors

Production lot size

Size of plant

Output stability

Laws of returns

Level of capacity utilization

Period under consideration

Technology

Learning effect

Breadth of product range

Geographical location

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COST-OUTPUT RELATIONSHIP

The 2 aspects are

1.Cost output relationship in short run (firms

cannot alter its fixed equipment)

2.Cost output relationship in Long run (firms

has sufficient time to alter its fixed

equipments)

1 Cost output relationship in

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1.Cost output relationship in

short runIt is studied in terms of

(a)Average Fixed Cost & output

(b)Average Variable Cost & Output

(c)Average Total Cost & Output

(a) Average Fixed Cost (AFC) & output

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(a) Average Fixed Cost (AFC) & output

Increase in output results in decrease in FC/unit

Total Fixed cost(TFC) is same for any output Average Fixed cost(AFC) = TFC

units of o/p produced

Example,

(a) when TFC is Rs.1000, O/P units is 10

Then AFC =1000/10 = 100 units

(b) when TFC is Rs.1000, O/P units is 20

Then AFC =1000/20 = 50 units

Therefore AFC falls as O/P increases

(b) Average Variable Cost (AVC) & Output

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( ) g ( ) p It will first decrease & then rise as more & more

units are produced

Because when increase in variable factors willleads to efficiency of inputs which first increases

& then decreases

Once optimum capacity of production is

reached, any future increase in output beyond

optimum capacity will surely increase the AVC

Example: To produce increase in output after

reaching optimum level , more & more workershave to be appointed which leads to

overcrowding & results in high wage rates.

(c) Average Total Cost (ATC) & Output

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(c) Average Total Cost (ATC) & Output

It decreases with increase in output to

certain level & then starts to increase up

Turning point in cost from downward trend

to upward trend in ATC comes little later

than in case of AVC

ATC = AFC + AVC

Least cost output level is where ATC is

minimum & not AVC

Short R n o tp t cost c r es

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fig

Output

Costs

AFC

AVC

MC

x

ATC

z

y

Short-Run output cost curves

Relationship between ATC AVC & MC

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Relationship between ATC, AVC & MC

3 costs fall atfirst & then remains constant

& rise as output increases Rate of change in MC is less than AVC &

hence minimum MC is at output lower than

output at which AVC is minimum ATC falls for a longer range of output than

AVC & hence the minimum AVC

AVC = MC, when AVC is the least ATC =MC , when ATC is the least

Cost Output relationship in long run

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Cost Output relationship in long run

There wont be any fixed cost in long run

It also referred as cost of producing differentlevels of output by changing size of plant / scale

of production.

Cost

output0

ATC1

ATC2ATC3

C D

E

X

Y

A B

A minimum point of ATC2 is at C

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A minimum point of ATC2 is at C,

produces output of OA

If output increases to OB & when firmcontinues in old scale, then the least cost

point in ATC2 is E

If the output increases to OB with increasein scale, then the new least cost point is D

in ATC3 curve

Here BD will be less than BE Long run Average cost (LAC) curve is

drawn using no. of Short run Average Cost

(SAC) curves

Deriving a long-run average cost curve:

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LRAC(Envelope curve)Cos

ts

OutputO

Deriving a long run average cost curve:

A1(E=D)

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Nature of Long Run Cost Curves

1.LAC curve is tangential to SAC curve & alsocalled as envelope curve

2.LAC curve is U shape, it is because lower

average costs at first till optimum scale of

production & then it rise

3.LAC curve never cut by any SAC curve

4.LAC curve will touch the optimum scale curve at

optimum scale curves least cost point(A1)5.At A1, Economies = Diseconomies

Usefulness of LAC curve

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Usefulness of LAC curve

It helps the organization to determine size of

plant to be adopted for producing the givenoutput

When firm operate in increasing return to scale,

it is economical to under use a slightly largerplant operating at less than its minimum cost

output level than to over use a smaller plant

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Economies & Diseconomies of scale

The existence of this is responsible for U shapedLAC curve

It is concerned with behavior as plant sizechanges

When LAC declines as output increases whichsays the cost structure is characterized byeconomies of scale

When LAC increases as output increases whichsays the cost structure is characterized by

Diseconomies of scale When LAC is constant it is neither economies

nor diseconomies of scale

A typical long-run average cost curve

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yp g g

OutputO

C

osts

LRACEconomies

of scale

Constant

costs

Diseconomies

of scale

2 types of economies & Diseconomies

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ypa) External Economies

which are available to all firms in an industry

Ex: Constructing railway line will decrease transport costfor all firms

b) Internal Economies Which are available to a particular firm & gives it an

advantage over other firms engaged in production of

same products in industry Various factors involved are

(1)Labour economies & Diseconomies

(2)Technical Process economies & Diseconomies

(3)Managerial economies & Diseconomies(4)Marketing economies & Diseconomies

(5)Financial economies & Diseconomies

(6)Diversification in output economies & Diseconomies

(7)Diversification of market economies & Diseconomies

(8)Risk spreading economies & Diseconomies

ESTIMATION OF COST OUTPUT RELATIONSHIP

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ESTIMATION OF COST OUTPUT RELATIONSHIP

It can be estimated through the following 3 approaches

(1)Accounting Method

Here the TC is classified to fixed, variable & semi-variable costs

Average VC, range of o/p within which the semi variableis fixed & amount of FC are determined on the basis ofinspection & experience

After these steps TC, average & marginal costs for eachoutput level is obtained through simple arithmetic

(2)Engineering Method It is derived by estimating the physical units of various

input factors i.e., plant size, man hours, etc

Once it is determined, they are multiplied by therespective current/expected factor prices & addedtogether to yield cost estimates for that output level

(3)Econometric Method

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(3)Econometric Method

Expressions of common forms are

(i) Linear : TC = a1 + b1x

(ii) Quadratic : TC = a2 + b2x + c2x2

(iii) Cubic : TC = a3 + b3x + c3x2 + d3x3

where,

x - O/Pa1,b1,c1,d1 --- constant

To determines not only partial cost function cost outputrelationship on assumption that other determinants

of cost (factor prices technology) are constant butalso to determine the comprehensive cost function, which allows variations in all the factorsinfluencing cost