(UNIT – 3)

PRODUCTION & COST ANALYSIS

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.Labour

3.Capital

4.Organisation or management

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)

Production function (Equation)

Q = f (L, K, Ld, M, T, etc.)WhereQ -- Output of commodity XL -- Labour employed in the production of XK – Capital employed in the production of X

Ld – Land employed in the production of XM – Managerial function employed in the production of XT – Technology employed in the production of X

Two time frames of production function

1.Short run :--Here at least one of the inputs remain constant, while

other 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 in production function

--If input change in the same proportion, then the pattern of production function is referred as ‘return to scale’

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

1.production function with one variable input factor/short run analysis of production function**It is explained with Law of variable Proportions/Law of Diminishing Marginal Returns/Law of Diminishing

Marginal ProductivityLaw 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 will eventually be reached where additional quantities of varying input will yield diminishing marginal contributions to total product

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= Δ Q/ Δ LAverage Product of Labour APL=Q/L

Example:Capital is Fixed

Var input(L)

TP MP(ΔQ/Δ 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

Output (Q)

Var input Labour (L)

x1 x2 x3

TPL

APL

MPL

X

YMP>1 0<MP<1 MP<0

STAGE I STAGE II STAGE III

High Return Less Return Negative Return

3 stages of production function from the graph

1.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 point where 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

2.production function with two variable input 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 of capital(K)

250 500 750

• From the above table ,If a firm want to produce 42 units of

output, 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-product curve/Equal product curve/Production indifference curve

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

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

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

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

2.Input-Output Isoquant / Right angled Isoquant / Leontief Isoquant

• We assume strict Complementary /Zero substitutability between the inputs

• When there is only one method of production of any commodity

Example: Wheels cannot be replaced by carts & vice versa

y

x

carts

wheels

Q1=1 vehicle

Q2=2 vehicle

Q3=3 vehicle

3.Kinked Isoquant /Convex Isoquant /Activity analysis 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 L3X

Y

Q1

Q2

Units of labour

Units of leather

shoe

Example: labour(L1) & leather(K1)

or

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

or

more labour(L3) & more leather(k3) (more carefully reducing wastages)

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• To get least cost of production, optimal

combination of inputs(resources) will be considered

• 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 K

1 17 2 17 3 15

2 10 3 12 4 11

3 9 4 11 5 10

• 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

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

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

• 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 no

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

graphically called Isocost line for M=95

IsocostDefinition: An isocost (isocost line) is the locus

of all those combinations of input factors (factors of production) that can be bought with a given sum of money here Rs.95)

Units of Capital (K)

x

M=95

y

Units of labour (L)

M=90

M=85

Determination of least cost input combinations

• Here isocost map is superimpose on isoquant map• It is possible because the axes in both maps represent

the same input variable

Units of Capital (K)

x

y

Units of labour (L)

AB

C

Scale line

3.Production function with all variable inputfactors/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

3 alternative situation arise in return to scale

1.Increasing return to scale

2.Constant return to scale

3.Decreasing return to scale

3 alternative situation arise in return to scale

1.Increasing return to scale:• If output increases more than proportionate to increase in all inputsCauses:• 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

advantagesExample: industries where storage is important such as chemical

2.Constant return to scale:• if output increases by same percentage as all inputs3.Decreasing return to scale:• If increase in output is less than proportionate to increase in all inputsCauses:• 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

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 labour

K - units of capital

b - parameters

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 Lα K β

when α + β = 1; return to scale is constant

when α + β > 1; return to scale is increasing

when α + β < 1; return to scale is decreasing

3.Parameter represents input factors - shares in output

Example: α=wage share & β=rental share

total share total income

4.It is used to find short run relationship of inputs & output

Marginal physical product of labour (MPPL)= α(Q/L)

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

5.It has elasticity of substitution as unity , which is used in formulation of an income policy

Managerial uses of Production Function

• Used to Compute least cost Input combination for given output

• Used to Compute maximum input output combination for a given cost

• It is useful in deciding on the value of employing a variable 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

COST• It is the money spent (directly/indirectly) on

producing & selling a product to the customers

• It refers to the outlay of funds for productive 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) the product to customer.

COST TYPES/COST CONCEPT

1.Actual Cost & opportunity cost2.Incremental cost & sunk cost3.Explicit cost & Implicit cost4.Past cost & Future cost5.Accounting & economic6.Private & social7.Direct & Indirect Cost8.Controllable & Non Controllable costs9.Replacement & Original Costs10.Shut down & abandonment cost11.Urgent & Postponable Cost12.Business cost & full cost13.Fixed & Variable Cost14.Short run & Long run cost15.Incremental & Marginal cost16.Average cost, Marginal costs & total cost

1.(a) Actual Cost /acquisition costs/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 cost &

(b) sunk cost(a) It is the additional cost due to a change

in 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 out cost & (b)Implicit /book/

imputed cost(a) Those expenses which are actually paid

by 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

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

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

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

assignable Cost

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

(b) Costs whose course cannot be easily & definitely traced to the plant , a product , a process or departmentEx: land cost, building cost cannot be directly attributed to cost of per unit of product

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

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.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

(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.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

(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

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.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 unit increase in output

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

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

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 short run

It 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• 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• It will first decrease & then rise as more & more

units are produced• Because when increase in variable factors will

leads 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 workers have to be appointed which leads to overcrowding & results in high wage rates.

(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

figOutput

Co

sts

AFC

AVC

MC

x

ATC

z

y

Short-Run output cost curves

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

•There wont be any fixed cost in long run

•It also referred as cost of producing different levels of output by changing size of plant / scale of production.

Cost

output0

ATC1ATC2

ATC3

C D

E

X

Y

A B

• A minimum point of ATC2 is at C, produces output of OA

• If output increases to OB & when firm continues in old scale, then the least cost point in ATC2 is E

• If the output increases to OB with increase in 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

LRAC (Envelope curve)

Co

sts

OutputO

Deriving a long-run average cost curve:Deriving a long-run average cost curve:

SAC1

SAC2

SAC3

SA

C4

SA

C5

A1(E=D)

Nature of Long Run Cost Curves

1.LAC curve is tangential to SAC curve & also called 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 curve’s least cost point(A1)

5.At A1, Economies = Diseconomies

Usefulness of LAC curve• It helps the organization to determine size of

plant to be adopted for producing the given output

• When firm operate in increasing return to scale, it is economical to under use a slightly larger plant operating at less than its minimum cost output level than to over use a smaller plant

Economies & Diseconomies of scale• The existence of this is responsible for U shaped

LAC curve• It is concerned with behavior as plant size

changes• When LAC declines as output increases which

says the cost structure is characterized by economies of scale

• When LAC increases as output increases which says 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 curveA typical long-run average cost curve

OutputO

Co

sts

LRACEconomiesof scale

Constantcosts

Diseconomiesof scale

2 types of economies & Diseconomiesa) External Economies

which are available to all firms in an industryEx: Constructing railway line will decrease transport cost

for all firmsb) 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 RELATIONSHIPIt 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 variable

is fixed & amount of FC are determined on the basis of inspection & experience

• After these steps TC, average & marginal costs for each output 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 the

respective current/expected factor prices & added together to yield cost estimates for that output level

(3)Econometric MethodExpressions 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/P a1,b1,c1,d1 --- constantTo determines not only partial cost function cost output

relationship on assumption that other determinants of cost (factor prices technology) are constant but also to determine the comprehensive cost function , which allows variations in all the factors influencing cost.