Unit 2 c

PRODUCTION AND COST

INTRODUCTION

• Up to this you have learnt all about demand, consumers , their preferences and decision making.

• Now we would learn about producers preference and their behavior though the concept of optimum production with efficient choice of differ factor inputs.

….contd

• The basic problem that any firm faces is duality of paradoxical objectives – Maximum output.

– Minimum cost.

• In the next sessions we are going to discuss how can a firm achieve this objective.

• What are the resources they may use, how to combine them , what are the constraints in optimization of production etc

PRODUCTION • Production is the process of transformation

of inputs into goods and services of utility to consumers and /or producers.

• It is a process of creation of value or wealth through the production of goods and services that have economic value to either consumers or other producers.

• The process of adding value may occur – By change in form(input to out put)

– Change in place(factory to retailer)

– By change in hands(retailer to consumer)

TYPES OF INPUTS

• You know what is production……………..?

• What are the inputs…………….?

• What are their characteristics…………….?

• Let us start with technology – Technology is one of the most important input in any

of production process.

– Technology determines the type, quantity and proportion of inputs

– It determines the maximum limit of output from a given combination of inputs.

FIXED AND VARIABLE INPUTS

• Typically the production analysis of a firm is done using two distinct time frames

– Short run production

• Period of time when the firm cannot vary some of its inputs

• Supply of some inputs are fixed

– Long run production

• Have sufficient time to vary all inputs including technology.

.. contd

• Based on short run and long run the inputs are classified in to variable and fixed.

• Variable input

– Made to vary in short run

– Example – raw material , unskilled and skilled labor

• Fixed input

– It cannot be varied in short run

– Example – land, machine, technology skill set etc.

• Each of this input has a unique cost associated itself

FACTORS OF PRODUCTION

5 FACTORS OF PRODUCTION

LAND

LABOR

CAPITAL ENTERPRISE

ORGANIZATION

PRODUCTION FUNCTION

“Production function is the technical relationship between inputs and outputs over a given period of time”

• A commodity may be produced by various methods using different combinations of inputs with given state of technology. – Example–textiles(different raw materials,

technology)

• Production function includes all such technically efficient methods.

…contd

• Production function

– Always related to a given time period

– Always related to a certain level of technology

– Depends upon relation between inputs

• Production function shows the maximum quantity of the commodity that can be produced/unit of time for each set of alternative inputs.

MATHEMATICAL EXPRESSION OF PRODUCTION FUNCTION

• Normally a production function is written as

Q = F ( L , K , I , R ,E )

Where Q is the maximum quantity of output

Where L = Labor, K = Capital, I = Land, R= Raw material, E = Efficiency parameter

TYPES OF PRODUCTION FUNCTION

• On the basis of characteristics of inputs production function normally divided into 2 broad categories

– With one variable input or variable production function.(short run)

– With two variable inputs or constant production function.(long run)

PRODUCTION FUNCTION WITH ONE VARIABLE INPUT

• In the short run producers have to optimize with only one variable input.

• Let us consider a situation in which there are two inputs

– Capital and labor

– Capital is the fixed and labor is the variable input.

• The amount of capital is kept constant and labor is increased to increase output.

• Any change in output can be manifested only through a change in labor input only

..contd

• This production function also known as variable proportion production function.

“The short run production function shows the maximum output a firm can produce when only one of its inputs can be varied other inputs remaining constant”

• It can be written as

Q= F ( L , Kc)

Q- Out put

L- labor

Kc – Fixed amount of capital

AVERAGE PRODUCT, MARGINAL PRODUCT, TOTAL PRODUCT

• The short run production function is governed by law of variable proportions.

• Concept of average , marginal products, total product of factor inputs.

• Assuming capital to be constant and labor to be variable. So total product of labor function is given as

TP L = F (Kc , L)

• If instead labor is fixed in short run, capital is varied

TP k = F (K, Lc)

• AVERAGE PRODUCT (Ap) is total product per unit of variable input

AP L = TP/L (Capital fixed)

AP k = TP/K (Labor fixed)

MARGINAL PRODUCT

• Marginal product (MP) is defined as addition in total output per unit change in variable input thus marginal product of labor (MPL)

MPL = ∆ TP / ∆ L

MPL = d TP / d L

EXPLANATION – WITH EXAMPLE • Assume that a manufacturer starts production

with an investment of Rs 10 C in plant and machinery.

• The manufacturer increases units of labor keeping investment in plant fixed …….

• LAW OF VARIABLE PROPORTIONS

law of variable proportions states that with the increase in the quantity of variable factor its marginal and average product will eventually decline other inputs remain unchanged (constant)

SEE THE TABLE………..

….contd

“The law of variable proportions is also called as law of diminishing marginal returns”

LAW OF VARIABLE PROPORTIONS

LABOR (L) (000 UNITS)

TOTAL PRODUCT (TP) (000 TONNES)

MARGINAL PRODUCT (MP)

d TP /d L

AVERAGE PRODUCT

(TP/L)

STAGES

1 20 - 20

2 50 30 25 INCREASING

3 90 40 30 RETURNS

4 120 30 30

5 140 20 28 DIMINISHING

6 150 10 25 RETURNS

7 150 0 21.5

8 130 -20 16.25 NEGATIVE

9 100 -30 11.1 RETURNS

-40

-20

0

20

40

60

80

100

120

140

160

1 2 3 4 5 6 7 8 9

OU

TPU

T LAW OF VARIABLE PROPORTIONS

TOTAL PRODUCT

MARGINAL PRODUCT

AVERAGE PORODUCT

LABOR

GRAPH - INFERENCE

• With small increase in units of labor, capital being constant, extra units of labor manifests through an increase in output.

• After a certain point where there are too many workers with fixed capital.

• So the part of the workforce becomes ineffective and the marginal products of labor starts falling.

• This law is based on the assumption that each unit of labor is homogenous (i.e. each worker has same skills)

TOTAL ,MARGINAL AND AVERAGE PRODUCT CURVE

B C

PANEL A

A

STAGE I STAGE II STAGE III

A* B*

PANEL B

X AXIS – LABOR Y AXIS – TOTAL OUTPUT TP MP AP

GRAPH INFERENCE

• PANEL A explains the behavior of TP

• PANEL B exhibits the nature of AP and MP curves. With successive change in the variable input labor.

• Point A – inflexion of TP curve

• Point A* on the MP curve in PANEL B it corresponds to Point A.

• Point A*- It is the point where MP attains its highest and starts falling thereafter.

• Point B on TP curve is where AP is equal to MP

• After point B* in PANEL B the AP starts falling.

• Point C- TP is maximum after it falls

• Point C* - where MP cuts x axis

STAGES IN GRAPH • STAGE I – Increasing returns to the variable

factor – This is first stage – In this additional units of labor are employed the total

out put increases. So marginal product rises. – In this MP > 0 and MP > AP

• STAGE II – Diminishing returns to the variable factor – It is second stage – Total output increases but less than proportionate to

increase in labor – This stage marginal product falls and this is known as

law of diminishing returns to the variable factor. – Both AP and MP are positive but declining – Here MP > 0 but AP is falling MP < AP where TP is

increasing at diminishing.

..contd

• STAGE III – Negative returns to variable factor

– This is third stage

– Which MP < 0 and TP is falling

– Technically this is inefficient stage of production

– A rational firm never operate in this stage.

PRODUCTION FUNCTION WITH TWO VARIABLE INPUTS

• So far we dealt with production functions with one variable input – short run

• Let us move a head to long run in which all the inputs are variable.

• Thus the firm has the opportunity to select the combinations of inputs and maximizes returns.

• We restrict ourselves to most simplistic form of production function with 2 variable inputs and a single out put

ISOQUANT

• ISOQUANT (iso- equal quant- quantity) is the locus of all technically efficient combinations for producing a given level of output.

• ISOQUANT are similar to concept of indifference curve/iso utility curve.

• ISO QUANT

– It is the different combinations of two inputs that corresponds to the same output.

• It is also referred to as ISOPRODUCT curve.

EXPLANATION

• Taking the production function • Q = F ( L , K)

• With a fixing level of out put Q at some quantity we have an implicit relationship between units labor( L ) and capital (K)

• Qc = F ( L , K )

• It is possible to produce the same amount of output by using different combination of input.

EXAMPLE

• Firm produces 150 thousand tones of out put, with investment of Rs 40 C and 600 labor units.

• The manufacturer wants to know which different combinations of this inputs can be used to produce 150 thousand tones of out put

see the table…………..

INPUT COMBINATIONS

POINT CAPITAL (Rs CRORE) LABOR (000 UNITS)

A 40 6

B 28 7

C 18 8

D 12 9

E 8 10

GRAPH – ISOQUANT

A

B

C

D

Q1

X AXIS – LABOR Y AXIS – CAPITAL

GRAPH - INFERENCE

• The curve in graph shows the locus of different combinations of labor and capital that produce 150 thousand tones of out put.

• Locus of points

– A at curve Q1 shows Rs 40 c and 600 Labor units give the 150 Thousands tones of output.

– like that all points B , C,D,E (combinations) may infer that the level of output remains the same at all points on the same isoquant.

GRAPH – ISOQUANTS

C

B

A Q2

Q1

Qo

X AXIS – LABOR Y AXIS – CAPITAL

CHARACTERISTICS OF ISOQUANTS

• Down ward sloping

– Slope downwards from left to right

– Using more of input to produce the same level of output must imply using less of other input

– slope = -(∆K / ∆L)

• A higher isoquant represent a higher output.

• Iso quants do not intersect.

• Convex to the origin.

MARGINAL RATE OF SUBSTITUTION MRTS

“MRTS measures the reduction in one input due to unit increase in the other input that is just sufficient to maintain the same level of out put”

..contd

• For the same quantity of output , MRTS of labor ( L ) for capital (k) = MRTS LK

• MRTS LK would be the amount of capital that the firm would be willing to give up for an additional unit of labor.

• It is similarly for MRTS KL.

• MRTS LK is expressed in

– MRTS LK = - ( ∆K / ∆ L)

..CONTD

• MRTS of labor for capital is equal to the slope of the isoquant.

• MRTS also equal to the ratio of the a marginal product of one input to the marginal product of other input.

• Let see how – Since output along isoquant is constant

– If units of labor( ∆L) is substituted for units of capital ( ∆K) then the increase in output due to increase in labor ( ∆L) should match with decrease in output due to decrease in capital ( ∆K)

..CONTD

• SO

• ∆L X MP L = - (∆K X MP K )

• MP L / MP K = - (∆K/ ∆L)

MRTS LK = - ( ∆K / ∆ L) = MP L / MP K

TYPES OF ISOQUANTS

• LINEAR ISO QUANT – Two inputs are perfect substitutes

– Qc = F ( L , K ) = α K + β L

– Where α , β are constant

– In this case MP L = d Q / d L , MP K = d Q / d K

– MP L = α , MP K = β

– Therefore MRTS LK = α / β

– ISOQUANTS in this case is down ward sloping straight lines

GRAPH – LINEAR ISOQUANT

O Q1 Q2 Q3

X AXIS – LABOR Y AXIS - CAPITAL

…contd

• RIGHT ANGLED ISO QUANT

– In this the inputs are perfect complements.(assumption)

– Non substitutability between the two factors

– This isoquant is right angled

– Production function

• Q = MIN (L / α, K / β)

• Where β, α fixed coefficient.

Q3

Q2

Q1

X AXIS – LABOR Y AXIS - CAPITAL

GRAPH – RIGHT ANGLED ISOQUANT

ISOCOST LINES

• The concept of ISOCOST line is similar to budget line.

• ISOCOST line is the budget line of a producer in terms of two inputs.

“ ISOCOST line is the locus of points of all the different combinations of labor and capital that firm can employ given the total cost and prices of inputs”

…contd

• ISOCOST lines expressed as – C = w L + r K

– Where price of labor is wage = w

– The price of the capital is interest = r

– The total cost is C

• The total cost C of the firm is fixed and the input prices are given the ISOCOST line gives various combinations of labor and capital

• Usually the ISOCOST line is linear with slope equal to ratio of the factor prices. …..*

..contd

• See the graph

– The intercept of the ISOCOST line on the capital axis is the maximum amount of capital employed when labor is not used in the production process is given by C / r

– Similarly the intercept in labor axis is given by C / w

– SO therefore

• Slope = (∆K /∆ L) = {(C/r)/(C/w)} = w/r … *

A2

A

A1 O B1 B B2

X AXIS – LABOR Y AXIS - CAPITAL

GRAPH- ISOCOST LINE

A2

A

A1 O B2 B B1

X AXIS – LABOR Y AXIS - CAPITAL

GRAPH- ISOCOST MAP

GRAPH - INFERENCE

• The set of parallel ISOCOST lines is called ISOCOST map.

• Line AB basic ISOCOST line.

• AB1 shows a rise in W more of labor can acquired.

• AB 2 shows a fall in W.

• Same as for BA2 and BA1

PRODUCERS EQUILIBRIUM • A firm may maximize its profits at given

production function. • When producers faced with several technically

efficient combinations the decision is taken on basis of economic efficiency.

• Producers use the combinations which minimize the cost of production.

• The producers must determine the combinations of inputs that produces the output at minimum cost.

• Assume that producers act rationally that means choosing which combination gives minimize cost and maximum output.

..contd

• For minimum cost we need ISOCOST line and maximum output we need ISOQUANTS.

• Combining the ISOQUANTS and ISOCOST lines will help to understand the producers equilibrium.

A

C

K* E

Q3

D Q2

Qo

X AXIS – LABOR Y AXIS – CAPITAL

GRAPH - PRODUCERS EQUILIBRIUM

L* B

CONDITION FOR PRODUCE

REQUILIBRIUM SLOPE OF ISOCOST LINE = ISOQUANT

CURVE

• Point E is producer equilibrium.

• At this point the firm would employ L* and K* units of labor and capital respectively.

• Q2 amount of output can also be considered to be the maximum output that can be produced at a given cost.

• Any amount of output above AB is not feasible

• Below AB is feasible but not desirable because the firms aims to maximize output so like to use entire funds.

GRAPH - INFERENCE

contd

• Point C and D are also on the ISOCOST line

• But C and D are on Q1 which is lower than Q2.

• So point C , D, E shows the combinations of inputs L and K which come for the same cost but give different output.

• Thus E is preferred to C and D which is on the highest possible ISOQUANT.

A2 R A

A1 E K S Q O L B1 B B2

X AXIS – LABOR Y AXIS - CAPITAL

PRODUCERS EQUILIBRIUM- FOR GIVEN LEVEL OF OUT PUT(CONSTANT)

v

CONDITION FOR PRODUCE

REQUILIBRIUM SLOPE OF ISOCOST LINE = ISOQUANT

CURVE

GRAPH - INFERENCE

• In this the firm already decided the level of output at ISOQUANT Q.

• So we have a single ISOQUANT line.

• Q out put can be produced with three combinations of two inputs shown by points R , S , E. which are on different ISOCOST line.

• Given the assumption of rationality the firm will take the combination which minimize its cost for given out put.

• So the firm choose point E ( OL AND OK of inputs) on AB as equilibrium.

EXPANSION PATH

“ Expansion path is the line formed by joining the tangency points between various isocost lines and the corresponding highest attainable isoquants.”

• It is also defined as the locus of equilibrium points of the isoquant with lowest possible isocost line

A E2 E K* E1 Q1 O L* B

X AXIS – LABOR Y AXIS - CAPITAL

EXPANSION PATH – LONG RUN GRAPH

• Expansion path is a long run concept and each point on the expansion path represents a combination of inputs that minimizes cost.

• The arrow from the origin shows all the cost minimizing input combinations for various levels of out put the firm could produce in the long run.

• Long run expansion path E1 E E2

GRAPH - INFERENCE

…CONTD

• Is the expansion path always linear …………. No.

• The slope of the expansion path depends on the ratio of the input prices.

• When production function is homogenous then the slope of expansion path is linear.

• If production function not homogenous then expansion path is not linear.

RETURNS TO SCALE

• Returns to scale refer to the degree by which the level of out put changes in response to a given change in all the inputs in a production system.

• Types of returns to scale

– Constant return to scale

– Decreasing return to scale

– Increasing return to scale.

..contd • Constant return

– If a proportional increase in all inputs yields an equal proportional increase in output.

– Example = if labor and capital are doubled then output also doubled.

• Decreasing return – If a proportional increase in all inputs yields a less

than proportional increase in output. – Example = if labor and capital are doubled then

output is less than doubled.

• Increasing return – If a proportional increase in all inputs yields an more

than proportional increase in output. – Example = if labor and capital are doubled then

output is more than doubled.

GRAPHS – RETURN TO SCALE CONSTANT DECREASING

50 100 200 50 125

B C

A

90

INCREASING 50 150 400

PRODUCTION FUNCTION

Cob-Douglas Production Function

• Type of Empirical production function. • Proposed by WICKSELL • Tested against statistical evidence by CHARLES

W.COBB & PAUL H.DOUGLAS. • Equation is

– Q = Total Output – L = Units of Labor. – K = Units of Capital. – A = a constant – B = a parameter

bbKALQ 1

COB-DOUGLAS FUNCTION - PROPERTIES

• Both L and K should be positive for Q to exist.

• b + (1-b) =1. It assumes only constant returns to scale. It does not support Increasing or Decreasing returns to scale.

• Cob-Douglas equation rewritten

• α = Wage share / Total Income.

• β = Capital share / Total Income.

KALQ

PROPERTIES CONTD…

• If (α+β) = 1, it is Constant return to scale.

• If (α+β) > 1, it is increasing returns to scale.

• If (α+β) < 1, it is decreasing returns to scale.

bbKALQ 1

LIMITATIONS OF COB-DOUGLAS

• It cannot show marginal product of an input passing the 3 stages of Production.

• It assumes Constant return to scale. Certain Production function cannot be increased in the same proportion.

• Difficulty in measurement of various inputs.

• It assumes there is a fixed relation of raw materials and output.

CES – CONSTANT ELASTICITY OF SUBSTITUTION PRODUCTION FUNCTION

– X = Output, C = Capital, L = Labour

– γ = Efficiency parameter (scale effect)

– K = Capital intensity factor coefficient

– K-1 = Labour intensity factor coefficient

– ν = Degree of returns to scale.

– α = Substitution parameter.

/)1( LKKCX