Production Analysis Prof Prema Basargekar

Introduction

Basic concepts

Production function with one variable

Optimal use of the variable input

Production function with two varible

inputs

Optimal combination of inputs

Returns to scale

Innovation process

Production and cost belong to supply side

economics.

The core concern and survival of the firm is to

become competitive, both in terms of price and

quality.

Managers try to minimize cost and optimize

production within given resources(inputs).

How can production be optimized or cost minimized.

How does output behave when quantity of inputs is increased? How does technology matter in reducing the cost.

How can the least-cost combination of inputs be achieved.

Given the technology what happens to the rate of return when more plants are added to the firm.

Production : Transformation of inputs or resources into outputs of goods & services. It refers to all activities involved in production of G &S, from borrowing to set up plant to running quality control to market G & S.

Inputs: All the resources used in the production of G & S - Labor, Capital, Land, mgmt, technology, entrepreneur, information

Fixed Inputs: Those which cannot be changed during a time period under consideration such as Plant, machinery, permanent staff (K)

Variable Inputs : Those which can be varied easily & on a very short period of timem such as Raw material, Casual labour which can vary according to the output (L)

Short Run

At least one input is fixed

Long Run

All inputs are variable

Short run / Long run is relative & differs from

industry to industry

The importance of FOPs is also relative

Production function is an equation, table or graph showing the maximum output of a commodity that a firm can produce per period of time with each set of inputs.

Inputs & outputs are measured in physical qty rather than in monetary units.

Technology is assumed to be constant.

Q = f(X, Y) = XY

If Q = 2X + 7Y; then if X = 10 & Y = 7; then Q = 70

Q = f(L, K)

In the short run the input output relationship is studied with one variable input & other inputs considered as constants. It is also known as Laws of Variable Proportions or Laws of Returns to Variable Inputs or Law of Diminishing Returns or Laws of Return to Factor.

Assumptions:

A. Technology is constant

B. Labour is homogeneous

C. Input prices are given

K Q

6 10 24 31 36 40 39

5 12 28 36 40 42 40

4 12 28 36 40 40 36

3 10 23 33 36 36 33

2 7 18 28 30 30 28

1 3 8 12 14 14 12

1 2 3 4 5 6 L

Q = f(L, K)

Discrete Production Surface

Eg. Sachin Tendulkars score:

Total runs in 3 Matches: 150

Average runs : 50

Runs scored in 4th match: 70

Total runs : 150 +70 = 220

Average runs : 220/4 = 55

Marginal runs : 220-150=70

Runs scored in 5th match = 40

Total runs: 220+40 = 260

Average runs : 260/5 = 52

Marginal runs : 260-220 = 40

When average is rising, marginal is above

the average.

When average is falling, marginal is below

the average.

When average remains constant, marginal

and average are equal to each other.

Total Product

Total product is whole output.

Marginal product is the change in output caused by increasing any input X.

If MPX=Q/X> 0, total product is rising.

If MPX=Q/X< 0, total product is falling (rare).

Average product

APX=Q/X.

Returns to a Factor

Shows what happens to MPX as X usage grows.

MPX> 0 is common.

MPX< 0 implies irrational input use (rare).

Diminishing Returns to a Factor Concept

MPX shrinks as X usage grows, 2Q/X2< 0.

If MPX grew with use of X, there would be no

limit to input usage.

Total Product

Marginal Product

Average Product

Production or

Output Elasticity

TP = Q = f(L)

MPL = TP

L

APL = TP

L

EL = MPL APL

L Q MPL APL EL

0 0 - - -

1 3 3 3 1

2 8 5 4 1.25

3 12 4 4 1

4 14 2 3.5 0.57

5 14 0 2.8 0

6 12 -2 2 -1

Total, Marginal, and Average Product of Labor, and Output Elasticity

LDR postulates that production undergoes three stages

Stage 1 of production refers to the rate of increase in average product of the variable input up to the pt where AP & MP are equal.

Stage 2 is the range of maximum average product of the variable input to where the marginal product of the input is zero

Stage 3 of the production refers to the negative range of marginal product of the variable input

As the fixed factor capital has some given

capacity, it gets better utilised as we go

on increasing the variable input labour.

In this process because of division of

labour the productivity of the labour also

increases.

Once the maximum capacity of the

capital is utilised further increase in

labour results in fall of production.

Stage I of the production states that MP of labour is rising; thus it will help firm to increase the production by increasing L.

Stage III of the production states that MP of Labour is negative. Hence even if labour is available free of cost, rational producer will not operate in this stage.

Stage II of the production states that MP of L & C are positive but is declining; the stage in which the rational producer will operate. The point at which he will operate will depend on prices of inputs & prices of outputs.

A well known economist Thomas Malthus

believed in the law of diminishing returns

from agriculture. Because land is limited in

quantity and marginal and average

productivity of labour would always fall, the

agriculture production would not be

sufficient to feed rising population and

eventually it would lead to mass starvation.

Fortunately Mathus was proved wrong

technological improvements in agriculture

increased land and labour productivity

multiple times.

How much labour the firm should employ?

As long as extra revenue generated from the sale of the output exceeds extra cost of hiring the labour.

MRPL = Extra revenue generated by use of additional unit of labour

MRCL = Extra cost of hiring additional labour

Marginal Revenue

Product of Labor MRPL = (MPL)(MR)

Marginal Resource

Cost of Labor MRCL =

TC

L

Optimal Use of Labor MRPL = MRCL

L MPL MR = P MRPL MRCL

2.50 4 $10 $40 $20

3.00 3 10 30 20

3.50 2 10 20 20

4.00 1 10 10 20

4.50 0 10 0 20

Use of Labor is Optimal When L = 3.50

LDR addresses questions such as how much to produce and what no. of variable inputs to apply to a given fixed income.

In stage 3, labour capital ration is very high which suggests that additional employment of labour is not desirable.

In stage 1, since capital is underutilised firm can increase the labour input to optimise its production.

Whereas stage second provides the best opportunity to the firm to determine its level of production.

Maruti Udyog Ltd. Has a physical capital stock valued

at about Rs. 144.5 Crs. About 4004 workers are

employed to use this employment of labour?

In general, to maximise profits, the firm should hire

labour as long as the additional revenue associated

with hiring of another labour exceeds the cost of

employing that labour.

For instance, if marginal product of additional labour

is two units of output (two cars) and each unit is

worth Rs. 2 lakh. The additional revenue is Rs. 4

lakh. If additional cost of employing is Rs. 3 lakh,

then the firm can and should employ him or her. If

additional cost is Rs. 4.5 lakh, the firm should not

employ him/ her.

In the long run both the inputs viz L & C

are variable.

The Supply of both the units is elastic &

firms can hire larger quantities ofboth the

inputs.

The technological relationship between

both the inputs is given by Laws of Returns to Scales

K 6 10 24 31 36 40 39

5 12 28 36 40 42 40

4 12 28 36 40 40 36

3 10 23 33 36 36 33

2 7 18 28 30 30 28

1 3 8 12 14 14 12

1 2 3 4 5 6

L

Isoquants show combinations of two

inputs that can produce the same level

of output.

Firms will only use combinations of two

inputs that are in the economic region of

production, which is defined by the

portion of each isoquant that is negatively

sloped.

Isoquants

Economic

Region of

Production

Marginal Rate of Technical Substitution: Isoquatnt has a negative slope in the economic region; or the region in which substitution between two inputs is possible.

The negative slope implies that if one input is reduced, the other input has to be so increased that the total output remains unaffected.

The manger can choose from among various

different combinations of K and L.

The optimal combination is one which

maximises the output with the lowest cost.

This combination comes where MP divided by

input price is same for all inputs used.

= MPl/Pl = MPk/Pk or MPl/w = MPk/r

Suppose C = 100K + 250L

Budget is Rs. 1500

Thus 1500 = 100K + 250L

Thus K = 15 2.5L

If budget increases to Rs. 2000

Then K = 20 2.5L

If relative factor prices change, the slope of

isocost line will change.

Farmers in USA & Canada usually use more

capital intensive technology as compared to

farmers in India & China where more labour

intensive technology is used.

This means that the same quantity of foodgrain

(eg wheat) can be produced either with using

more capital or more labour.

Suppose the isoquant showing an output of

10,000 quintals is using L of 500 hours & K of 100

machine hours. If the farmer decides to

experiment with using 90 hours of machine and

he needs to replace this machine with 260 hours.

It means MRTS is equal to 0.04(-10/260 = 0.04)

Production Isoquants

Show efficient input combinations.

Technical efficiency is least-cost production.

Isoquant shape shows input substitutability.

Straight line isoquants depict perfect substitutes.

C-shaped isoquants depict imperfect substitutes.

L-shaped isoquants imply no substitutability.

Marginal Rate of Technical Substitution

Shows amount of one input that must be

substituted for another to maintain constant

output.

For inputs X and Y, MRTSXY=-MPX/MPY

Rational Limits of Input Substitution

Ridge lines show rational limits of input

substitution.

MPX

Isocost lines represent all combinations of two

inputs that a firm can purchase with the same

total cost. By using Isocost & Isoquant a firm

can determine the optimal input combination to

maximise the profits.

C wL rK

C wK L

r r

C TotalCost

( )w WageRateof Labor L

( )r Cost of Capital K

MRTS = w/r

Suppose a firm is using two inputs K and L.

MPl = 5 and MPk = 40.

The prices of inputs are Pl = Rs. 5 and Pk =

Rs. 25.

Is the firm optimizing the use of its

resources? If not explain.

Here MPl/Pl = 1 and MPk/Pk = 1.6

MPl/Pl < MPk/Pk

So the firm would be better of by using less

labour and more capital.

If the firm spends additional Rs. 25 on labour

it gain less than 25 units of output.

But if it spends additional Rs. 25 on capital it

would gain 40 units of output.

Budget Lines

Show how many inputs can be bought.

Least-cost production occurs when MPX/PX = MPY/PY and PX/PY = MPX/MPY

Expansion Path

Shows efficient input combinations as output grows.

Illustration of Optimal Input Proportions

Input proportions are optimal when no additional output could be produce for the same cost.

Production Function Q = f(L, K)

Q = f(hL, hK)

If = h, then f has constant returns to scale.

If > h, then f has increasing returns to scale.

If < h, the f has decreasing returns to scale.

Constant

Returns to

Scale

Increasing

Returns to

Scale

Decreasing

Returns to

Scale

Economic Productivity

Productivity growth is the rate of change in

output per unit of input.

Labor productivity is the change in output per

worker hour.

Causes of Productivity Growth

Efficiency gains reflect better input use.

Capital deepening is growth in the amount of

capital workers have available for use.

Product Innovation

Process Innovation

Product Cycle Model

Just-In-Time Production System

Competitive Benchmarking

Computer-Aided Design (CAD)

Computer-Aided Manufacturing (CAM)

Units of labour Total Product Avg Product Mar Product

1 40

2 48

3 138

4 44

5 24

6 210

7 29

8 -27

Production function for an agricultural

commodity is

TP = 15L2 L3

A. How much labour (L) should be employed

to maximise the output?

B. What is the value of MPL when TP is at

maximum?

TP is maximised when MPL = 0

= TP/ L = 30L 3L2 = 0

= L (30 -3L) = 0

= L = 10

Output is maximum when L = 10

MPL is zero when TP is maximum.

Production function

Short run and long run production function

Law of variable proportions/ Law of

diminishing returns/ Law of returns to

variable inputs

Law of returns to scale

Isoquant & isocost

Marginal rate of technical substitution

Increasing, constant & decreasing returns to

scale