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CHAPTER-1

INTRODUCTION

1.1PRODUCTION

Aproduction function is a function that specifies the output of a firm,

an industry, or an entire economy for all combinations of inputs. This

function is an assumed technological relationship, based on the current

state of engineering knowledge; it does not represent the result of

economic choices, but rather is an externally given entity that influences

economic decision-making. Almost all economic theories presuppose a

production function, either on the firm level or the aggregate level

A production function can be expressed in a functional form as the right

side of

Q = f(X1,X2,X3,...,Xn)

where:-

Q = quantity of output

X1,X2,X3,...,Xn = quantities of factor inputs (such as capital, labour, land

or raw materials).

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Fig 1.1 Stages of production

To simplify the interpretation of a production function, it is common to

divide its range into 3 stages.

In Stage 1 (from the origin to point B) the variable input is beingused with increasing output per unit, the latter reaching amaximum at point B (since the average physical product is at itsmaximum at that point). Because the output per unit of the variable

input is improving throughout stage 1, a price-taking firm will

always operate beyond this stage.

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In Stage 2, output increases at a decreasing rate, and the averageand marginal physical product are declining. However, the average

product of fixed inputs (not shown) is still rising, because output is

rising while fixed input usage is constant. In this stage, the

employment of additional variable inputs increases the output perunit of fixed input but decreases the output per unit of the variable

input. The optimum input/output combination for the price-taking

firm will be in stage 2, although a firm facing a downward-sloped

demand curve might find it most profitable to operate in Stage 1.

In Stage 3, too much variable input is being used relative to theavailable fixed inputs: variable inputs are over-utilized in the sense

that their presence on the margin obstructs the production process

rather than enhancing it. The output per unit of both the fixed and

the variable input declines throughout this stage. At the boundary

between stage 2 and stage 3, the highest possible output is being

obtained from the fixed input.

1.2 PRODUCTION WITH ONE VARIABLE FACTOR

Law of variable proportions Cobb Douglas production function

Production function-it is described as thetechnological relationship

between inputs and outputs in physical terms.

Q= f(Ld, K, L, M, E)

But for simplicity we assume that there are only two inputs Labor and

Capital.

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There are two kinds of production function-

1)Short Run Production Function2)Long Run Production Function

SHORTRUN PRODUCTION

It is the period in which output can be changed only by changing the

level of variable input labour. This is explained with the help of law of

variable proportions.

LONG RUN PRODUCTION FUNCTION

It is the period in which output can be changed by changing the level of

all the factors of production.

LAWOF VARIABLEPROPORTIONS

This law states that as more and more variable factors are employed theaddition to total production goes on decreasing.

Assumptions:

T

here are only two inputs labour and capital Technology is given Variable factors is homogeneous

1.3 STAGES OF PRODUCTION

FIRST STAGE-increasing returns to factor SECOND STAGE-Diminishing returns to a factor THIRD STAGE-Negatives return to a factor

Stages of Production

Stage 1: Increasing Returns Point of inflection MP max End of stage where AP is maximum AP cuts MP at its maximum

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Stage 2: Diminishing Returns TP increases at a diminishing rate TP reaches maximum and is constant second stage ends. MP is zero when TP is maximum

Stage 3: Negative Returns TP declines MP negative AP falling

Fig 1.2 Total, Average & Marginal product

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Stages of production:-

Key points:-

First stage: TP increases at an increasing rate and MP increases reachesmaximum. AP increases.

Second stage: TP increases at decreasing rate,AP decreases but is positive, MP isfalling but is positive.

Third stage: TP decreases, AP decreases and MP becomes negative.

1.4 COBB -DOUGLAS PRODUCTION FUNCTION

The generalized form of this function is A, and are parameters. A: This is known as the efficiency parameter. It indicates the level of

technology. : This indicates the elasticity of output with reference to capital. : This indicates the elasticity of output with reference to labour. This generalized function is homogeneous of degree one If and =1, this function becomes homogeneous of degree one or linearly

homogeneous.

Cobb -Douglas Production Function

The generalized form of this function is

A, and are parameters. A: This is known as the efficiency parameter. It indicates the level of

technology.

: This indicates the elasticity of output with reference to capital. : This indicates the elasticity of output with reference to labour.

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This generalized function is homogeneous of degree oneIf and =1, this function becomes homogeneous of degree one or linearly

homogeneous

1.5 COST

In production, research, retail, and accounting, a cost is the value of money that

has been used up to produce something, and hence is not available for use

anymore. In business, the cost may be one of acquisition, in which case the amount

of money expended to acquire it is counted as cost. In this case, money is the input

that is gone in order to acquire the thing. This acquisition cost may be the sum of

the cost of production as incurred by the original producer, and further costs of

transaction as incurred by the acquirer over and above the price paid to the

producer. Usually, the price also includes a mark-up for profit over the cost of

production.

More generalized in the field of economics, cost is a metric that is totaling up as a

result of a process or as a differential for the result of a decision. Hence cost is the

metric used in the standard modeling paradigm applied to economic processes.

1.6 DETERMINANTS OF COST FUNCTION:

The cost of production may be defined as the aggregate of expenditure incurred bythe producer in the process of production. Cost, is therefore, the valuation placedon the use of resources.

C=f (S,O,P,T,M)

Several concepts of costs such as; Fixed Cost, Variable Cost, Total Cost AverageCost, Marginal Cost, Money Cost, Real Cost, Implicit Cost, Explicit Cost, PrivateCost, Social Cost, Historical Cost, Replacement Cost And Opportunity Cost.

Fixed costs are those costs which remain fixed, irrespective of the output. Theyhave to be incurred on equipment, building etc and they are incurred even when theoutput is zero. Fixed costs are also called Supplementary costs orOverheads orIndirect costs.

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Variable costs are those costs which vary with the output. For example the cost ofraw materials, electricity, gas, fuel etc. the Variable costs are also called Primecosts, direct costs orOperating costs.

Marginal cost changes due to variable cost and hence is independent of fixed cost.

-Secondly the shape of Marginal Cost is determined by the law of variable

proportions.

-Price of a factor input remains constant is a vital assumption

MC= TCn-TC

n-1

=(TVCn

+ TFC) (TVCn-1

+ TFC)

=TVCn

+ TFC-TVCn-1

TFC

MC = TVCn

TVCn-1

-The difference between the short-run and long run production function is based on

the distinction between fixed and variable costs. In the short-run production

function, the output is increased only by employing more units of variable factors;other factors of production remaining fixed. In the long run all factors are variable

and thus all costs are variable.

MP

wMC

Q

L

MP

L

QMP

Q

LwMC

Q

TVCMC

QTCMC

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(

(!

(

(!

(

(!

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((!

1

*

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1.7 MARGINAL PRODUCT AND MARGINAL COST:

When Marginal Product is increasing Marginal Cost is decreasing and when

Marginal Product is decreasing MC is increasing. MC increases in the range where

production faces diminishing returns.

Fig 1.3 Total Cost Curve

Total cost Average cost and Marginal Cost Total cost is the aggregate (sum-total) cost of producing all the units of

output. It is the summation of total fixed cost and total variable cost. Thus,

TC = TFC + TVC The Total Fixed Cost curve is a horizontal straight line, parallel to the X-axis.

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The total variable cost curve slopes upwards as output increases. The total costcurve is parallel to the total variable cost curve as it is the lateral summation of

total fixed cost and total variable cost curves.

Average Cost: The Average Cost is the cost per unit of outputproduced. Thus, the Average Cost is obtained by dividing the total cost by

the total output.

TC = TFC and TVC.

AC can be rewritten asAC = TFC + TVC

Q

Therefore AC= AFC+AVC The Average Fixed Cost is the fixed cost per unit of output. i.e. AFC = TFC

Q

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Fig 1.4 AFC Curve

Now, if the output goes on increasing, the AFC will go on falling because the total

fixed cost will be thinly spread over the number of units of output.

AVC=TVCQ

1. In the starting the average variable cost is rather high.2. When more and more units of output are produced, the firm starts enjoying

several advantages in the form of transport, commercial and marketing

economies and thus the average variable cost goes on falling.

3. Any further effort to increase the output brings about disadvantages inmarketing and other processes involved in production, mainly associated

with the employment of variable factors and thus the average variable costbegins to rise.

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Fig 1.5 AVCCurve

The Average Cost Curve in the Short-RunThe AC curve is the lateral summation of the average fixed and variable cost

curves.

AC = AFC + AVC

The average fixed cost curve slopes downwards from left to right (AFCcurve) and average variable cost curve first goes downwards and then bendsupwards (AVC curve).

Each point ofAC curve can be plotted as the sum ofAFC and AVC.

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Fig 1.6 Average cost curves

The U-Shape of Average Cost Curve is explained in two ways :

The Geometrical explanation: The shape ofAC curve depends on theslopes ofAFC and AVC curves. Therefore, the AC curve acquires U-

shape.

The Theoretical explanation :Economies of Scale

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Fig 1.7 AC & MCCurves

1.When AC is falling, the MClies below it

2. Secondly MC cuts the AC at

the lowest point of AC curve

3. when AC curves begin to rise,

the marginal cost curve will be

above the AC curve

ACMCdQ

ACd

ACMCdQ

ACd

ACMCdQ

ACd

AC

ofslopemeasuresdQ

ACd

ACdQ

ACdQMC

dQ

QACdMC

dQ

TCd

MC

QACTC

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,0)(

,0)(

,0)(

)(

)(

).(

)(

.

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i)WhenAC is falling, the MC lies below it.ii)Secondly MC cuts theAC at the lowest point ofAC curve.

iii) Thirdly, when AC curves begin to rise, the marginal cost curve will be

above the AC curve showing that MC rises faster than the AC curve.

1.8 LONG- RUN AVERAGE COST CURVE:

Long- Run Average Cost Curve will envelope the related series of all short-run

AC curves

In case of short-run since some factors are Indivisible the producer has toremain contented by making best use of the given plant; whereas in the longrun the scale of operation can be altered and the producer will choose the

most feasible plant. There will be a new short run average cost each timethe scale is revised.

Fig 1.8 Two SACCurves

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Fig 1.9 Three SACCurves

1.9LONG-RUN COSTS

Another way to look at the long-run is that in the long-run a firm can chooseany amount of fixed costs it wants for making short-run decisions.

In the long-run there are no fixed inputs, and therefore no fixed costs. Allcosts are variable.

1.10 THE LONG-RUN AVERAGE COST CURVE

The long-run average cost curve shows the minimum average cost ateach output level when all inputs are variable, that is, when the firm canhave any plant size it wants.

There is a relationship between the LRAC curve and the firm's set ofshort-run average cost curves.

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1.11 SR AND LR AVERAGE COSTS

Economists use the term plant size to talk about having a particularamount of fixed inputs. Choosing a different amount of plant and equipment(plant size) amounts to choosing an amount of fixed costs.

Economists want you to think of fixed costs as being associated with plantand equipment. Bigger plants have larger fixed costs.

Economists use the term plant size to talk about having a particularamount of fixed inputs. Choosing a different amount of plant and equipment

(plant size) amounts to choosing an amount of fixed costs.

Economists want you to think of fixed costs as being associated with plantand equipment. Bigger plants have larger fixed costs.

If each plant size is associated with a different amount of fixed costs, theneach plant size for a firm will give us a different set of short-run cost curves.

Choosing a different plant size (a long-run decision) then means moving from one

short-run cost curve to another

Economists usually assume that plant size is infinitely divisible (variable). In thecase of finely divisible plant size, the LRAC curve might look like this:

Fig 1.10Average costs for a typical firm.

Each small U-shaped

curve is a SAC

TheLRACcurve.

$/Q

Q

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In the preceding graph, each short-run cost curve corresponds to a particular

amount of fixed inputs.

As the fixed input amount increases in the long run, you move to different SRcost

curves, each one corresponding to a particular plant size.

Notice in the graphs ofLRAC curves presented so far that the curves have been drawn to be U-shaped. That is, when output is increasing LRAC at

first falls, and then eventually rises.

The overall shape of the long-run average cost curve depends on thetechnology of production.

For example, advantages implicit in large scale production (with largeplants) may allow firms to produce large outputs at lower cost per unit.

On the other hand, firms may get so big that ever increasing managerial andmonitoring costs may cause unit costs to rise.

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CHAPTER-2

PRACTICAL ILLUSTRATION

2.1 IILUTRATION FROM SHOE INDUSTRY

The data is collected from a shoe industry named BATA. The data is followed as:-

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Table 2.1DATA FROM BATA

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2.2 PRODUCTION STAGES

The three stages of production are characterized by the slope and shape of the total

product curve. The first stage is characterized by an increasingly positive slope, the

second stage by a decreasingly positive slope, and the third stage by a negativeslope. Because the slope of the total product curve IS marginal product, these three

stages are also seen with marginal product. In Stage I, marginal product is positive

and increasing. In Stage II, marginal product is positive, but decreasing. And in

Stage III, marginal product is negative.

Fig 2.1Production stages

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Fig 2.2 TP , AP, MP curve

2.3 SHORT RUN COST CURVES

A firm faces three production options in the short run based on a comparison

between price, average total cost, and average variable cost. If price is greater than

average total cost, a firm earns an economic profit by producing the quantity that

equates marginal revenue with marginal cost. If price is less than average total cost

but greater than average variable cost, a firm incurs an economic loss, but produces

the quantity that equates marginal revenue with marginal cost. If price is less than

average variable cost, a firm shuts down production in the short run, incurring an

economic loss equal to total fixed cost.

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Fig 2.3 Short run cost curve

2.4 AVERAGE COST CURVES

A curve that graphically represents the relation between average fixed cost

incurred by a firm in the short-run product of a good or service and the quantity

produced. This curve is constructed to capture the relation between average fixed

cost and the level of output, holding other variables, like technology and resource

prices, constant. The average fixed cost curve is one of three average curves. The

other two are average total cost curve and average variable cost curve. A related

curve is the marginal cost curve.

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Fig 2.4 Average Cost Curve

2.5 TOTAL COST CURVE

The total cost of producing a good can be represented by three related curves, total

cost curve, total variable cost curve, and total fixed cost curve. The total cost curve

is the vertical summation of the total variable cost curve and the total fixed costcurve.

Fig 2.5 Total Cost Curve

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