Chapter 03.1 - Production Analysis

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Chapter- 3.1

Production Function

and Analysis

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Production

Consumption

Creation of utilities.

Destruction of utilities.

What is Production?

Concerned with the way in which resources (inputs) are employedto produce a firms products (outputs).


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FIRM

(Processing)Inputs

Outputs

Production does not refer to just the physicaltransformation of resources.

Production process includes acquisition of

capital resources, efficient employment ofresources, besides the normal process ofconverting raw materials into finished goods.

Production process

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Production Function

Expresses the technological or engineeringrelationship between outputs and inputsused in the production.

Q = f (La, Lb, K, M, T)

The dependent variable, output Q is a

positive function of the independentvariables, i.e., factors of production.

Where

Q = output in physical units


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La = Land units employed in the prod. of Q

Lb = Labor units employed in the prod. of Q

K = Capital units employed in the prod. ofQ

M = Managerial units employed in the prod.Q

T = Technology employed in the prod. of Q

Characteristics of a Production

FunctionShows physical relationship between inputs

and the level of output.

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Depicts the maximum output that can beproduced from a given amount of variousinputs.

or

minimum quantity of inputs necessary toproduce a given level of output.

It assumes that output is an increasingfunction of all inputs but if an input isexcessively applied in relation to otherinputs, an increase in it, other inputs heldconstant, might lead to decrease in output.


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The production is not possible without usingat least one of the inputs.

The inputs and outputs are perfectlydivisible.

AnalysisFor analytical simplicity, if the two inputs

considered are labor and capital, theproduction function can be rewritten as:

Q = f ( L, K )

which means Q depends on L and K.

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Short-run ProductionFunction

Short-run is defined as a situation in whichthe firm has at least one fixed factor ofproduction.

During SR, production could be increased ordecreased by changes in other (variable)

inputs.Assuming capital as the fixed input and labor

as the variable input, the SR production

function can be written as Q = f (L, K ).


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Long-run ProductionFunction

During LR all the factors of production arevariable.

During LR, production could be increasedthrough a change in any one or more of theinputs.

Short-run is a time concept and not a timeperiod.

These time horizons (SR and LR) do notcorrespond to any definite periods of

calendar time as the nature of theproduction process differs.

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Fixed and Variable Inputs

Factor inputs whose quantity does not varywith output are known as fixed factors.

Factor inputs whose quantity may vary withoutput are known as variable factors(Labor, raw material etc.).

In SR at least one factor does not vary withoutput.

In LR all factors may vary.In LR the distinction between fixed and

variable factors disappears as in the LR allfactors can vary.


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Production Function in ManagerialEconomics

Input-output relations where some inputs arefixed while quantities of other inputs vary SR production function. Two situations are:

One input is variable, all other inputs arefixed.

wo inputs are variable, all other inputs arefixed.

Input-output relations where all the inputsare variable LR production function.

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Total Product (TP): Refers to the totaloutput of the firm per period of time.

Average Product (AP): Total productdivided by the amount of the variable input

used to produce this output (AP = TP/L).

Marginal Product (MP): Addition to TP dueto the addition of one unit of the variable

input to the production process, fixed inputremaining the same.

(MP = TP/ L ).


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SR Production Function

(Fixed Factors + One Variable Input)

Assuming capital as the fixed input (K) andLabor (L) as the variable input, expressed asQ = f (L, K ).

When quantity of variable factor increase,quantity of fixed factors remain unchanged,the proportions between fixed and variable

factors keep on changing VariableProportions.

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As per the Law of Variable Returns (Law ofDiminishing Returns), as more and moreunits of the variable input are employed inthe production, fixed inputs remainingunaltered, production first increases at anincreasing rate and then at a diminishingrate, leading to a decline in total productioneventually.

MP increases over a certain range of inputup to a point, after which it decreases andeventually becomes negative.


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Simply, when increasing amounts of thevariable input are combined with a fixed

level of another input, a point will bereached where the marginal product of thevariable input will decline (Law ofDiminishing Marginal Returns).

Assumptions:

The state of technology is given.

One input must always be kept constant.

Factor inputs must be divisible.

16Rate of Labor

input

( L ) TPL APLMPL

0

1

2

3

4

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7

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0

20

50

90

120

140

150

155

150

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20

25

30

30

28

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20

30

40

30

20

10

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Total, Average and Marginal Product of levels


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L 2 L 3L 1 MP L

AP LRate of Labor

Input ( L )

Average Product,Marginal Product

IMR DMR NMR

L 3Rate of LaborInput ( L )L 1

a

TPL

b

a

Stage I

Stage IIStage III

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Initially, TP increases at an increasing rateover the range 0 to L1, and then increases ata decreasing rate.

Beyond L3, TP declines.

Initially, the input proportions are inefficient,i.e., there is too much of the fixed factor,capital.

As the L increased from 0 to L1

, output risesmore than in proportion to the increase in L,i.e., MP per unit of L increases as a betterbalance of L and K inputs is achieved.


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As the L is increased beyond L1, diminishingmarginal returns set in and thus MP declines

as the L finds the fixed factor inadequate.When the labor input has increased to L3, TP

reaches a maximum.

Beyond L3, the amount of labor has becomeexcessive with the result that TP actuallydeclines.

Relationships among TP,

AP & MP functionsMP reaches a maximum at L1, indicating an

inflection point (a) on the TP function.

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At inflection point, the TP function changesfrom an increasing at an increasing rate toincreasing at a decreasing rate.

MP curve intersects AP curve at itsmaximum point, i.e., at L2.

Whenever MP is above AP, the average isrising.

When MP is below AP, the average isfalling.

MP becomes negative at L3, whichcorresponds to the point where TP curvereaches a maximum.


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Production over the range 0 to L2, isdefined as stage 1, in which the MPL is

positive, but the MPK is negative.In this range, there is not enough Labor to

efficiently use the Capital stock.

In stage 1, fixed input is underutilized, APincreases when additional variable input isused.

Beyond L3 (stage 3), the MPL is negative astoo much of labor is combined with the

capital stock, thus variable input causesoutput to fall.

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The firm will not operate in either stage 1 or3 as the MP of either L or K is negative.

Production will occur only in stage 2,as the MP of both L and K is positive.

In stage 2, greater output is the result ofspecialization and teamwork and fixed inputis being properly utilized.

In stage 1 the firm would be underutilizingits fixed inputs, and in stage 3, it would beover utilizing its fixed inputs.


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K L TP AP MP

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0

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0

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2.5

2.5

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1.1/3

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Assignment 1

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Optimal Employment of aFactor of Production

Additional units of the variable input shouldbe hired until marginal revenue product(MRP) of the last unit employed = to thecost of the input.

MRP is equal to the MR multiplied by MP,

MRPL = MR x MPLMR = TR/ Q, and MPL= Q/ L,

Hence MRPL = TR/ Q. Q/ L

= TR/ L


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Marginal revenue product can be thechange in total revenue per one unit change

in the rate of Labor input.MRP = MLC rule guides the firm in deciding

the units of variable inputs to be employedrelative to its fixed input.

The firm should employ an input up to thepoint at which the revenue contribution ofthe additional input is equal to the costincurred by the firm to employ that input.

The Labor is hired until MRP L = W.

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Chapter 03.1 - Production Analysis