PRODUCTION ANALYSIS • INTRODUCTION • Production is basically an activity of transformation which transfers inputs into outputs. • Farms use land, labor, seeds and small amount of capital as inputs to produce output like corn. • Similarly, a flour mill uses inputs like wheat, labor, capital for machinery, factory building to produce output like wheat flour. • So, an input is the goods or services which produce an output. • The firm generally uses many inputs to produce an output. • Output of any firm may be the inputs of other firms, e.g., steel is an output of the steel producer, but this steel is also an input of automobile or rail coach manufacturing or refrigeration manufacturing or air-condition manufacturing industries.
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• INTRODUCTION• Production is basically an activity of transformation which
transfers inputs into outputs.• Farms use land, labor, seeds and small amount of capital as
inputs to produce output like corn.• Similarly, a flour mill uses inputs like wheat, labor, capital
for machinery, factory building to produce output like wheatflour.• So, an input is the goods or services which produce an
output.
• The firm generally uses many inputs to produce an output.• Output of any firm may be the inputs of other firms, e.g.,steel is an output of the steel producer, but this steel is alsoan input of automobile or rail coach manufacturing orrefrigeration manufacturing or air-condition manufacturingindustries.
• Production Function • A production function is the technical relationship between
inputs and outputs.• A commodity may be produced by various methods using
different combinations of inputs with given state of
technology.• Take the example of cloth, it may be produced by usingcotton or silk or polymer as raw materials with handloom,power loom or computerized machines.
• You can see various types of raw materials and technologyoptions will create several possible ways of producing thesame product.
• Hence, there can be several technically efficient methodsof roduction.
• Production function includes all such technically efficientmethods.
• It can be said that production function is purely atechnological relationship between physical inputs and
physical outputs over a given period of time; production is afunction of inputs, their quality and quantity andinterrelation, i.e., complementarities and substitutability.
• Hence it can be said that production function is:
• Production function shows the maximum quantity of thecommodity that can be produced per unit of time for each
set of alternatives inputs, and with a given level of production technology.• A given amount of output can be produced by different
combinations of inputs and each of these combinations may
be technically efficient.• Technical efficiency is defined as a situation when usingmore of one input with either the same amount or more of the other input must increase output.
• Normally a production function is written as;• Q = f (x 1, x 2,.…..x n) …………….…………(i) • Where, Q is maximum quantity of output of a good being
produced, and x 1, x 2,.… ..x n are the quantities of variousinputs used in production.
• If we replace x1, x 2,.… ..x n in (i) by the factors of productiondiscussed above, then the production function may be;
• Q = f (L, K, I, R, E) ……………………… .. (ii)• Where, Q =output and the inputs are L, K, I, R, E; L=
labour, K = capital, I =land, R =raw material and E =efficiency parameter.
• In short run, some inputs like plant-size, and machineequipments cannot be changed, so a producer trying toincrease output in the short run will have to do so byincreasing only the variable inputs.
• On the contrary in the long run input options are very wide.
• On the basis of such characteristics of inputs, productionfunctions are normally divided into two broad categories:
• (i) with one variable input or variable proportion productionfunction
• (ii) with two variable inputs or constant proportionroduction function
PRODUCTION ANALYSIS• PRODUCTION FUNCTION WITH ONE VARIABLE INPUT
• In short run, producers have to optimize with only one
variable input.• Let us consider a situation in which there are two inputs,
capital and labour, capital is fixed and labour is variableinput.
• You will notice as the amount of capital is kept constant andlabour is increased to increase output, the ratio in whichthese two inputs are used will also change.
• Therefore, any change in output can be manifested onlythrough a change in labour input only.
• Such a production function is also termed as variableproportion production function; it is essentially a short termproduction function in which production is planned withvariable input.
PRODUCTION ANALYSIS• The short run production function shows the maximum output a firm
can produce when only one of its inputs can be varied, other inputsremaining fixed. It can be written as:
• Q = f (L, K 0)…………………… ..……………… (iii)• Where, Q is output, L is labor and K 0 denotes the fixed capital.• This also implies that it is possible to substitute some of the capital by
labor.
• It is easy to understand that as units of the variable input areincreased, the proportion of use between fixed input and variable inputalso changes.
• Therefore, short run production function is governed by law of variable proportions.
• To explain the concepts of average and marginal products of factorinputs consider the production function given in equation (iii),assuming capital to be constant and labor to be variable, total productis a function of labor and is given as:
• LAW OF VARIABLE PROPORTION OR LAW OFDIMINISHING RETURNS TO FACTORS
• The slope of the total product curve is determined from thelaw of diminishing returns.
• The law of diminishing returns, being empirical in nature,states that with a given state of technology if the quantity of one factor input increased, by equal increments, thequantities of other factor inputs remaining fixed, theresulting increment of total product will first increase andthen decrease after a particular point.
• The law is also known as diminishing returns to factors.• It states that as more and more one factor of production is
employed, other factor remaining the same, its marginal
• For example, if we increase labor input and capital inputremaining the same, then the marginal productivity of laborfirst increased, reaches maximum and then decreases.
• The law of diminishing returns to factors is depending onthree assumptions.
• i) It is assumed that the state of technology is given.
• ii) It is assumed that one factor of production must alwaysbe kept constant at certain level.
• iii) This law is not applicable when two inputs are used in afixed proportion and the law is applicable only to varyingratios between the two inputs.
• DIFFERENCE BETWEEN RETURNS TO A FACTOR ANDRETURNS TO SCALE
• The law of diminishing returns factors states that as moreand more one factor of production is employed, otherfactor remaining the same, its marginal productivity will
diminishing after some time, e.g., if we increase one factorof production i.e., labour and other factor of productioni.e., capital remaining the same, then the marginalproductivity of labour first increased, reaches maximum
and then decreases.• So, returns to a factor (variable factor) of production is first
increasing in the initial level of production and thendecreasing if we increase the amount of that variable factorof production.
• But, if we increase more and more of that variable factorthen the returns to the variable factor is negative.
• In the very first stage of production, if additional units of labour are employed, the total output increases more thanproportionately; so marginal product rises.
• In the following figure, stage I would begin from the originand continue to a point where AP L attains its maximumvalue.
• In this stage, MP L > 0, and MP L > AP L. This stage is calledas increasing returns to the variable factor.
• In the second stage, the total product increases but lessthan proportionate to increase in labor.
• In this stage, marginal product of labor falls and this stageis called as diminishing returns to variable factors. Here,MP L > 0 and MP L < AP L.
• The stage three is a technically inefficient stage of
production and a rational producer will never produce inthis stage. Here, MP L < 0 and total product is decreasing.• The law of returns to scale refers to the long run
analysis of production.
• It refers to the effects of scale relationships which impliesthat in the long run output can be increased by changingall factors by the same proportion, or by differentproportions.
• If the production function is Q0
= f (K, L) and we increaseall the factors of production by the same proportion p.
PRODUCTION ANALYSIS• So, the new production function is Q* = f [(p.K), (p.L)].• If Q* increases in the same proportion as the factors of production,
p, then we can say there are Constant Returns to Scale (CRS).
• If Q* increases less than proportionately with an increase in thefactors of production, p, then we can say there are DecreasingReturns to Scale (DRS).
• If Q* increases more than proportionately with an increase in thefactors of production, p, then we can say there are IncreasingReturns to Scale (IRS).
• TYPES OF ISOQUANT• Isoquants are various shapes depending on the degree or elasticity of
substitutability of inputs. These are as follows; • Linear Isoquant: This type assumes perfect substitutability between
factors of production, i.e., a given output can be produced by usingonly capital or only labor or by a large number of combinations of capital or labor.
PRODUCTION ANALYSIS• CHARACTERISTICS OF ISOQUANT • Isoquants are Downward Sloping: Technological efficiency
connotes that an isoquant must slope downwards from left to right,which implies that using more of one input to produce the same levelof output must imply using less of the other input.
• Thus if more of labour is used in the production process, then less of capital must be used to produce the same level of output. Slope of the
isoquant is equal to: K/L, ratio of capital and labour.
PRODUCTION ANALYSIS• A higher Isoquant represents a higher output• In the panel I of above figure, if we consider point A on the
curve Q 1 and the point C on Q 2, it can follow that C hasmore of both labour and capital as compared to A.• Thus as per given technology, more of both factors should
produce greater output.
• However you should learn that it is not necessary than on ahigher isoquant a point will have greater quantity of at leastone of the two inputs as in case of A and B.
• Hence a greater quantity of any one of the two inputs will
render a higher level of output.• In short, using more of both inputs and more of either of theinputs must increase output given the state of technology.
• Hence a higher isoquant Q 2 would represent a higher output
PRODUCTION ANALYSIS• Isoquants do not intersect each other• An isoquant represents the same level of outputs with
different units of two inputs: intersection of two isoquantswould signify single input combinations producing twolevels of output.
• This is explained by Panel II of above figure. Let A and Bbe two different points on Q 1 and Q 2 respectively.
• Suppose two isoquants Q 1 and Q 2 interested each other atpoint C. At point B and C of isoquant Q 1 the firm producesthe same level output Q 1.
• Again points A and C of isoquant Q 2 denote the same levelof output Q
2any the firm.
• Thus it follows that at points A and B, the same level of output should be produced.
• But from the fig it is clear that point A denotes a higherlevel of output than B; this is contradictory, and hence weconclude that isoquants cannot intersect each other.
• Convex to the origin• Given substitutability between factor inputs, as the firm
continues to employ more of one input say labour and lessof other say capital, a situation comes when it becomesdifficult to substitute labour for capital.
• Since labour and capital are not perfect substitutes, thereforeas capital (K) is kept fixed to produce additional units of outputs only by increasing laour (L), it would requiresuccessively increasing units of labour.
• This is better understood with the help of the law of themarginal technical substitution (MRTS).
• The absolute slope of the isoquant falls as we move downthe isoquant and the declining MRTSlk determining theconvexity of an isoquant.
• Marginal Rate of Technical Substitution (MRTS) measuresthe reduction in per unit of one input, due to unit increase inthe other input that is just sufficient to maintain the samelevel of output.
• Thus for the same quantity of output, marginal rate of technical substitution of labour (L) for capital (K)(MRTS LK) would be willing to give up for an additional unitof labour.
• Similarly, marginal rate of technical substitution of capitalfor labour (MRTS KL) would be the amount of labour thatfirm would be willing to give up for an additional unit of capital.
• MRTS of labour for capital is equal to the slope of theisoquants, it is also equal to the ratio of the marginalproduct of one input to the marginal product of other input.
• Since output along an isoquant is constant, if dL units of labour are substituted for dK units of capital, then the
increase in output due to increase in dL, i.e (dLxdK) shouldmatch with the decrease in output due to decrease in dK i.e.,(-dKx MP K).
• A change in the level of output can be expressed as changein total output (Q) equals to the sum of change in labor
input (dL) times MP of labour and change in capital input(dK) times MP of capital.• In other words: Q = MP L x dL + MP K x dK• However, along a given isoquant, output remains
unchanged, ie. Q = 0.• Hence we have,• MP L x dL + MP K x dK = 0
• Or, MP L / MP K = -dK / dL• Or, MRTS LK = MP L / MP K
• So, the marginal rate of technical substitution between twoinputs is equal to the ratio of the marginal physical products