7.1 Introduction 7.2 Production Function 73 Types of Production Function Fixed-Proportions and Var 73.1 | 73.2 Linear and Non-Linear . Homogeneous Production 74 Isoquants (Iso Product Curves) 74.1 Marginal Rate of Technical 742 Properties of Isoquants i | Optimum Combination of Resources (0 743 Isoclines : #5) g 7.1 INTRODUCTION Production is an important economic activity, which directly or indirectly satisfies the wants |) and needs of the people. It is concerned with | _ thesupply side of the market. The standards of living of the people depend on the volume and #| the variety of goods produced. Without Production, there cannot be consumption. Richness or poverty of the nation and Performance of the economy is judged by itslevel {f Production. Those nations which produce ‘onmodities and services in large quantities are sidered rich and others which produce less pesmsidered poor. ae is the transformation of inputs into commaaeut of a commodity or several Speci ties Gn case of point production) in a technologet od of time at the given state of input acy, 2 Production process, even both vutput may be intangible. Thus, the a <¥. Ss Eesha 7.5 Expansion Path (Change in Outlay and Factor Comt word production in Economics is not simply confined to effecting physical transformation in the matter, it also covers rendering of services such as teaching, consultancy, transporting, financing, retailing, packaging, etc. In a broad sense, production implies the creation or addition of form, place and time utilities by the production, storage, distribution of different usable commodities and services. Production enhances the utility of the product by changing it to the form in which the consumers need it, Distribution through transportation increases the usefulness of the product by bringing it to the location where the consumer needs it. In the absence of transportation, the product may be just as useless to the consumer as it would be if it were still a collection of raw materials. Likewise, storage gets the product to the consumer when. he needs it.120 7.2. PRODUCTION FUNCTION Production, as said before the transformation of inputs into outputs at the given state of technology. Output is, thus, a function of inputs. ‘Technical relation between physical inputs like capital and labour (factors of production) and the physical outputs is depicted by production function (Fig. 7.1), Production function denotes an efficient combination of inputs and output. It shows for a given technological knowledge and managerial ability, the maximum amount of a good that can be obtained from different combinations of productive factors per unit of time or minimum quantities of various inputs required to yield a given quantity of output. ‘Thus, production function is a catalogue of output possibilities, Prices of factors or of the pproductdo not enter into the production function, y Q=f(,K) Output ‘Labour and Capital Production Function ‘Mathematically, it can be expressed in the form ofan equation, Q=fK, L,1, 0) ‘Q stands for the quantity of output, K,L,7 and ‘0’ stand for the quantities of capital, labour, land and organisation (factors of production) respectively used in producing output. Output quantity,thus, depends on the quantities of these inputs. The above production function describes the technological or Business engineering relationships involyeq eererieciachion ar rem ofa commodity. ‘The production function of a firm technical methods available to produce! output of acommodity by combining the! of production in various possible ways, 4, at, producer always uses technically most gf method of production. A method oto issaid to be technically more efficient methods, if it uses less of at least ong ti input and no more ofthe other factoring produce one unit of the commodity, Sump the two methods of production P, and P mm and 2 units of labour, while 3 and uniyg capital respectively. Here the rational prone willchoose method P, to produce the comme’ since it saves one unit of capital without uses more amount of labour. Hence, this method economical and more efficient. The theory of production considers only on efficient methods A However, itis often not possible to diredly compare the production processes, when production of a commodity requires more f some factor and less of some other factor ()as compared to any other production process, Suppose, the production method P, requines® units of labour and 4 units of capital, while production method P, require 4 units of labour and3 units of capital. Here, neitherofthetw production methods is more efficient than le other. Since the two methods are not diredtly comparable, they are considered as technically efficient and included in the production neton ‘The choice of a particular method will depend on the prices of factors. This choice, of # particular production method among technically efficient methods for decision making at the firm level is an economic 00 rather than technical. Therefore, a technical efficient production method needs not be % economically efficient method. Derivation of0% economically efficient process (given the phos of the inputs) is discussed in Section 7.430 ‘Optimum Combination of Resources’ ee One Pen oe ee eee ees 8 ee ee SS ee ee ee ee eePER ELLS i zB. eegeias £5 2607 £; juction, spsvotPee sation wil make the difference between aereficiney and economic eficieney more oo poatuction function expresses the way ‘he Pr produced by inputs and the way inputs output with each other in varying propértions pemjuce any given output. These relations fopmen inputs and outputs and inputs betwen es are determined by technology that them at any given time. The technology is vars dded in the production function, which acts em constraint in decision making. Thus, 8 Suction function depicts the present limits Phe firm. A firm can produce higher output nly by using more inputs or with advanced technology. At the same time, production faaction indicates the manner in which a firm can substitute one input or output (as the case maybe) for the other without altering their total mounts respectively. Production function differs from firm to firm, industry to industry. Any change in the state af'technology or managerial ability disturbs the original production function. New production function may have a smaller or larger flow of output for a given quantity of inputs in ease of deterioration or improvement in the state of firm respectively. The production function shifts downwards/upwards in the two cases respectively. An estimated production function is a statement of technological specification. Production function can be estimated by statistical techniques using historical data on inputs and output. Estimation of the production fuction can help business firm in taking correct long-run decision such as capital expenditure. er, the short-run production estimates at mn Jevel are helpful in arriving at the optimal tant inputs to achieve a particular output "eet, L.e., least cost combination of inputs. various 72 function can be represented in cdulee TS: It can be represented by ules, tables, input-output tables, graphs, — 121 mathematical equations, total, average and marginal product curves, isoquants (equal Product curves) and so on. 7.3 TYPES OF PRODUCTION FUNCTION ‘The formulation of the production function is a highly technical job. This engineering concept should be undertaken by those persons, who possess the necessary technical and engineering knowledge relevant to firm or industry in question. Certain pioneer studies were made in the field of agriculture for the measurement of production function. Various production functions can be formulated on the basis of statistical analysis of the relationship between changes in physical inputs and physical outputs, 7.3.1 Fixed-Proportions and Variable- Proportions Production Functions When the amount of a productive factor required to produce a unit of product (i.e. technical coefficient) remains fixed irrespective of the level of production, the production function is of fixed proportion form. A fixed proportion production function indicates a technological feasibility lacking for sudden change in technique. In this case, the factors of production, say, labour and capital, must be used in definite fixed proportion in order to produce a given level of output. Here, the possibility of substitution of the factors of production is ruled out. As it happens in the long-run, it is called as long-run production function. On the other hand, when the amount of a factor required to produce a unit of product can be varied by substituting some other factor in its place, the production function will be of variable proportions form. Most of the commodities in the real world are produced under conditions of variable proportions production functions. In case of variable proportions production function, agiven amount of a product can be produced by122 several alternative combinations of factors. As it happens in the short-run, it is called as short- run production function. In the real world, more than one fixed proportions productive processes to produce a commodity are available, where each process involves a fixed factor ratio. No factor substitution is possible within one productive process. However, different processes make use of various factors of production in different quantities, as they involve different fixed factor ratios. 7.3.2 Linear and Non-Linear Production Functions (Homogeneous and Non- Homogeneous Production Functions) Q= aK+ Lis the simplest form of the linear production function. Here, ‘Q’ represents the ‘output. The contribution of capital (K) to output equals cand that of labour (L) to output equals 6. This simple form of production function is not normally preferred for empirical use, since, this form assumes that the two factors of production are perfect substitutes. This means that production is possible even with any one of the two factors of production, Linear homogeneous production function or homogeneous production function of degree one is the most-popular form of linear production function. In this case, if all the factors of production are increased in some proportion, output also increases in the same proportion. Mathematically, for linear homogeneous production function nQ=f(K, L), n Q= fin K, nL). Here, Q’ stands for the total production, ‘K’ and ‘L’ are the two factors of production, say capital and labour and ‘n’ is any real number. This relation shows that if factors ‘K’ and ‘L’ are increased ‘n’ times, the total production also increases ‘n’ times. Thus, homogeneous function of first degree yields constant returns to scale, Its graph is linear. Bu: Business In general, when all the erga iy o homogeneous —_ production Fr Q=(K, L) are changed by scale faceted i S ke ry’ Mt the function changes by n¥. Itcan ben, as function of n’ (to any power %e) ang 24 level of output. ing N'Q=f(oK, nL) =n* f (KL) Here ‘k’ is constant. “(ay This function is homogeneous of degree yp, classical production function). The valuegpt will determine the degree of production neg If ‘k’ is equal to zero, the function beooma homogeneous of degree zero. If ® is equalg one, the above function will be of degree ong ie., linear homogeneous production function with constant returns to scale and so on, If is greater than one, i.e., proportional increase in output exceeds the proportional increasein the factors of production, we have inereas returns to scale. If, on the other hand, Kis less than one, the production function exhibits decreasing returns to scale. Here, the Proportional increase in output is less than the Proportional increase in inputs®. Homogeneous production functions for which ‘k’ is not equal toone are non-linear homogeneous production functions. Inview of limited analytical tools at the disposal of the economists, linear homogeneous pion functions can be handled easily and economists aptival analysis, That is why, uc such functions as well: inctions. Due to important : for whieh satisfied are agar Mich this relationship is not functions, *°4 n0n-homogencous production Beste 0 Pretncrsin: anatyie 8 detail," ~ UAW of Returns wo Sonte” forof Production ee ges, because of simplicity and close peside’ mation to reality, it has wide 07jons in model analysis in production, applic#jon and economic growth. yaribU aa pansion path ofthe Tinear homogeneous The exten function is always a straight line lth the origin. Thus, the proportion throug the factors that will be used for betweefion will always remain the same prod tive of the amount of output produced, sy constant relative factor prices while Seeing the production. The entrepreneuris “orbothered to take decision again and again et optimum factor proportions, so Tong as as ative factor prices do not change. On he basis of empirical studies carried outin several countries of the world like United States sd Britain, it has been found that many stanufacturing industries face a long phase of pnstant long-run average cost (LAC) curve. Farm management studies carried out for various states in India brought similar fonclusion for agriculture, i.e., prevalence of constant returns to scale, 7.4 ISOQUANTS (ISO PRODUCT CURVES) Given a production function for a certain output, one can derive isoquant showing all the ‘combinations of the factors of production that yield the same level of output. This is done by substituting the value of output in the production function and by getting different Values of one factor for different values of another factor. Isoquants® or equal-product or iso- Product curves are analogous to the indifference curves of the consumer theory. An isoquant is one of the ways of presenting production, where the two factors of production are explicitly Se ccca 1. ‘ iscussed later in this chapter in Section 7.5 Expansion Path (Change in Outlay and Factor *mbinations), ‘qual, quant = quantity 6. iso 123 shown. It represents all possible input combinations (input ratios) of the two factors, which are capable of producing the same level of output. Thus, input ratio keeps on changing along an isoquant. As producer would be indifferent between such combinations, so itis often referred to as the producer's indifference curve or production indifference curve. All combinations yielding the same level of output lie on the same iso-product curve or production indifference curve. It is a contour line showing the points of equal production on a map showing production as its dimensions. In the words of Keirstead, “Iso-product curve represents all possible combinations of the two factors that will give the same total product”. According to KJ. Cohen and R.M.Cyert, “An iso-product curve is a curve along which the maximum achievable production is constant”. Iso-product curve analysis helps a producer to find a combination of two factors, which gives him maximum output at the minimum cost. In other words, this analysis solves the problem of optimum combination of factors. Various factor combinations ‘A’, ‘BY, ‘C’,‘D’ and ‘E’ producing the same level of output, say 100 units are shown in the following Fig. 7.2 in the form of isoquant 1Q. These points depict different techniques of production. For example, point ‘A’ represents capital intensive technique, while point ‘I’ represents labour intensive technique. ‘Technology is assumed to remain unchanged and inputs are assumed to be perfectly divisible. In isoquant IQ shown in Fig. 7.2, as the quantity of one factor is reduced,the quantity of other factor will have to be increased, so that the total product remains the same. A number of isoquants (.e., family of isoquants) depicting different amounts of output are known as isoquant map. It represents technical conditions of production for a product. Input ratio may remain constant at various points of different isoquants, where a ray from origin cuts them. Fig. 7.2 shows such an isoquant map, where124 isoquant IQ represents the lowest output level of 100 units, while isoquants Q,, 1Q, and IQ, represent higher output levels of 200 units, 300 units and 400 units respectively. It must be noted that each higher isoquant shows higher output than the lower one, because, every point ‘on such curve implies greater amount of at least one factor than some point on the lower isoquant one, while every individual isoquant shows the same level of output. Various levels of output may be producable by the same input ratio, while the input ratio may change for a given level of output. This family of isoquants represents a production function with two variable inputs. ee 400 300 200, 100 [oa 1015 0-25 a Fig. 7.2: Isoquant Map 7.4.1 Marginal Rate of Technical Substitution Marginal rate of technical substitution (MRTS) in the theory of production is similar to the concept of marginal rate of substitution (MRS) in the indifference curve analysis of consumer theory. MRTS indicates the rate at which factors can be substituted at the margin in such a manner that the total output remains unaltered. If capital (K) and labour (L) are the two factors of production, then the marginal rate of technical substitution of labour (L) for capital (K) is defined as the quantity of “K’ which can be given up in exchange for an additional unit OF 5 Business Fong of ‘L’, so that the level of output unchanged. ‘The marginal rate of technical substitu, a point on the isoquant can be measured Ps a negative of the slope of the isoquant at. the Consider a small movement down fron eat ‘A’ to point ‘B’ in isoquant IQ in Fig, 79 Hee ca romain, asmall amountof factor K, say, AK, isrep by an amount of factor ‘L’, say, AL, wig any loss of output. The slope of the isoquanth at point ‘B’ is, therefore, equal to. ARIAL Thag MRTS =slope =AKIAL. This slope is nega, as the amount of two factors change in oppo? directions. Marginal rate of techniea, substitution can be known from the ratio ofthy marginal physical productivities of the tm, factors. This is explained below. As the total output remains same at every poing of the isoquant, so, loss in physical output from a small reduction in factor ‘K’ will be equal iy the gain in physical output from a small increment in factor ‘L’. Thus, Loss of output= Gain of output i.e., Reduction in ‘K’ x Marginal Physical Product of ‘K” increment in ‘L x Marginal Physical Product ofl Or, AK x MP, = AL x MP, AK to MP, AL” MPx So, MP, ». MRTS, x= yap, AK (By definition — 7 ~ =MRTS,, « = slope of isoquant at that pail! Thus, marginal rate of technical substitu of factor ‘L’ for factor ‘K’ is the ratio of Physical productivities of the two factors The following table would make the cone? marginal rate of technical substitutio” clear. ihproduction 1: ‘Table 7.1 Marginal Rate of Technical Substitution wa mations Labour(L) Capital (K) ‘Marginal Rate of Technical Substitution of Labour for Capital (MR’ 1 12 = 2 8 an 3 5 8:1 as 4 3 a 5 2 aL “oh ach of the five above input combinations Bat sponds to the same level of output. Moving ryan the table from combination ‘A’ to ‘BY, 4 dovis of capital (K) are replaced by 1 unit of Iubour (L). So, the marginal rate of technical te patitution is 4 at this stage. Hence, marginal v oduct of labour must be four times as large Pathe marginal product of capital. Similarly, moving from input combination ‘B’ to ‘C” involves the replacement of 8 units of ‘K’, output remaining the same. Therefore, the marginal tate of technical substitution is now 3. Likewise, MRTS between factor combinations ‘C’ and ‘D’ is 2, and between ‘D’ and ‘E’ is 1. This explains that the marginal ate of technical substitution diminishes, as more and more of labour is used. That is, the slope of the isoquant diminishes, as one moves from left to right on the curve. ‘The degree of substitutability of factors of production or the ability to use one factor (or input) in place of other is measured by the marginal rate of technical substitution. As the quantity of labour (L) increases and that of capital (K) decreases, the marginal physical productivity (contribution of additional unit) of labour (MP,) falls and that of capital rises, because relatively inefficient labour units are foming into employment, while relatively Getticient capital units are going out of ceoyment. So, lesser and lesser units of naitinnrs required to be substituted for each fame etal unit of labour so as to maintain the asthe Be of output (see Fig. 7.8). Thisis known inciple of Diminishing Marginal Rate — of Technical Substitution®. As we move along an isoquant downward to the right in the figure given below, each point on it represents the substitution of labour for capital. The diminishing marginal rate of technical substitution occurs, as different factors are imperfect substitutes of each other in the production of a commodity. Capital Fig. 7.3: Diminishing Marginal Rate of Technical Substitution ‘The rate at which this substitution (MRTS) diminishes is a measure of the extent to which the two factors can be substituted for each other and hence the degree of convexity of the isoquants. The smaller is the rate, greater will be the substitutability between the two factors. 6. The principle is merely an extension of the law of diminishing returns to the relation between marginal physical productivities of the two factors.If this rate remains constant, the two factors Aare said to be perfect substitutes of each other. Here, each one of the two factors can be used equally well in place of other. In other extreme case, where the two factors are jointly used for the production in fixed proportions (no Substitution at all), the two factors are called Perfect complements, 7.4.2 Properties of Isoquants The properties of isoquants are very much Similar to those of indifference curves. Moreover, their proofs are also based on the same lines. The following are the important Properties of the isoquants () Tsoquants Slope Downward from Left to Right :Isoquants have negative slope This is so because, when the quantity of one factor (say, ‘X’) is increased, the quantity of other factor (say, ‘Y) must be Teduced, so that total product remains constant (Fig. 7.4). If, however, the ‘marginal produetivity ofthe factor becomes negative, the isoquant bends back and acquires positive slope, (segments AD and BF in Fig 7.4) Y y (a) isoquants are Convex to Origin es eee of isoquants is based upon the ‘Principle of Diminishing Marginal Rate of Technical Substitution’ (Fig. 7.2), Employment of each successive unit ofone factor (say, labour) will be required to compensate for smaller and smaller sacrifice of the other factor (say, capital) @) Isoquants Never Cut, Touch o, Intersect Each Other : Intersection isoquants showing different level output is logical contradiction. Iewoug mean thatisoquants representing difeen levels ofoutput (’and‘C’in Fig, 75)ane showing the same amount of output (B in Big. 7.5) at the point of intersection, Which is wrong. Thus, we rule out the following cases in case of isoquants, © paso sheet the same level of output Against the "the isoquants would be Marginal pateve Principle of Diminishing eof Technical Substitution of conve: n the rate he degree xity of isoquants at which marginal ical substitu ine ion changes, ‘Fhe ter the rate at which MRTS falls, the ee eeTE EEEL are ris the convexity of the isoquants greate® ' ersa. In extreme situation, when vice Motors are perfect substitutes of the tt er, then for all practical purposes, snoen be regarded as the same factor. they SN rRTS between two perfect ‘ates will be constant. (Fig. 7.6 (a). Here, equal addition in one factor requires fice of other factor by same amount saci time addition is made. Henee, the SXchnical coefficient of production is (ariable. Isoquant in this case will be a Myaight line with negative slope, This Soquant touches both the axes implying that a given output can be produced by using even any one input. Jnanother extreme situation, when the two factors are perfect complements (factors used in fixed proportions), isoquant will be right-angled (Fig. 7.6 (b)). Here, MRTSis. undefined. This type of isoquant is known as input-output isoquant or Leontief isoquant (after the name of Wassily Leontief, who did pioneer work in the field al Q Labour (L) (a) Perfect Subsitutes o by increasing the amount of bo factors by the required rc other input is held constant. Th factor will be redundant. Leonti does not imply that increase quantities of the two factors of (abour and capital) will al output proportionately. It only im for producing any quantity of act the factors must be proportions. The ray OE shows the capital labour rat be maintained for ensuring production. y Capital (K) Labour (L) () Perfect Complements Fig. 7.6 : Exceptional Shapes of Isoquants Re ae. there are various techniques of techniee Sven amount of output, each of facts Naving a different fixed combination Kinkeg ge? Produce a given level of output. of a con oquant is an example of the production mmodity for which few different fixed — proportions processes are available, This form is also called activity analysis isoquant or linear programming isoquant, because it is basically ‘used in linear programming. The kinked or linear programming isoquant can be illustrated by using L-shaped isoquants (Fig. 7.7).128 Capital (K) ¥ Labour (L) Fig. 7.7 Kinked isoquant In Fig. 7.7, OA, OB, OC and OD are four process-rays, whose slopes represent different capital-labour ratios. By jointing ‘A’, ‘B,C’ and ‘D’, we get the kinked isoquant. Each of these four points on the kinked isoquant represents a factor combination, which can produce the same level of output. However, it is different from ordinary isoquant in the sense that every point on the kinked isoquant is not a feasible factor combination capable of producing the given level of output. Only the kinks (four factor combinations corresponding to four available processes) show the technically feasible factor combinations. ‘The kinked isoquants are more realistic than smooth convex isoquants. Engineers, managers and production executives consider the production processes as discrete rather than continuous, since machinery, equipment, etc. are available in limited range. Therefore, the possibilities of substitutability between capital and labour (and for other inputs also) are limited. The continuous isoquant is only an approximation to the more realistic form of kinked isoquant, particularly when the number of processes become too large. The smooth convex isoquants are considered because they are easy to handle in practice. Business 7.4.3 Optimum Combination of (Optimum Decision Rule yy A profit maximising producer aims to mp, his cost for producing a given oye Wy maximise the output, given the total oo op : 60 aim can be achieved by securing the gry ‘ combination of factors. The ultimate depends upon, () technical possibilities of productio Gi) the prices of factors used for the prodye. ofa particular product. Metin Anumber of technical possibilities are o a firm or producer from which it has to haa” Inother words, there are various combina” of factors which yield equal level of output ang producer has to select one for productia therefrom, These technical possibilities of production are shown by isoquant map, whish has already been discussed. The prices offictig are shown by the iso-cost line or factor costling to which we now turn al Iso-Cost Line ‘The iso-cost line is the counterpart of the budget line or the price line of consumer theory. It shows all the combinations of the two factors (say, labour and capital) that the firm can buy with a given outlay for a given set of pricesof the two factors. It plays an important part a determine the combinations of factors, the firm will choose for production ultimately te minimise cost. Fig. 7.8 shows the way iso-cost line is drawn We measure the units of factor ‘X’ on the X-axis and those of factor ‘Y’ on the Y-axis Suppose, the firm has at its disposal 2200ft the two factors. The price of the factor” is 710 per unit and that of factor ‘Y’ is %5 per um With outlay of 2200, the firm can buy either™! units of X’ (OA) or 40 units of ‘Y’ (OB), spends exclusively on the purchase of only’ te factor ‘X or Y’, as the case may be. In thea two cases, the firm will be at point ‘A’ an" respectively, The firm can also choose a5¥ _esi ie ‘al oo ton partly OF pt \d part ee sr pass throud) AB wi dx which tl one oF it, the yen prices oF jine #8 ina! com outlay. THUS iyiine. The sO autratio of the tO vame for i80-cO8! fons that can other celine Cike # Bre analysis) Le PHC is ri E 10 20° 30 40 Fig. 7.8: Iso-Cost Lines joining points ‘A’ and ‘B’ 'p), ifit partly spends on the other. The straight hall combinations of he firm can buy with jneAlsg and nds the entire outlay on 0, fit SP th). This line is called either firm has to incur the same the firm neur i as hichever combination of the huey oF rt, the firm may choose to buy ge lying the factors. An iso-cost pe give gs the locus of factor i efined “Gn be purchased for agiven the iso-cost line is also called pe of this line is equal to the factors (Py /Py) . So, the t line is factor-price line ‘example, the slope of the factor Inthe current Oe price line in indifference .¢ ratio of the two factors outlay (C) that a firm factors. There will the iso-cost line, ift spends on the factors i the factors decline in the sa vice-versa. The reason ist factors can be purchased outlay or proportionate. the two factors and vice-t example, if the outlay is do %200 to $400), keeping the pri constant, quantities of both the purchased twice as much as earlier (80; of 40). Same result will follow, if the p both the factors become half of the situation (total outlay remaining con ‘Thus, any number of iso-cost lines! all parallel to one another, by: the total outlay (given prices of same proportionate change in the p two factors (given total outlay). ay Producer Equilibrium (Least Cosi Combination of Factors): _ ‘ Producer always tries to a possible volume of outp outlay on factors with given prices these are combined in an optimal m Alternatively, producer minimises his production for producing a given level of ou In this way, the producer maximises his pro! ‘and produces a given level of output with least cost combination of factors. This least cost combination of factors will be optimum for him. Given iso-cost line and the series of isoquants (isoquant-map), the producer will choose the level of output, where the given iso-cost line is tangent to the highest possible isoquant. In Fig. 7.9 (a), B, is the point of equilibrium, where isoquant 1Q, is tangent to iso-cost line AB. Given budgeted expenditure, all other points are either notin the reach of producer (like points ‘P’,‘Q” ete. on the same isoquant 1Q, or any point on130 Business higherisoquant 1Q,) or give lesser output (like choose to produce the given g, Se Points R’, ‘S’on isoquant 1Q,) than the pointof (on isoquant IQ, in Fig. 7.9 ‘tut at ‘equilibrium E, with the same cost and hence are inefficient. Similarly, when the series of iso-cost lines and ‘one isoquant is given, then the producer equilibrium will be at the point, where the given ‘isoquant touches the lowest possible iso-cost line , in Fig. 7.9 (b)). All other points are either not desirable (implying higher total cost indicated by points lying on higher iso-cost line than EF) or not feasible though preferable (Points lying on lower iso-cost line than EF),as the given output cannot be produced with factor combinations indicated by these points. How the entrepreneur ultimately arrives at the point of equilibrium, can best be explained with the help of the concept of marginal rate of technical substitution (MRTS) and the price ratio” of the two factors. The producer will not Capital ( i (a)) isoquants IQ in Fig. 7.9 Or point MRTS (slope of the sean i het the price ratios (slopes of the pra & factors. Hence, producer will yar” °X abou for factor Y' (eapitgg ete on the corresponding isoquants to han off. Similarly, at point Q' (on jgoqaet® f ee a Fig 7.9(4) 0 point‘U (on isoquanet ue tie 1 7.9 (b), we face the reverse situent iin producer will substitute factor "at ang factor'X (labour) and will co up on i Pal iy isoquants to ultimately reach the eq at points E, and Ey to achieve greater ett lower cost in the two cases respectively, - nite points, marginal rate of technical subst is equal to the price ratio of the factors at producer would be maximising the outeu minimising the cst using the factor commineat® inthis manner. ation 4 1Q xX an ie Labour B o DOF OH Fig. 7.9: Producer Equilibrium a oe MRTS, y= 2 Slope of isoquant = Slope of iso-cost line Sx y= Py 7, Ashas been stated earlier, the marginal rate of Or, MRTS, ae technical substitution is given by the slope of the * Py isoquant at various points and the price ratio of Mh Me the factors is given by the slope of the iso-cost Or, x= x Tine. While the former is the rate at which inputs Px Py m, the can be substituted in production, the latter That is, at the point of equilibria ta indicates the rate at which one input can be marginal physical products of the (Wo ior substituted for another in purchasing are proportional to the factor prices:ee spent on one factor (say, the last PP ve as the last rupee spent spout er any capital) and prover has rr, to change the combination of two of centive ntance, the price of factor is If, for Isis that of factor ‘Y’, then the fact fnuch aS tI as mi purchase and use such quantities sy factors that the marginal physical afte 18°) + ‘X’ is twice the marginal prot oduct of factor 'Y. The result ean be mead fr more number of factors as MPJP, = MPP, aa noticed that at the point of It i tum, the isoquant must be convex tothe equ Le. at the pointof equilibrium, MRTS,. ye diminishing for equilibrium to be ue In Fig. 7.11, ‘e’ cannot be the point of ulibrium, ‘ns isoquant IQ, is concave at this ind MRTS increases here. With a concave Bequant, we have corner solution (point e, in fig. 7.10). Thus, e is the point of stable equilibrium, where isoquant is ata higher level and it is convex. c ° x Labour! AQINIGs Fig. 7.10 par of the producerin choosing the 1 pat offactorsis exactly symmetrical with Doigeen UF of the consumer. Both the ch qa the consumer purchase thingsin bsitaton ios #8 0 equate marginal rate of in equi at the price ratio. The consumer, sb ilibtium, equates his marginal rate on (or the ratio of the marginal Capital IQ factors) with the price rs Example: A firms p Q=5L ' unit and that of capital is least cost combination of] anoutputlevel of20. Solution: The least cost requires the equality of rice (P,) tothe price of capital (Py) ar rate of technical substitution The condition of equilibrium gives 7k 3L oy koe Or, Leia Asoutputlevel in 20. Therefore, 5 L°-7 K°3 = 99 Kot bett8) Substituting the value of from (7.2) in (7.9), weget ay? : L= (4) =6.4 (Approx) Substituting the value of ‘L' in (7.2), we get Kis sisye = 1.4 Approx.)182 capital is 6.4 units of labour and 1.4 units of capital. The cost is LP, + K Py =1x 6.4 +2 1.4=%9.20. Example: Suppose a product (Q) uses two inputs labour (L) and capital (K). Production situation. KIL 40 | 1s | 9 500 | 15 | 100 If wage rate (w) = %5 and rate of interest (r) = %10, does the input combination 15K + 100L represent the least cost method of producing output of 500. Ifnot, should you use more labour and less capital or less labour and more capital? Solution: Here, MP, = 2 = 10 units, Expansion Path &c A x 2. Bee DEE teen Labour (a) Non-linear production Fig. 7.11: Expansion Path & Eve ime proportionate variation in prices, wo ma, Jevels of output, given constant total cost or gutlay, sins ‘Thus, the | combination of labour and Moet () Linear Homogeneous Production Function B as eed, = rol = MRTS, oe As the marginal product of labours. the marginal product of capital, the fing ea use less labour and more capital, Muy 7.5 EXPANSION PATH (CHANGp IN OUTLAY AND FACTOR COMBINATIONS) Sofar we have assumed away the expansion financial resources ofthe firm. As the prods becomes financially well-off, he has to chang the factor combinations with the expansione, his output, given the factor prices. In iy 7.11(@), AB,CD,BF and GH are the four isoeny lines representing different levels of total cog oroutlay, All iso-cost lines are parallel to one another indicating that prices of the two factors remain the same®. E,, H,, Ey and By, are the Points of producer's equilibrium corresponding tothe point of tangencies of the above fouriso. cost lines with the highest possible isoquantin each case. Long-run Expansion Path have parallel iso-cost lines representing differemtproduction — d SS . the least cost combinations like i joining n° alled the expansion path. nel and Baise, it shows how for the 5B called, ree of the two inputs (theslope Tine), the optimal factor arFactot PTC» which the producer plansits of spinations as he expands the volume of ouput Wil ion path may be defined as the output Erecient combinations of the factors tus of efor gency between the isoquants (ihe Pats ° et lines). It is the curve along the 80-008" penditure changes, when tos remain constant. Hence, the see portion of the inputs will remain oplimal, PFs also known as scale-line,asit unchanged. TY, producer will change the shows Pov the two factors, when it raises the afoot production. heexpansion path may have different shapes ‘hi slopes depending upon the relative prices mihefactors used and shape of the isoquant. fh case of constant returns to scale (linear homogeneous production function), the expansion path will be a straight line through theorigin, indicating constancy of the optimal proportion of the inputs of the firm, even with thanges in the size of the firm's input budget. (Fig. 7.11 (b)). The isoquant map in such situation is called homothetic. In short-run, however, the expansion path will be parallel to X-axis (when capital is held constant at K as shown in Fig. 7.11(b). As expansion path depicts least cost combinations for different levels of output, it shows the cheapest way of producing each output, given the relative prices of the factors. a difficult to tell precisely the particular point xpansion path at which the producer in fact ee unless one knows the output Conor wats to produce or the size ofthe iscertain ae it wants to incur. But, this much ee though for a given isoquant map, diferent rong, Giiferent: expansion paths for ries of the tie Prices of the factors. Yet, when Producer w]e factors are given, a rational er pol always try to produce at one or int of the expansion path. >. 7.5.1 Isoclines i ‘The slope of expansion path is. the factor price ratio. Here, factor p1 (ie., the slope of isocost line) is tt account of parallel isocost lines. Since t price ratio is equal to the technical substitution on the es sio marginal rate of technical substitution constant along an expansion path. expansion path is a special type of an: which is a locus of points along which 1 marginal rate of technical sul ition constant. In the case of isoclines, tanger isoquants are parallel to each other. i lines discussed earlier in this chapter, ‘Economic Region of Production’ are isoclines with constant marginal technical substitution. Isoclines may have any shape. Like expansion path, isoclines including ridge lines associated with homogeneous production function of degree one are straight lines. Further, in the case of perfect substitutes, the expansion path is either X-axis or Y-axis, since the producer's ‘equilibrium (point where iso-cost lines meet the highest possible isoquant occurs at the corner point. For perfect complements, the expansion path of the firm is a ray from the origin passing through producer's equilibrium points, where iso-cost lines (not shown in the figure) meet the highest possible isoquants. Check Your Progress 1. Discuss the importance of the various factors of production in the production process. 2. What is production ? Explain the role of the theory of production in various fields. 3, Explain the concept and managerial uses of production function, What are the various types of production function? 4, Enumerate the inputs and outputs in the production function of (a) B.B.E. and B.Com.(H) students, and (b) agriculture and industrial product. ’introduction of Products 2.1 Total Product or Pi 2.2 Average Product or Prod g2.3 Marginal Product or Prodi , Fixed Factors and Variable Factors “a4 Law of Variable Proportions (Short Run Classical Approach Internal Economies 6.2 Internal Diseconomies 8.6.3 External Economies (and Dis 7 Returns to a Factor versus Returns 81 INTRODUCTION Inthe theory of demand, individual consumer wasconsidered as an economic unit. Similar to that in the theory of production, individual firm arindustry is the economic unit. Product refers tothe volume of goods produced by a firm or an industry during a specified period of time. Itis ‘Important to note that product has reference to Physical volume (or money value of output), thereas productivity is a ratio and has reference aca ettPer unitof input. We may talkof total age rreiuctivity’ or ‘partial factor a one ce Pending on whether we consider neinputat a time. If more output.ean be ed by the same input, or same output can be produced by less input by minimisation of wastage of raw materials or otherwise, the output per unit input goes up. This productivity enhancement indicates an improvement in physical efficiency of input. Durability of the product produced by an input also shows physical efficiency. 8.2. TYPES OF PRODUCTS The product (or productivity) can be looked at from three different angles (a) total product, (b) marginal product and () average product. Both the marginal product and average product can be used as a measure of physical efficiency.136 8.2.1 Total Product or Productivity (TP) ‘The total quantity of goods produced byafirm (ora factor) during a specified period of time is called its total product, Total product of a firm can be raised only by increasing the quantity of the variable factor. Generally, total product goes on increasing with an increase in the quantity of factor employed in the production, But, the rate of increase in total product varies at different levels of employment, As can be seen from Fig. 82, total product rises at increasing rate in the beginning, with increase in the employment ofthe variable factor. After a point, total Product starts ‘rising at a diminishing rate With further increase in the employment of the factor. This fact has also been proved tobe valid by empirical evidences, Tnerease in the variable facto of production will not always increase the total product, For example, employment of workers beyond the capacity of the factory will cause over-erowding. In such a situation, labour will not be ine osition to work most efficiently. Thus, the total Product curve slopes steeply upward at firs, then flattens out and finally declines. Initially, itis convex from below and then concave from below 8.22 Average Product or Productivity (AP) Average product ofa factor is the total product (cr output produced) divided by the total number of units ofa variable factor. Thus, Average Product = Total product ‘Number of units of variables factor In Fig. 8.2, the average product at a point is given by the slope ofa ray from the origin upto point on the total product curve. lainey cmp ee esc goed average produetof the factor. Average Proust of workers determines the compattvenes of one’s products in the markets. Further, the swage revisions arelinked tothe average product. The concepts ike ‘quality crles' and worker participation in management are als based on .ge product of workers. Itis clear: avel Busing 82thataverage product shows 9 tendency as does the marin! pat, marginal product, average prodyae att la, frtand then tfalls. However unig tig product, average product can ney it negative. Further, marginal Product 2, average product, when the latter ig equals average product, when the latte maximum and les below average pad 8 the latter is falling. In other wordy mot Droductrises ata greater rate than they brodt. The maryina! produ! rag maximum much earlier than the ane produc. Thus, when the marginal pra startling, the average productootins rise. During the downward phase, both product and marginal product dedine burt latter declines at a higher rate, 822 Marginal Product or Productivity (4p) Marginal product ofa factor i the adtinta the total production by the employment of an extra unit of a variable factor. For example, When 9 workers were employed in Frontier Biscuit Factory Pvt. Ltd., total ‘Production of biscuits was 10,000. Now, if one additional worker is employed, total production rises to 10,500 biscuits, ‘attributable to 10 workers. Since tenth worker has added 500 biscuits to the total Production, th ¢ marginal product of tenth Worker is 500 biscuits, ‘The formula for marginal product is Mp =TP~TP Mhere PPis total produc, nisthe number of variable factor units and fees the marginal product of n‘* variable 8.2 (given in Sub-section nal product rises in the mes 2er0, when the total Product is maximum Here, use ot edo | ‘arg eesi Resets total aactor does not inerease es max ginal product becomes ip fall juthe total product. el pelati (AP) ‘The relationship among total pro product and average product can b in the form of given Table 8.1 onship among Total Product, Average Product and Marginal | ‘Average Product that of the marginal product. Continues to increase and becomes maximum, Becomes equal to MPand then begins to diminish. mies to increase ing rate and mum. Contin at diminish becomes maxi —— 43. FIXED FACTORS AND VARIABLE FACTORS sion is the result of combined efforts of oof production. These factors may be ‘A fixed factor is one, whose quantity cannot readily be changed in response (Miesired changes in output or market 'e Gitions. Its quantity remains the same, hather the level of output is more or less or vm, Buildings, land, machinery, plants and topmanagement are some common examples offixed factors. A variable factor, on the other hand, is one whose quantity may be changed in response to a change in output. Raw materials, ordinary labour, power, fuel, ete. are examples ofvariable factors. Such factors are required nore, when output is more; less, when output is ess and zero, when output is nil. For the sake of analytical simplicity, semi-variable factors are not considered here. foe distinction between fixed and variable seftsirelated to two periods-—the shortrun en one-run. The period of short-run istoo inthe seatee variation in fixed factors, Thus, eaten, some factors are fixed, while coed ane Viable. The production can be rahe flyby increasing the quantity ofthe 's or by having additional shifts Product the facto fed or variable. _— Continues to diminish, but will always be greater than zero. © Reaches a maximum ; and begins to diminish. = Continues to diminish and becomes equal to zero. Becomes negative. om or by increasing the hours of work. But, in the long-run (also called as planning period of the firm), all the factors are variable, i.e., quantity ofall the factors required can be varied to produce an output ranging from zero to an. indefinite quantity. All investment options are open including installation of new plant and machinery. In the long-run, itis possible for a firm to branch out into new products or new areas or to modernise or reorganise its method of production through invention of new techniques. f ‘The distinction between fixed and variable factors helps us to study the law of variable. proportions and the law of returns of scale. ‘These laws of production show the relationship between the factors of production and ouput in. the short-run and long-run respectively. 8.4 LAW OF VARIABLE PROPORTIONS (SHORT RUN PRODUCTION ANALYSIS) ‘The short-run production function gives the maximum output obtainable from different amounts of variable input, given a specified amount of the fixed input and the required amounts of the ingradient inputs. The law of variable proportions is one of the most.138 important, fundamental and unchallenged law of production. This law is also termed as returns toa factor, as under it one factor is varied, while keeping all other factors fixed. With these variations in the quantity of one factor, keeping the quantity of other factors constant, the ratio of employment of the variable factor to that of the fixed factor keeps on changing. As we study the effects of variations in factor proportions under this law, this is called the law of variable proportions. There are two important approaches available to study this law: 8.4.1 Classical Approach The law of variable proportions is the new name for the famous ‘Law of Diminishing Returns’ of classical economists like Adam Smith, Ricardo, Malthus, etc. But, the real credit goes to Marshall for providing a logical and scientific basis of the law, which was confined to agriculture only. He defines the law as follows: “An increase in the capital and labour applied in the cultivation of land causes, in general, a less than proportionate increase in the amount of product raised unless it happens to coincide with an improvement in the art of agriculture”.! The following Table 8.2 explains the operation of the law of diminishing returns; Table 8.2 : Total and Marginal Product Units of Total Marginal Average Labour Product Product (Gn quintals) (in quintals) (inquintals) Product 1 20 20 2 2 30 19 15 3 38 8 126 4 44 6 i 5 48 4 96 6 6 2 a3 ee “Table 8.2 shows that the cultivator employs cae eed aut Wie PUREE pe oe reduce. One unit of labour gives a total product FF 90 quintals. When two units of labour are <. Marshall, Alfred: Principles of Economies, 5% Edition, P.150 Business p ‘ ey employed, the total product rises to gp ‘The marginal product (i.e., Addition ih, product with employment of ong 2 !2t factor) in this case is 10 quintale aiding additional unit of labour is further emit te the marginal product becomes Saquineae is less than the marginal product i previous situation. With each succentt increase in the units of labour, the total pray’? words, the marginal product diminishes yt employment of additional units of labour fe 8.1 depicts the operation of the law of diminiay returns. Curve AB in the figure has anegai’ slope. Thus, more units of labour (variable factor) provide diminishing marginal produe, Yoa 10 8 6 4 2 B 6. ae RBS SHR 5905 Fig. 8.1 + Marginal product Limitations of Law Law of diminishing returns assumes static technology. That is why, it is more often fpplicable to agriculture, where there is very little scope for improvement in the technology: However, improvements in the art, of agriculture cannot be perfectly assumed away. This lawis Subject toa number of limitations @ Guprovements in Methods of imprevatioR! The law assumes away any Marshatlint i the arts of agriculture. phrage «2° “larified it by inserting the ith or 2 ness it happens to coincide in the arts of ion of this law. If provement Sericulture” in his defin ee+1 nisrelaxed, ie, scientific or {his8eu TP cthods of cultivation (use of improve petter agriculture implements, seed ped, the returns are bound to re adoF che law will no longer hold jnorease “ver, there is some limit to the e. Howe in the methods of production. wemenner or later, the law of returns is bound to operate. ia virgin soil is brought under tion, the additional return from h ‘sive dose of labour and capital each styse increasing returns initially. me able Factors Working with Fixed : This law will not operate, if it ‘ble to keep some factor fixed Variabl © Factors js not possi (cay, land). @) Heterogeneous Variable Factors: All the units of variable factors are assumed tobe homogeneous or identical. In other words, diminishing marginal returns are fot due to the use of inferior units of the variable factor. However, in real world factor units are heterogeneous. variou @) Inadequate Units of Variable Factor: ‘The operation of the law of diminishing returns is also held up for sometimes, if the units of variable factors, ie., labour and capital applied to a certain fixed piece of land is insufficient to cultivate to the full capacity of that piece of land. Appraisal Alfred Marshall gave a fairly satisfactory explanation of the law of diminishing returns. He discussed the law in relation to agriculture. Applicability of the law to agriculture can be advocated on several grounds: ) Overdependence of agriculture on unpredictable natural factors like rainfall, climate and weather conditions, gy raricularly in less developed countries. ) Little scope for the use of implements, machines and other improved methods of Production. > ii) Seasonal employmentin agriculture 7 the productivity of agriculture pithy (iv) Effective supervision is not possible due to scattered agricultural operations over a vast area and over a number of months. (©) Quantity ofland remainsfixed (i) Last, but the most important reason ist fertility of the soil gradually falls. So, use of additional units oflabour and capit will result in less than proportionate increase in output. The law is equally applicable to the mines, forests and fisheries, which get exhausted as more and more are taken out of them. Hence, same quantities of labour and capital produce or extract lesser and lesser quantity of final product. For instance, in the beginning, coal is found near the surface of earth. Gradually, one has to go deeper and deeper into the bowels of the earth to get the same amount of coal and fish in the two cases respectively. Marshall's law of diminishing returns applies not only to agriculture (for which it was originally developed), but also to extractive industries and to other industries, where land or other natural resources are important. However, there is little scope of applicability of this law for most of the other manufacturing industries, which enjoy the advantages of large scale production through specialisation by machinary, men and management. But, this is possible only temporarily. Ultimately, the tendency to diminishing returns is bound to appear. In brief, the law has been found to be applicable in agricultural production more: quickly than in industrial production, because in the former a natural factor (i.e., land) plays a predominant role, while in the latter, man made factors play the major role. 8.4.2 Modern Approach Law of diminishing returns enunciated by the classical and neo-classical economists like ‘Marshall was peculiar to agriculture. Modern economists have given universal law which