Definition of the Law | "A candle ...



Gopal SalimProductionfunction PRODUCTION Production Function: Meaning, Definitions & FeaturesProduction is the result of co-operation of four factors of production viz., land, labor, capital and organization. These are termed as inputs in production process. The producer combines all the factors of production and produces output. So we can say that production is the transformation of inputs into output.Production function“The production function is purely a technical relation which connects factor inputs and output.” (Prof. Koutsoyiannis)Production function explains the technical relationship between the inputs and output during the course of production process. It can be mathematically expressed as follows:Q = f (K, L, N)Where ‘Q’ is the outputK, L and N are the inputsSince the aim of the producer is to maximize his profit, he decides to maximize the production at minimum cost by means of the best combination of factors of production.FEATURES OF PRODUCTION FUNCTIONFollowing are the main features of production function:1. Substitutability:The factors of production or inputs are substitutes of one another which make it possible to vary the total output by changing the quantity of one or a few inputs, while the quantities of all other inputs are held constant. It is the substitutability of the factors of production that gives rise to the laws of variable proportions.2. Complementarity:The factors of production are also complementary to one another, that is, the two or more inputs are to be used together as nothing will be produced if the quantity of either of the inputs used in the production process is zero.3. Specificity:It reveals that the inputs are specific to the production of a particular product. Machines and equipment’s, specialized workers and raw materials are a few examples of the specificity of factors of production. Importance of Time Period in ProductionProduction involves time; hence, the way the inputs are combined is determined to a large extent by the time period under consideration. The greater the time period, the greater the freedom the producer has to vary the quantities of various inputs used in the production process. Hence production function is analyzed with respect to two time periods. They are short run production function and long run production function.PRODUCT CONCEPTS IN PRODUCTION FUNCTIONIn production, we use three different concepts in economics. They are:a.Total Product (TP) of Total Physical Product (TPP)The total product is the sum total of the output produced by the combined effort of all factors of production. For examples, if 20 laborers can produce 500kg of wheat, then the TP is 500 kg.b.Average Product (AP or APP)Average productivity is the productivity per head of the variable factor. For example 20 laborers can produce 500 kgs of wheat, then the average product is 25kg per laborer. Mathematically, AP can be given as follows:AP = Total Product/ No of Laborers EmployedC.Marginal Product (MP or MPP)Marginal product is the additional products produced by an additional variable factor. For example, if the number of laborers is increased from 20 to 21, and the output increases from 500 to 520, then the marginal product is 20. MP can be mathematically calculated as follows:MP = ?TP/?LSHORT RUN PRODUCTION FUNCTIONDuring the short run, all inputs of production cannot be changed. For example, factory building, machines etc cannot be changed during the short period. Hence the producer is able to increase or decrease the output by varying certain factors upon the fixed factors. The short run production function is explained by the Law of Variable Proportion in economics.LAW OF VARIABLE PROPORTION OR LAW OF DIMINISHIING RETURNS OR SHORT RUN PRODUCTION FUNCTION WITH SINGLE FACTOR VARIABLELaw of Variable Proportions or Law of Diminishing Returns occupies an important place in economic theory. This law is also known as Law of Proportionality. This law is introduced in economic by the famous economists Alfred Marshall.Definition of the Law“The law of variable proportion states that if the inputs of one resource is increased by equal increment per unit of time while the inputs of other resources are held constant, total output will increase, but beyond some point the resulting output increases will become smaller and smaller.” (Leftwitch)Assumptions of the LawLaw of variable proportions is based on following assumptions:(i) Constant Technology:The state of technology is assumed to be given and constant. If there is an improvement in technology the production function will move upward.(ii) Factor Proportions are Variable:The law assumes that factor proportions are variable. If factors of production are to be combined in a fixed proportion, the law has no validity.(iii) Homogeneous Factor Units:The units of variable factor are homogeneous. Each unit is identical in quality and amount with every other unit.(iv) Short-Run:The law operates in the short-run when it is not possible to vary all factor inputs.Explanation of the Law:In order to understand the law of variable proportions we can take the example of agriculture. Suppose land and labor are the only two factors of production, the production function can be shown as below:Q = f (L, N)Where - Q is the agricultural outputL is the number of laborers usedN is the size of landBy keeping land as a fixed factor and varying the quantity of variable factor (Labor), the output changes as per the table shown below:From the table, it is clear that there are three stages of the law of variable proportion. Stage 1In the first stage average production increases as there are more and more doses of labor employed with fixed factor, land. During this stage, the total product, average product, and marginal product increases but average product and marginal product increases up to 40 units. Later on, both start decreasing because proportion of workers to land reached optimum level. This is the end of the first stage.Stage 2The second stage starts from where the first stage ends or where AP=MP. In this stage, average product and marginal product start falling. During this stage, the marginal product falls at a faster rate than the average product. Since marginal product decreases, the total product increases at a diminishing rate. TP reaches maximum when 7 units of labor is employed and marginal product becomes zero at this level of production. Stage 2 is the operating stage of production for a farmer.Stage 3The third stage begins where second stage ends. This starts from 8th unit. Here, marginal product is negative and total product falls but average product is still positive. At this stage, any additional dose of labor leads to negative contribution. Graphic Presentation:In fig. 1, on OX axis, we have measured number of laborers while quantity of product is shown on OY axis. TP is total product curve. Up to point ‘E’, total product is increasing at increasing rate. Between points E and G it is increasing at the decreasing rate. Here marginal product has started falling. At point ‘G’ i.e., when 7 units of laborers are employed, total product is maximum while, marginal product is zero. Thereafter, it begins to diminish corresponding to negative marginal product. In the lower part of the figure MP is marginal product curve.Up to point ‘H’ marginal product increases. At point ‘H’, i.e., when 3 units of laborers are employed, it is maximum. After that, marginal product begins to decrease. The marginal product becomes zero at point C and it turns negative. AP curve represents average product. Before point ‘I’, average product is less than marginal product. At point ‘I’ average product is maximum. Then the average product decreases. Condition or Causes of Applicability:There are many causes which are responsible for the application of the law of variable proportions.They are as follows:1. Under Utilization of Fixed Factor:In initial stage of production, fixed factors of production like land or machine, is under-utilized. More units of variable factor, like labour, are needed for its proper utilization. As a result of employment of additional units of variable factors there is proper utilization of fixed factor. In short, increasing returns to a factor begins to manifest itself in the first stage.2. Fixed Factors of Production.The foremost cause of the operation of this law is that some of the factors of production are fixed during the short period. When the fixed factor is used with variable factor, then its ratio compared to variable factor falls. Production is the result of the co-operation of all factors. When an additional unit of a variable factor has to produce with the help of relatively fixed factor, then the marginal return of variable factor begins to decline.3. Optimum Production:After making the optimum use of a fixed factor, then the marginal return of such variable factor begins to diminish. The simple reason is that after the optimum use, the ratio of fixed and variable factors become defective. 4. Imperfect Substitutes:Mrs. Joan Robinson has put the argument that imperfect substitution of factors is mainly responsible for the operation of the law of diminishing returns. One factor cannot be used in place of the other factor. After optimum use of fixed factors, variable factors are increased and the amount of fixed factor could be increased by its substitutes.Applicability of the Law of Variable Proportions:The law of variable proportions is universal as it applies to all fields of production. This law applies to any field of production where some factors are fixed and others are variable. That is why it is called the law of universal application.1. Application to Agriculture:With a view of raising agricultural production, labor and capital can be increased to any extent but not the land, being fixed factor. Thus when more and more units of variable factors like labor and capital are applied to a fixed factor then their marginal product starts to diminish and this law becomes operative.2. Application to Industries:In order to increase production of manufactured goods, factors of production has to be increased. It can be increased as desired for a long period, being variable factors. Thus, law of increasing returns operates in industries for a long period. But, this situation arises when additional units of labor, capital and enterprise are of inferior quality or are available at higher cost.ISO-QUANTSIso-quant explains the production function with two variable factors. An isoquant is a curve that shows various combinations of two inputs that yield the same level of output. ‘Iso’ means equal and ‘quant’ means quantity. Therefore, an isoquant represents a constant quantity of output. The isoquant curve is also known as an “Equal Product Curve” or “Production Indifference Curve” or Iso-Product Curve.” The concept of isoquants can be easily explained with the help of the table given below:Isoquant ScheduleAn isoquant schedule is a tabular representation of various combinations of two factors of production that can produce the same level of output. An iso-quant schedule is given below: COMBINATIONSUNITS OF CAPITAL(K)UNITS OF LABOUR(L)TOTAL OUTPUT(Meters of Cloth)A50(OK)1 (OL1)100 B45(OK2)2(OL2)100C41(OK3)3(OL3)100D38(OK4)4(OL4)100The above schedule shows various combinations of labour and capital that gives the same level of output of 100 units.IQ 100In the above diagram, IQ100 is the isoquant which shows various combinations of labor and capital that gives the same level of output. The combinations are OK1+OL1, OK2+OL2, OK3+OL3 and OK4+OL4. The IQ100 shows 100 units of output that can be produced with the help of various combinations of labor and capital.Iso-quant map or iso-product map or equal product mapAn iso-product map or iso-quant map shows a set of iso-product curves. They are just like contour lines which show the different levels of output. A higher iso-product curve represents a higher level of output. In the following diagram, there is a family iso-quants, each representing a particular level of output.In the above diagram, units of labor is measured along the X axis and units of capital is measured along the Y axis. The diagram shows four iso-quants which shows various levels of output. There can be innumerable number of iso-quants in the space. Properties of Iso-quantsThe properties of Iso-product curves are summarized below:1. Iso-Product Curves Slope Downward from Left to Right:Iso-quants slope downward because, when more labors are added, the quantity of capital should decrease to maintain the same level of output. This can be shown with the help of a negatively sloping curve only. This is shown in the diagram below:The Fig. 3 shows that when the amount of labour is increased from OL to OL1, the amount of capital has to be decreased from OK to OK1, The iso-product curve (IQ) is falling as shown in the figure.2. Isoquants are Convex to the Origin:Like indifference curves, isoquants are convex to the origin. This can be explained with the help of diminishing marginal rate of technical substitution (MRTS), because convexity of an isoquant implies that the MRTS diminishes along the isoquant. The marginal rate of technical substitution between L and K is defined as the quantity of K which can be given up in exchange for an additional unit of L. It can also be defined as the slope of an isoquant.It can be expressed as:MRTSLK?= – ?K/?L = dK/ dLWhere ?K is the change in capital and AL is the change in labour.The convexity is explained with the help of the following diagram:As we move from point A to B, from B to C and from C to D along an isoquant, the marginal rate of technical substitution (MRTS) of capital for labour diminishes. Every time labor units are increasing by an amount, the corresponding change in the capital diminishes.3. Two Iso-quant Curves Never Intersect Each Other:As two indifference curves cannot cut each other, two iso-product curves cannot cut each other. In the following diagram, two Iso-product curves intersect each other. Both curves IQ1 and IQ2 represent two levels of output. But they intersect each other at point A. This means that combination A = B and combination A= C. Therefore B must be equal to C. This is against the principle of logic as B and C lie on two different iso-product curves. Therefore two curves which represent two levels of output cannot intersect each other.4. Higher Iso-quant Curves Represent Higher Level of Output:A higher iso-product curve represents a higher level of output as shown in the figure below:In the diagram above, units of labor have been taken on OX axis while on OY, units of capital. IQ1?represents an output level of 100 units whereas IQ2 represents 200 units of output. Higher level of output needs higher quantity of both inputs.5. Isoquants Need not be Parallel to Each Other:Isoquants need not be parallel to each other. The shape depends upon the substitutability of the factors in production process.6. No Isoquant can touch either Axis:If an isoquant touches X-axis, it means that the product is being produced with the help of labour alone without using capital at all. Similarly, OC units of capital alone cannot produce anything without the use of labour. Therefore as seen in figure below, IQ and IQ1?cannot be isoquants.Principle of Marginal Rate of Technical Substitution (MRTS)The principle of marginal rate of technical substitution (MRTS ) is based on the production function where two factors can be substituted in variable proportions in such a way as to produce a constant level of output. The marginal rate of technical substitution between two factors C (capital) and L (labour), MRTSLC?is the rate at which L can be substituted for C in the production of good X without changing the quantity of output. As we move along an isoquant downward to the right each point on it represents the substitution of labour for capital. MRTS is the loss of certain units of capital which will just be compensated for by additional units of labour at that point. In other words, the marginal rate of technical substitution of labour for capital is the slope of the isoquant at a point. Accordingly, Slope = MRTSLC?= dC/dL. (‘d’ is the change ). This can be understood with the aid of the isoquant schedule, in Table below:The above table shows that in the second combination to keep output constant at 100 units, the reduction of 3 units of capital requires the addition of 5 units of labour, MRTSLC?= 3 : 5. In the third combination, the loss of 2 units of capital is compensated for by 5 more units of labour, and so on.In Fig above, at point B, the marginal rate of technical substitution is AS/SB, t point G, it is BT/TG and at H, it is GR/RH. The isoquant AH reveals that as the units of labour are successively increased into the factor- combination to produce 100 units of good X, the reduction in the units of capital becomes smaller and smaller. It means that the marginal rate of technical substitution is diminishing. Iso-Cost Line or Budget LineIso-cost line is the line which shows the various combinations of factor units that will result in the same level of total cost. It refers to those different combinations of two factors that a firm can obtain at the same cost. The concept of iso-cost line can be explained with the help of the following table and figure. Suppose the producer’s budget for the purchase of labour and capital is fixed at Rs. 100. Further suppose that a unit of labour cost the producer Rs. 10 while a unit of capital is costing Rs. 20.From the table cited above, the producer can adopt the following options:(i) Spending all the money on the purchase of labour, he can hire 10 units of labour (100/10 = 10)(ii) Spending all the money on the capital he may buy 5 units of capital.(iii) Spending the money on both labour and capital, he can choose between various possible combinations of labour and capital such as (4, 3) (2, 4) etc.Diagram Representation:In the figure above, labour is given on OX-axis and capital on OY-axis. The points A, B, C and D convey the different combinations of two factors, capital and labour which can be purchased by spending Rs. 100. Point A indicates 5 units of capital and no unit of labour, while point D represents 10 units of labour and no unit of capital. Point B indicates 4 units of capital and 2 units of labour. Likewise, point C represents 4 units of labour and 3 units of capital. So an isocost line show various combinations of two factors that gives the same level of budget or cost.Producer’s?Equilibrium or Optimum Combination of Factors or Least Cost Combination:The producers’ equilibrium implies to that situation in which producer maximizes his profit by producing a particular level of output by using a particular combination of two factors. In short, the producer is producing given amount of output with least cost combination of both the factors. It is also known as optimum combination of the factors.Optimum combination is that combination at which either:(i) The output derived from a given level of inputs is maximum or(ii) The cost of producing given output is minimum.Conditions for Producer’s Equilibrium(i) At the point of equilibrium the iso-cost line must be tangent to isoquant curve.(ii) At point of tangency i.e., iso-quant curve must be convex to the origin or MRTSLk?must be falling.The producer’s equilibrium can be shown with the help of the following diagram”In the above diagram, P1L1?iso-cost line which is tangent to isoquant IQ500 curve at point E. At this point, the slope of the iso-cost line is equal to the isoquant curve. The slope of the isoquant curve represents MRTS of labour for capital. The slope of the iso-cost line represents the price ratio of the two factors.Slope of Iso-quant curve = Slope of Iso-cost curveIe. MRTSLk?= – ?L/?L = MPL/MPK?= PL/PK[where ?K → change in capital, ?L → change in labour, MPL → Marginal Physical Product of Labour, MPk – Marginal Physical Product of capital, PL?Price of Labour, and PK?→ Price of capital, MRTSLK?=Marginal Rate of Technical Substitution of labour and capital.]At equilibrium, the firm employs OM units of labour and ON units of capital. It obtains least cost combination of the two factors to produce 5 00 units of the commodity. The points such as H, K, R and S lie on higher iso-cost lines. They require a larger outlay, which is beyond the financial resources of the firm.The same can be explained with the help of a numerical example. Suppose the firm decides to produce 10 units of output. The two factors are labour and capital. The price of labour per hour is Rs. 10 and the price of machine use per hour is Rs. 10. The following table shows the various combinations of labour and machine capital hours required to produce 10 units of output.…………………. ................
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