Production FunctionIn Long RunPresented By:TryambakAnkit Gupta
Concept of Production• In General Terms– Production means transforming inputs (labour, machines, raw materials, time, etc.) into an output. This concept of production is however limited to only ‘manufacturing’.• In Managerial Terms – Creation of utility in a commodity is production.• In Economical Terms – Production means a process by which resources (men, material, time, etc.) are transformed into a different and more useful commodity or service.Where;Input – It is a good or service that goes into the process of production.Output – It is any good or service that comes out production process.
The Production Function• A Production Function is a tool of analysis used to explain the input- output relationship. It expresses physical relationship between production inputs and the resultant output. It tells us that how much maximum output can be obtained in the specified set of inputs and in the given state of technology.• Mathematically, the production function can be expressed as Q=f(K, L)• Q is the level of output• K = units of capital• L = units of labour• f( ) represents the production technology
The Production Function(cont’d…)• When discussing production function, it is important to distinguish between two time frames.• The short-run production function which may also be termed as ‘single variable production function’ describes the maximum quantity of good or service that can be produced by a set of inputs, assuming that at least one of the inputs is fixed at some level which means that the production can be increased by increasing the variable inputs only. It can be expressed as; Q = f(L)• The long-run production function which may also be termed as ‘returns to scale’ describes the maximum quantity of good or service that can be produced by a set of inputs, assuming that the firm is free to adjust the level of all inputs. It can be expressed as; Q = f(K, L)
Production Function in the Long Run• Long run production function shows relationship between inputs and outputs under the condition that both the inputs, capital and labour, are variable factors.• In the long run, supply of both the inputs is supposed to be elastic and firms can hire larger quantities of both labour and capital. With large employment of capital and labour, the scale of production increases.
Isoquant Curve• The term ‘isoquant’ has been derived from the Greek word iso meaning ‘equal’ and Latin word quantus meaning ‘quantity’. The ‘isoquant curve’ is, therefore, also known as ‘Equal Product Curve’.• An isoquant curve is locus of points representing various combinations of two inputs - capital and labour - yielding the same output ,i.e., the factors combinations are so formed that the substitution of one factor for the other leaves the output unaffected.• It is drawn on the basis of the assumption that there are only two inputs, i.e., labour(L) and capital(K), to produce a commodity X.
Isoquant ScheduleA schedule showing various combinations of two inputs (saylabour and capital) at which a producer gets equal output isknown as isoquant schedule. The table depicts that allcombinations A,B,C,D and E of labour and capital give 2000units of output to a producer. Hence, the producer remainsneutral. Labour Capital Output Combination (L) (K) (Q,Units) A 1 15 2000 B 2 10 2000 C 3 6 2000 D 4 3 2000 E 5 1 2000
Isoquant Curve - Diagrammatic Presentation YCapital A K2 B K1 IP (2000 units) X 0 L1 L2 Labour
Characteristics of Isoquant Curve• They slope downward to the right : They slope downward to the right because if one of the inputs is reduced, the other input has to be so increased that the total output remains unaffected.• They are convex to the origin : They are convex to the origin because of Marginal Rate of Technical Substitution of labour for capital. (MRTSLK) is diminishing. MRTSLK is the slope of an isoquant curve. Isoquant curves are negatively sloped.• Two isoquant curves do not intersect each other : Two isoquant curves do not intersect each other as it is against the fundamental condition that a producer gets equal output along an isoquant curve.• Higher the isoquant curve higher the output : A producer gets equal output along an isoquant curve but he does not get equal output among the isoquant curves. A higher isoquant curve yields higher level of output.
Marginal Rate of TechnicalSubstitution (MRTS)The MRTSlk is the amount of capital forgone for employing anadditional amount of labour. Hence, it is a rate of change in factor K inrelation to one unit change in factor L. This rate of change isdiminishing. So the slope of iso-product curve is diminishing.Slope = -dK/dL = change in capital/change in labour = MRTSlk Combination Labour Capital MRTSlk (L) (K) (-dk/dl) A 1 15 - B 2 10 5/1 C 3 6 4/1 D 4 3 3/1 E 5 1 2/1
Isoquant Curve Y 5 E 4 Capital 3 A B C 2 Q3 =90 D Q2 =75 1 Q1 =55 1 2 3 4 5 X Labour
Iso-cost CurvesAn Iso-cost curve on the one hand shows the resources of producer and onthe other hand it shows relative factor price ratio. It shows variouscombinations of two factors (say labour and capital) that can be employed bythe producer in the given producer’s resources. Y K Slope = w/r Capital Cost Region X 0 Labour LIts slope is given by relative factor prices i.e. w/r where w is wage rate (priceof labour) and r is rate of interest (price of capital). The area under an iso-costline is known as cost region. In order to obtain least cost combination, costregion is super imposed over production region.
Increasing Constant Diminishing returns to scale returns to scale returns to scaleTotal output may increase Total output may Total output may increasemore than proportionately Increase proportionately Less than proportionately
Increasing Returns to ScaleWhen a certain proportionate change in both the inputs, K and L, leadsto a more than proportionate change in output, it exhibits increasingreturns to scale. For example, if quantities of both the inputs, K and L,are successively doubled and the corresponding output is more thandoubled, the returns to scale is said to be increasing. Schedule Labour and Output Proportional Proportional Capital (TP) change in change in labour and output capital 1+1 10 - - 2+2 22 100 120 4+4 50 100 127.2 8+8 125 100 150
Increasing Returns to Scale-Diagrammatic Presentation Y Scale Line A OP>PQ>QR>RS S R IP4 (400) Capital Q IP3 (300) P IP2 (200) IP1 (100) 0 X Labour
Constant Returns to ScaleWhen the change in output is proportional to the change in inputs, itexhibits constant returns to scale. For example, if quantities of both theinputs, K and L, are doubled and output is also doubled, then returns toscale are said to be constant. Schedule Proportional Proportional Labour and Output change in change in Capital (TP) labour and output capital 1+1 10 - - 2+2 20 100 100 4+4 40 100 100 8+8 80 100 100
Constant Returns to Scale-Diagrammatic Presentation Y Scale Line A OP=PQ=QR=RS S R IP4 (400) Capital Q IP3 (300) P IP2 (200) IP1 (100) 0 X Labour
Diminishing Returns to ScaleWhen a certain proportionate change in inputs, K and L, leads to a lessthan proportionate change in output. For example, when inputs aredoubled and output is less than doubled, then decreasing returns toscale is in operation. Schedule Labour and Output Proportional Proportional Capital (TP) change in change in labour and output capital 1+1 10 - - 2+2 18 100 80 4+4 30 100 66.6 8+8 45 100 50
Diminishing Returns to Scale-Diagrammatic Presentation Y Scale Line OP<PQ<QR<RS A S IP4 (400) R Capital IP3 (300) Q P IP2 (200) IP1 (100) X 0 Labour