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# Production function in long run

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### Production function in long run

1. 1. Production Function In Long Run
2. 2. 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.
3. 3. The Production Function • A Production Function is a tool of analysis used to explain the inputoutput 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
4. 4. 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)
5. 5. 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.
6. 6. 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.
7. 7. Isoquant Schedule A schedule showing various combinations of two inputs (say labour and capital) at which a producer gets equal output is known as isoquant schedule. The table depicts that all combinations A,B,C,D and E of labour and capital give 2000 units of output to a producer. Hence, the producer remains neutral. Combination Labour (L) Capital (K) Output (Q,Units) A 1 15 2000 B 2 10 2000 C 3 6 2000 D 4 3 2000 E 5 1 2000
8. 8. Isoquant Curve Diagrammatic Presentation Y Capital A K2 B K1 0 L1 L2 Labour IP (2000 units) X
9. 9. 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.
10. 10. Marginal Rate of Technical Substitution (MRTS) The MRTSlk is the amount of capital forgone for employing an additional amount of labour. Hence, it is a rate of change in factor K in relation to one unit change in factor L. This rate of change is diminishing. So the slope of iso-product curve is diminishing. Slope = -dK/dL = change in capital/change in labour = MRTSlk Combination Labour (L) Capital (K) MRTSlk A 1 15 - B 2 10 5/1 C 3 6 4/1 D 4 3 3/1 E 5 1 2/1 (-dk/dl)
11. 11. Marginal rate of technical substitution (MRTS) K 7 ΔK=3 6 5 4 ΔL=1 ΔK=1 3 MRTS = ∆K ∆L ΔL=1 2 ΔK=1/3 1 0 0 1 2 3 4 5 6 ΔL=1 7 L
12. 12. Isoquant Curve Y E 5 4 Capital 3 A B C 2 D 1 1 2 3 Labour Q3 =90 Q2 =75 Q1 =55 4 5 X
13. 13. Iso-cost Curves An Iso-cost curve on the one hand shows the resources of producer and on the other hand it shows relative factor price ratio. It shows various combinations of two factors (say labour and capital) that can be employed by the producer in the given producer’s resources. Y K Slope = w/r Capital Cost Region 0 Labour L X Its slope is given by relative factor prices i.e. w/r where w is wage rate (price of labour) and r is rate of interest (price of capital). The area under an iso-cost line is known as cost region. In order to obtain least cost combination, cost region is super imposed over production region.
14. 14. Increasing returns to scale Total output may increase more than proportionately Constant returns to scale Total output may Increase proportionately Diminishing returns to scale Total output may increase Less than proportionately
15. 15. Increasing Returns to Scale When a certain proportionate change in both the inputs, K and L, leads to a more than proportionate change in output, it exhibits increasing returns to scale. For example, if quantities of both the inputs, K and L, are successively doubled and the corresponding output is more than doubled, the returns to scale is said to be increasing. Labour and Capital Output ScheduleProportional (TP) change in labour and capital Proportional change in output 1+1 10 - - 2+2 22 100 120 4+4 50 100 127.2 8+8 125 100 150
16. 16. Increasing Returns to ScaleDiagrammatic Presentation Y Scale Line A OP>PQ>QR>RS S R Capital Q IP4 (400) IP3 (300) IP2 (200) P IP1 (100) 0 X Labour
17. 17. Constant Returns to Scale When the change in output is proportional to the change in inputs, it exhibits constant returns to scale. For example, if quantities of both the inputs, K and L, are doubled and output is also doubled, then returns to scale are said to be constant. Schedule Labour and Capital Output (TP) Proportional change in labour and capital 1+1 10 - - 2+2 20 100 100 4+4 40 100 100 8+8 80 100 100 Proportional change in output
18. 18. Constant Returns to ScaleDiagrammatic Presentation Y Scale Line A OP=PQ=QR=RS S R Capital IP4 (400) Q IP3 (300) P IP2 (200) IP1 (100) 0 X Labour
19. 19. Diminishing Returns to Scale When a certain proportionate change in inputs, K and L, leads to a less than proportionate change in output. For example, when inputs are doubled and output is less than doubled, then decreasing returns to scale is in operation. Schedule Labour and Capital Output (TP) Proportional change in labour and capital Proportional change in output 1+1 10 - - 2+2 18 100 80 4+4 30 100 66.6 8+8 45 100 50
20. 20. Diminishing Returns to ScaleDiagrammatic Presentation Y OP<PQ<QR<RS S Scale Line A IP4 (400) R Capital IP3 (300) Q P IP2 (200) IP1 (100) 0 Labour X
21. 21. Thank you for your time and attention!