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Premium member Presentation Transcript Production Function : Tanu Kathuria 1 Production Function Slide 2: Tanu Kathuria 2 Production Function : Tanu Kathuria 3 Production Function Production Function : Tanu Kathuria 4 Production Function States the relationship between inputs and outputs Inputs – the factors of production classified as: Land – all natural resources of the earth – not just ‘terra firma’! Price paid to acquire land = Rent Labour – all physical and mental human effort involved in production Price paid to labour = Wages Capital – buildings, machinery and equipment not used for its own sake but for the contribution it makes to production Price paid for capital = Interest Production Function : Tanu Kathuria 5 Production Function Inputs Process Output Land Labour Capital Product or service generated – value added Production Function : Tanu Kathuria 6 Production Function Mathematical representation of the relationship: Q = f (K, L, La) Output (Q) is dependent upon the amount of capital (K), Land (L) and Labour (La) used Analysis of Production Function:Short Run : Tanu Kathuria 7 Analysis of Production Function:Short Run In the short run at least one factor fixed in supply but all other factors capable of being changed Reflects ways in which firms respond to changes in output (demand) Can increase or decrease output using more or less of some factors but some likely to be easier to change than others Increase in total capacity only possible in the long run Analysis of Production Function:Short Run : Tanu Kathuria 8 Analysis of Production Function:Short Run In times of rising sales (demand) firms can increase labour and capital but only up to a certain level – they will be limited by the amount of space. In this example, land is the fixed factor which cannot be altered in the short run. Slide 9: Tanu Kathuria 9 Analysis of Production Function:Short Run If demand slows down, the firm can reduce its variable factors – in this example it reduces its labour and capital but again, land is the factor which stays fixed. Slide 10: Tanu Kathuria 10 Analysis of Production Function:Short Run If demand slows down, the firm can reduce its variable factors – in this example, it reduces its labour and capital but again, land is the factor which stays fixed. Short-Run Changes in ProductionFactor Productivity : Tanu Kathuria 11 Short-Run Changes in ProductionFactor Productivity How much does the quantity of Q change, when the quantity of L is increased? The Marginal Product of Labour : Tanu Kathuria 12 The Marginal Product of Labour The marginal product of labour is the increase in output obtained by adding 1 unit of labor but holding constant the inputs of all other factors Marginal Product of L: MPL= Q/L (holding K constant) = Q/L Average Product of L: APL= Q/L (holding K constant) Relationship Between Total, Average, and Marginal Product: Short-Run Analysis : Tanu Kathuria 13 Relationship Between Total, Average, and Marginal Product: Short-Run Analysis Total Product (TP) = total quantity of output Average Product (AP) = total product per total input Marginal Product (MP) = change in quantity when one additional unit of input used Short-Run Analysis of Total,Average, and Marginal Product : Tanu Kathuria 14 Short-Run Analysis of Total,Average, and Marginal Product If MP > AP then AP is rising If MP < AP then AP is falling MP = AP when AP is maximized TP maximized when MP = 0 Three Stages of Production in Short Run : Tanu Kathuria 15 Three Stages of Production in Short Run AP,MP X Stage I Stage II Stage III APX MPX Fixed input grossly underutilized; specialization and teamwork cause AP to increase when additional X is used Specialization and teamwork continue to result in greater output when additional X is used; fixed input being properly utilized Fixed input capacity is reached; additional X causes output to fall Law of Diminishing Returns(Diminishing Marginal Product) : Tanu Kathuria 16 Law of Diminishing Returns(Diminishing Marginal Product) Holding all factors constant except one, the law of diminishing returns says that: As additional units of a variable input are combined with a fixed input, at some point the additional output (i.e., marginal product) starts to diminish e.g. trying to increase labor input without also increasing capital will bring diminishing returns Nothing says when diminishing returns will start to take effect, only that it will happen at some point All inputs added to the production process are exactly the same in individual productivity Analysing the Production Function: Long Run : Tanu Kathuria 17 Analysing the Production Function: Long Run The long run is defined as the period of time taken to vary all factors of production By doing this, the firm is able to increase its total capacity – not just short term capacity Associated with a change in the scale of production The period of time varies according to the firm and the industry In electricity supply, the time taken to build new capacity could be many years; for a market stall holder, the ‘long run’ could be as little as a few weeks or months! Slide 18: Tanu Kathuria 18 Analysis of Production Function:Long Run In the long run, the firm can change all its factors of production thus increasing its total capacity. In this example it has doubled its capacity. Long-Run Changes in ProductionReturns to Scale : Tanu Kathuria 19 Long-Run Changes in ProductionReturns to Scale How much does the quantity of Q change, when the quantity of both L and K is increased? Optimal Combination of Inputs : Tanu Kathuria 20 Optimal Combination of Inputs Now we are ready to answer the question stated earlier, namely, how to determine the optimal combination of inputs As was said this optimal combination depends on the relative prices of inputs and on the degree to which they can be substituted for one another This relationship can be stated as follows: MPL/MPK = PL/PK (or MPL/PL= MPK/PK) An Isoquant : Tanu Kathuria 21 An Isoquant Law of Diminishing Marginal Rate of Technical Substitution: : Tanu Kathuria 22 Law of Diminishing Marginal Rate of Technical Substitution: Law of Diminishing Marginal Rate of Technical Substitution continued : Tanu Kathuria 23 Law of Diminishing Marginal Rate of Technical Substitution continued X = 2 Y = -1 X = 1 Y = -1 X = 1 Y =- 2 A B C D E Isocost Curves : Tanu Kathuria 24 Isocost Curves Assume PL =$100 and PK =$200 Isocost Curve and Optimal Combination of L and K : Tanu Kathuria 25 Isocost Curve and Optimal Combination of L and K Isocost and isoquant curve for inputs L and K 5 10 L K “Q52” 100L + 200K = 1000 Slide 26: Tanu Kathuria 26 Units of capital (K) O Units of labor (L) 100 200 300 Expansion path TC = £20 000 TC = £40 000 TC = £60 000 The long-run situation: both factors variable Expansion Path: the locus of points which presents the optimal input combinations for different isocost curves Returns to Scale : Tanu Kathuria 27 Returns to Scale Let us now consider the effect of proportional increase in all inputs on the level of output produced To explain how much the output will increase we will use the concept of returns to scale Returns to Scale continued : Tanu Kathuria 28 Returns to Scale continued If all inputs into the production process are doubled, three things can happen: output can more than double increasing returns to scale (IRTS) output can exactly double constant returns to scale (CRTS) output can less than double decreasing returns to scale (DRTS) Slide 29: Tanu Kathuria 29 Graphically, the returns to scale concept can be illustrated using the following graphs You do not have the permission to view this presentation. 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