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# Production theory

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### Production theory

1. 1. Chapter 6 Production Theory
2. 2. Chapter Objectives  To examine the economic analysis of a firm’s technology,     different types of inputs and the process of production. To help develop an understanding of the distinction between short run and long run production functions. To build up a critical appraisal of the law of variable proportions and returns to scale. To introduce the concepts of isoquant, isocost line, marginal rate of technical substitution, elasticity of substitution and expansion path. To develop an understanding of technical progress and its nuances.
3. 3. Production  Production of goods All tangible items such as furniture, house, machine, food, car, etc  Production of services  All intangible items like banking, education, management, consultancy, transportation  Process of transformation of resources (like land, labour, capital and entrepreneurship) into goods and services of utility to consumers &/or producers  Process of creation of value or wealth through the production of goods and services that have economic value to either consumers or other producers  by change in form (input to output, say steel into car), or  by change in place (supply chain, say from factory to dealers/retailer), or  by changing hands (exchange, say from retailer to consumer) 
4. 4. Types of Inputs Technology  Determines  type, quantity and proportion of inputs  the maximum limit of total output from a given combination of inputs.  at any point of time, technology will be given Fixed and Variable Inputs:  2 distinct time frames:  Short run: refers to a period of time when the firm cannot vary some of its inputs  Long run: refers to a time period sufficient to vary all of its inputs, including technology  Variable input : made to vary in the short run, e.g. raw material, unskilled/semi skilled labour, etc.  Fixed input: cannot be varied in the short run, e.g. land, machine, technology, skill set, etc.
5. 5. Factors of Production 5 factors of production Land: anything which is gift of nature and not the result of human effort Labour: physical or mental effort of human being that undertakes the production process. Capital: wealth which is used for further production Not a gift of nature, but is produced by human beings. Output of one production process that generally goes as input in another Enterprise: ability and action to collect, coordinate, and utilize all the factors of production for the purpose of economic gains Also defined as the ability to take risk Organization: acknowledges a special kind of function Combination of highly skilled labour and specialized human capital Organizational efficiency that differentiates one company from another in terms of success
6. 6. Production Function  Technological relationship between physical inputs and physical     outputs over a given period of time Shows the maximum quantity of the commodity that can be produced per unit of time for each set of alternative inputs, and with a given level of production technology Always related to:  a given time period  a certain level of technology Depends upon relation between inputs Normally a production function is written as: Q = f (L,K,I,R,E) (Q is the maximum quantity of output of a good being produced, and L=labour; K=capital; l=land; R=raw material; E= efficiency parameter)
7. 7. Production Function with One Variable Input  Also termed as variable proportion production function  Short term production function in which production is planned with one variable input (say L)  Shows the maximum output a firm can produce when only one of its inputs can be varied, other inputs remaining fixed Q = f ( L, K ) where Q = output, L = labour and K = fixed amount of capital  Total product is a function of labour TPL = f ( K ,L)  Average Product (AP) is total product per unit of variable input : TP AP = L L  Marginal Product (MP) is addition in total output per unit change in variable input MPL = ∆TP ∆L
8. 8. Law of Variable Proportions Total Product (’000 tonnes) MP AP 1 20 - 2 50 30 25 3 90 40 30 4 120 30 30 5 140 20 28 6 150 10 25 7 150 0 21.5 8 130 -20 16.25 9 100 -30 Stages 11.1 200 20 Increasing returns 150 Total Product (’000 tonnes) 100 Diminishing returns Output Labour (’00 units) Marginal Product 50 Average Product 0 1 2 3 4 5 6 7 8 9 -50 Labour Negative returns As the quantity of the variable factor is increased with other fixed factors, the MP and AP of the variable factor will eventually decline.
9. 9. Law of Variable Proportions Total Output C TPL B Panel a A Total Output O Labour Stage I A* Panel b O Stage II Stage III B* C* MPL APL Labour Increasing Returns to Variable Factor Very first stage MP>0 and MP>AP Diminishing Returns to Variable Factor 2nd stage MP>0 and MP<AP Negative Returns Technically inefficient stage of production A rational firm will never operate in this stage MP<0 while AP is falling but positive
10. 10. Production Function with 2 Variable Inputs  In the long run, all the inputs are variable  Firm has the opportunity to select that combination of inputs which maximizes returns  Isoquant  Locus of all technically efficient combinations (or all possible factors of production) for producing a given level of output  Also referred to as iso-product curves  Taking the production function and fixing level of output Q at some given quantity, we have an implicit relationship between units of labour (L) and capital (K) Q = f ( L, K )
11. 11. Isoquants Labour (’00 units) 40 6 28 7 18 8 12 9 8 10 Capital (Rs. Crore) Capital (Rs. crore) 45 40 35 30 25 20 15 10 5 0 6 7 8 9 10 Labour ('00 units) An isoquant is the locus of all technically efficient combinations for producing a given level of output. Characteristics: i. Downward sloping ii. A higher isoquant represents a higher output iii. Isoquants do not intersect iv. Convex to the origin
12. 12. Marginal Rate of Technical Substitution  MRTS measures the reduction in one input due to unit increase in the other input that is just sufficient to maintain the same level of output. ∆ K MRTS LK = − ∆ L  MRTS of labour for capital is equal to the slope of the isoquant  Also equal to the ratio of the marginal product of one input to the marginal product of other input ∆Q = MPL × ∆L + MPK × ∆K 0 = MPL × ∆ L + MPK × ∆ K MRTS LK MPL = − ∆ K = MPK ∆L
13. 13. Special Shapes of Isoquants Capital Capital Q3 Q2 Q1 O Q1 Q2 Q3 Labour Linear isoquants Q = f ( L, K ) = aK + bL Isoquants are downward sloping straight lines, indicating a constant MRTS O Labour Right angled isoquants Q =min( L , K ) α β Leontief production technology, capital is a perfect complement for labour, non existence of any substitutability between the two factors
14. 14. Isocost Lines Capital A2 Panel a With wage (w) and interest (r), the total cost incurred by the firm: Labour cost (wL) + Capital cost (rK) A A1 O B1 B B2 Labou r C = wL + rK The isocost line represents the locus of points of all the different combinations of two inputs that a firm can procure, given the total cost and prices of the inputs. The (absolute) slope of this line is equal to the ratio of the input prices. C ∆K w Slope = − = r = ∆L C r w
15. 15. Producer’s Equilibrium Capital Capital Panel a A2 A A C E K D Q0 L* R A1 E K* O Panel b B Q2 Q1 Q3 S O Labour Maximization of output subject to a cost constraint L B1 B Q B2 Labour Minimization cost for a given level of output Necessary condition for equilibrium: Slope of isoquant = Slope of isocost line