Lecture 15

LESSON-15 PRODUCTION PROCESS Learning outcomes After studying this unit, you should be able to: Develop a theoretical base for analyzing empirical situation define the concept and techniques relevant for production decision analysis distinguish between demand analysis and production analysis

OPTIMAL INPUT CHOICE: LEAST COST COMBINATION OF INPUTS As already discussed, the production function indicates the alternative combinations of various factors of production which can produce a given level of output. While all these combinations are technically efficient, the final decision to employ a particular input combination is purely an economic decision and rests on cost. An entrepreneur should choose that combination which costs him the least. To aid our thinking in thrs regard. economists have developed the concept of isocost (equal cost) line, which shows all combinations of inputs (a & b) that can be employed for a given cost (in rupees). In order to determine the least cost combination for a given output, we need to have the prices of factors of production. Let us consider, a production function for plastic buckets where the entrepreneur wants to produce 20 buckets. Let the price of L (P1) be Rs. 10 per unit and the price of capital (PK) be Rs. 5 per unit. It is assumed that unlimited amounts of labour and capital can be bought at given prices. We can now find the total cost of each of the five possible combinations of labour and capital for Q = 20.

Alternative Combination 1

Inputs in Physical Units Labour 4

Capital 17

Cost ( Rs. )

4 x 10 +17 / 5 = 125 2 5 12 5x10 + 12 / 5 = 110 3 6 8 6 x 10 + 8/ 5 =100 4 7 5 7 x 10 + 5 / 5 = 95 5 8 4 8 x 10 + 5 /4 = 100 Combination 4 represents the least cost for producing 20 plastic buckets.

Another way to determine the least cost combination is geometrical in nature which uses the isocost and isoquant curves. The isocost line can be defined in the following manner : C =PL . L + PK . K , where C= C0 Where C0 is the firms total cost of inputs for some specified time period, PL and PK are the prices of input L and Input K, respectively and L & K represents the physical quantities of two inputs. In other words, the isocost equation above states that when the firm’s total cost is Co, the price of input L times the amount of input L used plus the price of input K times the amount of input K used must equal Co. In FigureVI, we have drawn isocost lines for Co = 125, C1 = 110, C2 100, C3 = 95 and C4 = 100, where PL = 10 and Pl' = 5. Note that these five isocost lines are parallel. ' They must be parallel because the slope of each line is - -PL /PK or -10/5 = -2 Note that the slope of an isocost line must be equal to PL , since that represents the rate at which input Lean be substituted by input K while maintaining the same K Level of output. In our example, p.. = 10 and Pl' = 5, then we can substitute 1 unit of labour for every 2 unit of capital while maintaining the same cost level. Thus. ∆K /∆L = - ( PL/ Pk ) = -10/5 = -2 . We should remember that the marginal rate of substitution - which is the slope of an iso quant between two points, is also equal to the ratio of marginal products of the two inputs ( MPL / MPK ) We know that MPL = ( ∆Q / ∆L ) Along an isoquant the increase in output resulting from an additional unit of L must be exactly offset by the decrease in output from a reduction in input K. or ∆Q = 0 = MPL (∆ L) + MPK(∆ K). Thus, MPL (∆L) = - MPK (∆ K), or MPL -∆K ------- = -------- , Q constant. MPK ∆L

With this relationship clear in mind, we superimpose the isoquant map on the isocost map ill order to determine the least cost input combination 0'( the maximum output for a given cost. It can be seen from the figure that the maximum out put can be obtained with an outlay of Rs. 100 is 20 buckets where the isocost C = 100 is tanget to the isoquant Q = 20 . This is the least cost of producing 20 buckets and the least cost combination of inputs in the case is 5 units of labour and 5 units of capital. Any other combination on the isoquant Q = 20 well have a cost higher than 100. Drawing The least cost combination for different levels of output ie. Q = 15, (Q = 25) can be found in the same way. The line ABC in Figure VIII thus represents the least cost combination of inputs for different levels of output. This line is called the firm's expansion path or the scale line. Alternatively, you may frame and solve your optimization problem ( or input choice ) through the standard calculus technique anf Lagrangian multiplier. 8.8

ECONOMIC REGION OF PRODUCTION

In the long-run, a firm should use only those combinations of inputs which are economically efficient. A factor should not be used beyond a point, even if it is available free of cost, as it will result in negative marginal product for that factor. These input combinations are represented by the position of an isoquant curve which has a positive slope. RETURNS TO SCALE

The law of diminishing returns states that as more and more of the variable input is added to the fixed factor base, the increment to total output after some point will decline progressively with each additional unit of the variable factor. The law of diminishing returns is also broadly referred to as the 'law of variable proportions' which implies that as additional units of a variable factor are added to a given quantity of all other factors, the increment to output attributable to each of the additional units of the variable factor will increase at first, decrease later, and eventually become negative. The law of diminishing returns is strictly a shortrun phenomenon. Let us now look at what happens :f we change all inputs simultaneously which is possible only in the long-run_ What happens to the output level as all factor inputs are increased proportionately? This can be understood with the help of the concept known as returns to scale. Under this concept, the behavior of output is studied when all factors of production are changed in the same direction and in the same proportion. Returns to scale are categorized as follows: a) Increasing returns to scale: If output increases more than proportionate to the increase in all inputs. b) Constant return to scale: If a!! inputs are increased by some proportion, output will also increase by the same proportion. . . c) Decreasing returns to scale: If increase in output is less than proportionate to the increase ill all inputs. For example, if all factors of production are doubled and output increases by more than two times, we have a situation of increasing returns to scale. On the other hand, if output does not double even after a 100 per cent increase in input factors. we have - diminishing returns to scale. 8.10 FORMS OF PRODUCTION FUNCTION There are five different forms of production function. Understanding the form is important in the context of interpreting statistically' estimated production function i.e. empirical situation. However, it may be worthwhile to make a passing reference to the conceptual basis of different types of production function a) Cobb-Douglas type It is a linearly homogeneous production function of degree one i.e'- subject to constant returns to scale Q = Q ( K, L ) = AL a K 1- a where A and a are constants : 1> a > 0 You may note that [ (a) + ‘(1-a ) = 1 ]

This means if factor K and L are increased by y proportion, the input Q will also increase by the same proportion. This means constant returns to scale.

Slide 1

___________________________________ Isoquants Meaning: Isoquants are a geometric representation of the production function.

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Slide 2 Factor inputs of isoquant analysis Isoquant analysis takes into account only two factors of inputs: Increasing returns to scale Constant returns to scale

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Slide 3

Marginal rate of technical substitution it is defined as the rate at which two factors are substituted for each other.

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Slide 4

___________________________________ Input output relations Two types of input output relations: Law of variable proportion Returns to scale

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Slide 5 Returns to scale In this case the quantities of some units are fixed while quantities of other inputs are variable in the short Returns run. to scale

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Slide 6 Law of variable proportion In it all the inputs are variable. It is used in the long run of the firm.

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Slide 7

___________________________________ Economies of scale Meaning: It means reduction in per unit cost of production or benefits derived by expanding the scale of business.

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