EE&FA - ISOCOST - FINAL YEAR CS/IT - SRI SAIRAM INSTITUTE OF TECHNOLOGY - DR.K.BARANIDHARAN

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Engineering Economics & Financial Accounting ment E e & f a 2 18 August 2013

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INDEX Isocosts Least-cost Combination Of Inputs Cobb-Douglas production function Law of Return to Scale

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ISOCOSTS Isocosts refer to the cost curve that represents the combination of inputs that will cost a producer the same amount of money. Isocosts denotes IQ 2a particular level of total cost for a given level of production. The level of production changes, the total cost changes and, thus the isocosts curve moves upwards 4

Dr.K.Baranidharan:

The total cost as represented by each cost curve, is calculated by multiplying the quantity of each input factor with its respective price. The three download sloping straight line cost curves (assuming that the input prices are fixed, no quantity discount are available) each costing Rs.1.0 lakh, Rs.1.5 lakh and Rs.2.0 lakh for the output leavels of 20,000-30,000 and 40,000 units. capital Labour IC=1.0 IC=1.5 IC=2.0 5

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Least-Cost Combination A manufacturer has to “ produce at a lower cost to attain a higher profit” Isocosts and isoquants can be used to determine the input usage that minimizes the cost of production 6

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The slope of an isoquant is equal to that of an isocost is the place of the point of cost of production. This can observed by superimposing the isocosts on isoproduct curve 7

ISOCOSTS:

It is possible because the axes in both maps represent the same input variable The points of tangency A, B and C on each of the isoquant curves represent the least cost combination of inputs, yielding the maximum level of output. Any output lower or higher than this will result in a higher cost of production. Units of Capital (K) x y Units of labour (L) A B C Scale line 8

The total cost as represented by each cost curve, is calculated by multiplying the quantity of each input factor with its respective price.:

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Least-Cost Combination:

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Engineering Economics & Financial Accounting ment E e & f a 12 18 August 2013

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RETURNS TO SCALE Return to scale refer to the return enjoyed by a firm as a result of change in all inputs. It explains the behavior of the returns when inputs are changed simultaneously. 13

Dr.K.Baranidharan:

Returns to Scale Returns to scale is the rate at which output increases in response to proportional increases in all inputs. In the eighteenth century Adam Smith became aware of this concept when he studied the production of pins. 14

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Returns to Scale Adam Smith identified two forces that come into play when all inputs are increased. A doubling of inputs permits a greater “division of labor” allowing persons to specialize in the production of specific pin parts. This specialization may increase efficiency enough to more than double output. 15

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Constant Returns to Scale A production function is said to exhibit constant returns to scale if a doubling of all inputs results in a precise doubling of output. This situation is shown in Panel . 16

RETURNS TO SCALE:

Capital per week 4 A 3 2 1 Labor per week 1 2 3 (a) Constant Returns to Scale 4 0 FIGURE 5.3: Isoquant Maps showing Constant, Decreasing, and Increasing Returns to Scale q = 10 q = 20 q = 30 q = 40 17

Returns to Scale:

Decreasing Returns to Scale If doubling all inputs yields less than a doubling of output, the production function is said to exhibit decreasing returns to scale. This is shown in Panel 18

Returns to Scale:

Capital per week 4 A 3 2 1 Labor per week 1 2 3 (a) Constant Returns to Scale 4 0 Capital per week 4 A 3 2 1 Labor per week 1 2 3 (b) Decreasing Returns to Scale 4 0 FIGURE 5.3: Isoquant Maps showing Constant, Decreasing, and Increasing Returns to Scale q = 10 q = 10 q = 20 q = 20 q = 30 q = 30 q = 40 19

Constant Returns to Scale:

Increasing Returns to Scale If doubling all inputs results in more than a doubling of output, the production function exhibits increasing returns to scale. This is demonstrated in Panel In the real world, more complicated possibilities may exist such as a production function that changes from increasing to constant to decreasing returns to scale. 20

FIGURE 5.3: Isoquant Maps showing Constant, Decreasing, and Increasing Returns to Scale:

Capital per week 4 A q = 10 3 2 1 Labor per week 1 2 3 (a) Constant Returns to Scale 4 0 Capital per week 4 A 3 2 1 Labor per week 1 2 3 (c) Increasing Returns to Scale 4 0 Capital per week 4 A 3 2 1 Labor per week 1 2 3 (b) Decreasing Returns to Scale 4 0 FIGURE 5.3: Isoquant Maps showing Constant, Decreasing, and Increasing Returns to Scale q = 10 q = 10 q = 20 q = 20 q = 20 q = 30 q = 30 q = 30 q = 40 q = 40 21

Decreasing Returns to Scale:

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