Production Analysis

PRODUCTION ANALYSIS

PRODUCTION ANALYSIS

The Production Process Production is a process in which economic resources or inputs (composed of natural resources like labour, land and capital equipment) are combined by entrepreneurs to create economic goods and services (outputs or products).

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PRODUCTION ANALYSIS

The Production Function 'A production function defines the relationship between inputs and the maximum amount that can be produced within a given period of time with a given level of technology'. Two special features of a production function are: a.

Labour and capital are both inevitable inputs to produce any quantity of a good, and

b.

Labour and capital are substitutes to each other in production.

PRODUCTION ANALYSIS

Short Run and Long Run Production Function

Labour(L)

Capital (K) 0

0 1 2 3 4 5 6 7 8 9 10

0 0 0 0 0 0 0 0 0 0 0

1

2

0 5 12 35 48 56 55 53 50 46 40

0 15 31 48 59 68 72 73 72 70 67

3 0 35 49 59 68 76 83 89 91 90 89

4 0 47 58 68 72 85 91 97 100 102 103

5 0 55 66 75 84 92 99 104 107 109 110

6 0 62 72 82 91 99 107 111 114 116 117

7 0 61 77 87 96 104 112 117 120 121 122

8

9

0 59 72 91 99 108 117 122 124 125 126

Long Run Production Function

Both labour and capital are varying.

0 56 74 89 102 111 120 125 127 128 129

10 0 52 71 87 101 113 122 127 129 130 131

PRODUCTION ANALYSIS

Capital is constant Labour (L)

0

1

2

3

4

5

6

7

8

9

10

Output (Q)

0

15

31

48

59

68

72

73

72

70

67

Short Run Production Function

PRODUCTION ANALYSIS

The Three Stages of Production Total Physical Product (Total Product)

Marginal Physical Product (Marginal Product)

Stage I Increases at an increasing Increases and reaches its rate maximum Stage II Increases at a diminishing Starts diminishing and rate and becomes maximum becomes equal to zero Stage III Reaches its maximum, Keeps on declining and becomes constant and then becomes negative starts declining

Average Physical Product (Average Product)

Increases (but slower than MPP) Starts diminishing

continues to diminish but must always be greater than zero

Production with one variable input/law of diminishing marginal returns

One input increasing with other input fixed, total output increases at an increasing rate, then increases at a decreasing rate, then reaches maximum and then falls and ultimately reaches zero. Thus short run production function shows the maximum output a firm can produce when only one input can be varied, other inputs remain fixed. Total product, average product, marginal product and their shapes. Three regions of production and the efficient zone of production.

Total PhysicalMarginal Physical Product Product

Stage I Increases at an Increases and increasing rate reaches its maximum

Fixed inputs grossly under utilised, specialisation and team work cause APP to increase when additional X is used

Specialisation and teamwork continue and result in greater output when additional X is used, fixed input is being properly utilised.

Fixed inputs capacity is reached, additional X causes output to fall

Stage II Increases at a diminishing rate and becomes maximum

Stage III Reaches its maximum, becomes constant and then starts declining

Average Physical Product

PRODUCTION ANALYSIS

Increases (but slower than MPP)

Starts Starts diminishing and diminishing becomes equal to zero

Keeps on declining and becomes negative

continues to diminish but must always be greater than zero

PRODUCTION ANALYSIS

The Production Function with Two Variable Inputs A firm may increase its output by using more of two variable inputs that are substitutes for each other, e.g., labour and capital. The technical possibilities of producing an output level by various combinations of the two factors can be graphically represented in terms of an isoquant (also called iso-product curve, equal-product curve or production indifference curve).

PRODUCTION ANALYSIS

Isoquants Isoquants are a geometric representation of the production function. The same level of output can be produced by various combinations of factor inputs. Assuming continuous variation in the possible combination of labour and capital, we can draw a curve by plotting all these alternative combinations for a given level of output. This curve which is the locus of all possible combination is called the 'isoquant'. Isoquant shows the different combinations of capital and labour which can be used by the producer for producing a certain level of output. Shape of an isoquant is as follows:

PRODUCTION ANALYSIS

Characteristics of Isoquants Isoquants show the following characteristics: a.

They slope downward to the right/ they are negatively sloped.

b.

It is convex to origin.

c.

It is smooth and continuous.

d.

Two isoquants do not intersect

e.

Isoquants further from origin shows higher level of output.

PRODUCTION ANALYSIS

Marginal Rate of Technical Substitution The marginal rate of technical substitution (MRTS) is numerically equal to the negative of the slope of an isoquant at any one point and is geometrically given by the slope of the tangent to the isoquant at that point. It is the amount of one input sacrificed for using an additional unit of the other input. MRTS (L,K): amount of capital sacrificed for an additional unit of labour employed. MRTS(L,K)=

K/ L

MRTS diminishes as one substitutes labour for capital

Isocost line It shows various combinations of two factors of production that a firm can employ, given the total cost and prices of inputs. C=wL+rK C: total cost (funds), w: price of labour (wage), L: amount of labour employed, r: price of capital (interest), K: amount of capital employed wL: labour cost, rK: capital cost Slope of isocost line: w/r (ratio of input prices) K

L

PRODUCTION ANALYSIS

Constrained Optimisation There are two alternative ways of determining optimal input combinations, the prices of which are given as (a) a problem of maximising output subject to cost constraint or (b) a problem of minimising cost subject to output constraint (i.e., minimising the total cost of producing a specified level of output).

PRODUCTION ANALYSIS

Producer’s equilibrium

Optimum Factor Combination (a) Maximisation of output subject to a given cost constraint

PRODUCTION ANALYSIS

Returns to Scale: if both the inputs change in same proportion ,in what Proportion the output changes.

Returns to scale are classified as follows: a. Increasing Returns to Scale (IRS): If output increase more than proportionate to the increase in all inputs. b. Constant Returns to Scale (CRS): If all inputs are increased by some proportion, output will also increase by the same proportion. c. Decreasing Returns to Scale (DRS): If increase in output is less than proportionate to the increase in all inputs.

PRODUCTION ANALYSIS

The Importance of Production Functions in Managerial Decision Making i.

Careful Planning Can Help a Firm to Use its Resources in a Rational Manner.

ii.

Managers must understand the marginal benefits and cost of each decision involving the allocation of scarce resources.

Expansion path Expansion path is the line formed by joining the tangency points between various isocosts and the corresponding highest attainable isoquants.