Production Function

Production Function

by

Balaji K

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Overview What is a Production Function Importance & Uses of Production Function Linear Homogeneous Production Function Cobb Douglas Production Function Isoquants and its assumptions Marginal rate of substitution Laws of Production

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Production Function

Input process output Q=fn(a,b,c and d) Q=Quantity /output and a,b,c and d are inputs

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Importance of Production Function

D

Helps to estimate the level of Production. It becomes Isoquants It helps in the input substitution process

without altering the total output Price determination and choosing the

least combination of inputs

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Uses of Production Function

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How to obtain Maximum output Helps the producers to determine

whether employing variable inputs /costs are profitable

Highly useful in longrun decisions Least cost combination of inputs and

to produce an output

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Table showing Production Function

D

1 2 3 4 5 6

6 688 892 1188 1764 1530 1668

5 276 898 234 556 1390 1188

4 226 334 556 688 1435 1345

3 278 688 335 225 667 556

2 556 1345 688 444 1123 456

1 342 876 765 334 234 688

Input of Labour

Input of capital

Output Q per unit of time

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Assumptions

The production function is related to particular period of time

There is no change in technology The producer is using the best technique Production can be fitted to both short run and the long

run

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Isoquants

The term isoquants is derived from the words ‘iso’ and ‘quant’.Iso means and quant means quantity

In other words Isoquants are the curves which represent the different combinations of inputs producing a particular quantity of output.

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Assumptions of Isoquants

There are only two factors of Production Viz Labour and Capital

Two factors can substitute each other upto a certain limit.

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Properties of Isoquants

Always slope downwards from left to right Apply MRTS Perfect Subsitutes Do not intersect each other Higher isoquants represents higher outputs

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Isoquants with an Illustration

Combinations Labour(Units) Capital(Units) Output(quintals)

A 1 10 50

B 2 7 50

C 3 4 50

D 4 2 50

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Graphical representation of Isoquants

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Producers Equilibrium

The producer is in equlibrium when he secures maximum output with the least cost combination of factors of production.

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Computation of least cost combination of two inputs

X1 X2 3X1 4X2 Cost (Rs)

10 45 30 180 210

20 28 60 112 172

30 16 90 64 154

40 12 120 48 168

50 8 150 32 182

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Thank You

Complements (-) vs Substitutes (+)

defined by sign of cross price elasticity