THEORY OF PRODUCTION(continued…..)

Long Run Production Function/Returns To Scale

Sonu Chowdhury

Meaning of Returns To Scale

When all inputs are changed in the same proportion, we call this as a change in scale of production.

The way total output changes due to change in the scale of production is known as returns to scale. 

What is studied under laws of Returns to Scale?

The technological relationship between changing scale of inputs and output is explained under the laws of returns to

scale.

How Returns to Scale are Measured?

Returns to Scale are measured by comparing percentage change in

output with the percentage change in all input.

The laws of returns to scale can be explained through the

1. ISO-QUANT CURVE2. PRODUCTION FUNCTION

1.ISO-QUANT CURVE

ISOQUANT CURVE (Equal Product Map)

Derived from greek word “iso” means equal and Latin word “Quantus” meaning quantity.

An isoquant is a curve representing the various combinations of two inputs that produce same amount of output.

It is always possible to produce a given quantity of a commodity X with various combinations of labour & capital.

Assumption:-There are only two inputs i.e labour (L) & capital (K) to produce a commodity X.

The two inputs L &K can substitute each other but at a diminishing rate.

The technology of production is given.

In the schedule below, there are five possible combinations. All the five combinations yield the

same level of output i.e. 1000 units.

Combination Units of Labour Units of Capital Total Output

A 20 1 1000

B 15 2 1000

C 11 3 1000

D 8 4 1000

E 6 5 1000

Equal product combinations

PROPERTIES OF ISOQUANT CURVE

Isoquants have a negative slope. They cannot intersect each other. Upper isoquants represent higher level of

output. They are convex to the origin:- because of

diminishing marginal rate of technical substitution

In the diagram units of capital are measured on horizontal axis and units of labour on vertical axis. The five combinations are known as A, B, C, D and E. After joining these points, we get the iso product curve IQ. If quantity of labour is reduced, the quantity of capital must be increased toproduce the same output.

2.PRODUCTION FUNCTION

PRODUCTION FUNCTION

Qx = f(K,L)

1.Increasing Returns to Scale.

zQx = f(yK,yL)

2.Constant Returns to Scale.

zQx = f(yK,yL) *when y = z*

3.Diminishing Returns to Scale.

zQx = f(yK,yL) *when y = z*

*when z> y*

*when y = z*

*when z< y*

LAW OF RETURNS TO SCALE

“ The percentage increase in output when all inputs vary in the same proportion is known as returns to

scale.”

When returns to scale occurs, three alternative situations are possible.

1.Increasing Return to Scale:-total output may increase more than proportionately

2.Constant return to Scale:- total output may increase proportionately

3.Decreasing Return to Scale:- total output may increase less than proportionately

Increasing Return to ScaleOutput increases

by a greater proportion

than the increase in inputs. 100q

300q

k

0 6

3

6

3 l

For e.g. a 100 % increase in all inputs causes a 200% increase in output.

Inputs (units) Outputs (units)3 capital + 3 Labour 1006 Capital + 6 Labour 300

Constant return to Scale

Output increases in the

same proportion

as the increase in inputs.

100 q

200 q

0 3 6

3

6

l

k

Inputs (units) Outputs (units)3 capital + 3 Labour 1006 Capital + 6 Labour 200

For e.g. a 100 % increase in all inputs causes a 100% increase in output.

Decreasing Return to ScaleOutput increases in

lesser proportion than

increase in input.

3

l

k

0

3

6

6

100q

150qInputs (units) Outputs (units)3 capital + 3 Labour 1006 Capital + 6 Labour 150

For e.g. a 100 % increase in all inputs causes a 50% increase in output.

End of the topic