# Laws of returns to scale using isoquants.

The laws of returns to scale refer to the long run analysis of production. In the long run all the factors become variable. So output can be expanded by changing all the factors simultaneously, so that the scale of production is changed.

The term returns to scale refers to the situation of increase in output by increasing all the factors by the same proportion. Firms can choose any scale of production. They can double or triple output or go out of business completely. Return to scale can be constant, increasing or decreasing in the long run.

Constant returns to scale. Technically, the term constant returns, means that the quantitative relationship between input and output stays constant or the same, when output is increased. If a firm doubles its inputs, it doubles output if it triples inputs, it triples output; and so forth.

Furthermore, if input prices are fixed, constant returns implies that the average cost of production does not change with scale: In terms of following diagram I, in constant returns to scale, the isoquants are equidistant along the product line OP, where product line is defined as a line showing movement from one isoquant to another resulting from the change in factor input combinations.

This case, by doubling the capital and labour inputs, the firm is able to double the output at level of 20 units. The distance between consecutive. multiple isoquants remains the same under constant returns to scale thereforeOa = *ab.*

Increasing returns to scale. Technically, the phrase increasing returns to scale refers to the relationship between inputs and outputs. When we say that a production function exhibits increasing’returns, we mean that given percentage increase in inputs leads to a larger percentage increase in the production of output.

For example, if a firm doubled or tripled inputs, it would More than double or triple output. When the prices of inputs do not change with output levels, then the increasing.

Returns to scale also means that as output rises, average cost of production falls. In terms of the following diagram 2, increasing’returns to scale implies that the distance between consecutive multiple isoquants decreases along the product line *i.e., C a < ab.*

**Decreasing returns to scale: **In this case, increase in output is less than the increase in inputs in proportionate terms. In terms of diagram, the distance between successive multiple isoquants increases along the product line **OP **as shown below :

###### = 20 units Q = 18 units

###### Q= 10 units.

**L**_{i} L_{2} **Diagram 3**

_{i}L

_{2}

At the initial combination (L_{1}, K_{1}) at point a on the product line OP, output is 10 units. When the factor inputs are doubled *i.e., (L _{2}* K

_{2}) at point

*c,*the output is less than doubled

*i.e.,*Q’ = 18 units. Whereas doubling the output (Q’ = 20 units) requires more then double of the inputs. So the distance between isoquants has increased,

*i.e., Oa < ab,*indicating decreasing return to stale.