# Law of Returns to Scale – Meaning, categories, graph and examples

## Law of Returns to Scale

The law of returns to scale explains the proportional change in output with respect to the proportional change in inputs.

In other words, the law of returns to scale states when there are a proportionate change in the amounts of inputs, the behavior of output also changes.

The degree of change in output varies with change in the number of inputs. For example, an output may change by a large proportion, same proportion, or a small proportion with respect to change in input.

Based on these possibilities, the law of returns to scale can be classified into three categories:

i. Increasing returns to scale

ii. Diminishing returns to scale

iii. Constant returns to scale

### Increasing Returns to Scale:

The first law is the law of returns to scale is increasing returns to the scale, which is referred to as when an organization is having a greater proportional change in the output than in input. If an organization has doubled the quantity of input, and the output is more than double, than this is called increasing returns to scale. Moreover, the average cost of production decreases with the increase in the scale of production. At this stage, an organization enjoys high economics of scale.

#### For example:

Example of the law of returns to scale in increasing returns to scale, Suppose a pencil manufacturer invests successive raw material of Rs. 1,000 each in the production of pens, and the results are as given in the schedule below:

As the manufacturer goes on, the table clarifies that enlarging his business by investing successive amounts of Rs. 1,000 each. The total output goes on increasing (column 2), the cost of production per pen goes on falling (column 3), and the marginal or additional output of each extra dose of Rs. 1,000 goes on increasing (column 4).

We can show the above result with the help of a diagram also. The diagram shows the decreasing cost, as shown in column (3). Along OX are measured the total quantity of pens manufactured and along OX, the production cost per pen. IR is the cost curve. It is clear that as the scale of production increases, the cost per unit falls.

### Diminishing Returns to Scale:

The second law of returns to scale is diminishing returns to scale; when the proportionate change in output is less than the proportionate change in input, it is called diminishing returns to scale. In this case, if the level of input is doubled, the output which is gained is less than doubled.

When the usages of all inputs increase by a factor of 2, new values for output will be:

• Twice the previous output if there are constant returns to scale (CRS)
• Less than twice the previous output if there are decreasing returns to scale (DRS)
• More than twice the previous output if there are increasing returns to scale (IRS)

Assuming that the factor costs are constant (that the firm is a perfect competitor in input markets) and the production function is homothetic. A firm experiencing constant returns will have constant long-run average costs; in case of decreasing returns will have increasing long-run average costs. And in increasing returns will have decreasing long-run average costs. However, this relationship breaks down if the firm does not face perfectly competitive factor markets (i.e., in this context, the price one pays for a good does depend on the amount purchased). For example, if there are increasing returns to scale in some range of output levels, the firm is so prominent in one or more input markets that increasing its purchases of an input drives up the input’s per-unit cost. The firm could have diseconomies of scale in that range of output levels. Conversely, if the firm can get bulk discounts of an input, it could have economies of scale in some output levels even if it decreases production returns in that output range.

### Constant Returns to Scale:

The third law of returns to scale is constant returns to scale. In constant to scale, the proportionate change in input is equal to the proportionate change in output. For instance, the quantity of input is doubled; in this case, output quantity is also doubled.

Returns to scale occur in the long run – when both labor and capital are variable.

#### Constant returns and economies of scale

If a firm has constant returns to scale – we are more likely to have minimal economies or diseconomies of scale.

However, even with constant returns to scale, a firm could still experience economies of scale (lower average costs with increased output). This is because:

• Bulk buying economies – buying a larger quantity of input may enable lower cost of average purchase (due to bulk buying economies)
• Marketing/financial economies.

Cardinal Utility-Measures and Law of Diminishing Marginal Utility