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# Returns to Scale

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Factors of production and output have a fascinating relationship. What do you expect to happen if you increase the scale of all factors of production? What do you think will happen if the opposite is true? The relationship may not be as simple as you think. This article uses an interesting concept called 'returns to scale'.

## Returns to Scale

Returns to scale in microeconomics describe a production situation that occurs in the long run when the scale of production increases when all inputs used are variable, which affects the output level. A proportionate change in output results from a proportionate change in input. Returns to scale explain what happens to total output when all production inputs increase, assuming that technology is constant and the market is perfectly competitive.

Returns to scale is a term in economics that refers to a rate at which a change in output leads to a change in input. It is a long-run theory of production.

In the short run, the firm cannot build a new factory to increase its returns to scale because it takes time and money to build one. It can, however, hire additional workers to increase its short-run returns, but only up to a certain point due to the law of diminishing marginal returns. However after the factory is built, the firm can hire more workers. These changes in the firm's inputs (labour, land, etc.) can help increase the firm's output, known as returns to scale.

## Types of Returns to Scale

An increase in a firm's input can lead to various changes in output. These changes are called types of returns to scale. There are three types of returns to scale:

1. Increasing returns to scale

2. Constant returns to scale

3. Diminishing returns to scale

### Increasing Returns to Scale

Increasing returns to scale are the rate at which output increases when the factors of production are increased. If an increase in production labour and capital factors leads to a disproportionate increase in output, then a firm experiences increasing returns to scale. Increasing returns to scale occur in the long run.

Suppose a company increases its input by 10%, leading to a change in output of more than 10%, then it is said to have increasing returns to scale. A proportional change in production factors leads to a larger proportional change in output.

Figure 1. Increasing returns to scale - StudySmarter

From Figure 1 above, if capital and labour are 1, the output level is 20, 1 unit of labour and 1 unit of capital can produce 20 units. When inputs are 10, the output level is 50, and so on. Although output increases by 30 units each time, the increase in output is still greater than the increase in input.Therefore, we can conclude that when labour and capital in this enterprise increase, output also increases by a larger proportion.

#### Constant returns to scale

When a proportionate change in output equals the proportionate change in output, we speak of constant returns to scale. A production function with constant returns to scale is linear or considered homogeneous. Constant returns to scale can occur for a firm over the long run.

Figure 2. Constant returns to scale - StudySmarter

From Figure 2 above, 1 unit of labour and 1 unit of capital can produce 20 units of output. 10 units of inputs produce 40 units of output. With each increase, both inputs and outputs double, so they can increase by the same percentage, 100%.From this, we can conclude that if the company increases inputs, outputs will also increase by the same percentage.

#### Decreasing returns to scale

Decreasing returns to scale is the rate at which output changes less than the proportionate change in input – a proportionate change in input is greater than the proportionate change in output. Diminishing or decreasing returns to scale occur when a firm's production function becomes less efficient as its size increases. An example of this is when a firm expands beyond its ability to be effectively managed.

Remember, diminishing returns to scale are not the same as diminishing marginal returns.

Figure 3. Decreasing returns to scale - StudySmarter

Figure 3 shows that the output of firm A is 10 when the inputs of labour and capital are 1. Increasing inputs by 1 additional unit increases output from 10 to 15. However, if inputs increase from 6 to 8 by 2 additional units, output increases from 18 to 18.6, less than the proportionate increase in inputs. So it is not an increase or a doubling, and it does not remain constant, but the increase in inputs results in a lower output.

#### Difference between diminishing returns to scale and diminishing marginal returns

Decreasing returns to scale are also known as increasing costs. It is a situation where a portion of the production process increases the factors of production, such as labour and capital. However, the output does not increase by the same or a higher proportion. Diminishing returns to scale occur in the long run.

Diminishing marginal returns is a law that states an increase in the factor of production causes a relatively smaller increase in output. It assumes that the factor of production, capital, is fixed, and the factor, labour, is variable. Diminishing returns to scale occur in the short run.

## Law and Assumptions of Returns to Scale

The law of return to scale assumes that when a firm increases its variable factors of production and experiences a constant increase or decrease in its outputs, the following assumptions are in place:

1. All factors of production are variable.

2. Outputs are measured in physical terms.

3. The market is perfectly competitive.

4. Technology is constant; it does not change over time.

## Formula and Calculation of Returns to Scale

The mathematically gifted among us may be interested in calculating returns to scale. Even if math is not your strong suit, the calculation is not difficult!

By calculating returns to scale, you can determine whether a company is increasing, decreasing, or holding constant its output as it increases its input. You must multiply each input function by a positive constant (m > 0). The result shows whether the production function is equal, increased or decreased to the positive constant.

You can calculate it by determining whether an input's marginal product (MP) is increasing, decreasing or constant.

### Constant returns to scale formula

The formula for constant returns to scale is:

When L = Labour

K = Capital

m = Multiplier

If we increase our inputs (K and L) by our multiplier, m, we get:

Remember that Q = 2K + 3L, so it can be simplified as m x Q.

An increase in inputs by the multiplier m will cause outputs to increase by m. Therefore, we can conclude that there are constant returns to scale.

#### Increasing returns to scale formula

The formula for increasing returns to scale is:

When L = Labour

K = Capital

m = Multiplier

Again, if we increase our inputs by our multiplier, we get:

Remember that Q = 0.5KL and thus can be simplified as Q x m2.

Since m > 1 then m2 > 2, increasing inputs by the multiplier m will increase output by m2. From this, we can conclude that returns to scale increase for this output.

#### Decreasing returns to scale formula

Finally, the formula for decreasing returns to scale is:

When L = Labour

K = Capital

m = Multiplier

If we increase both K and L by the multiplier, m, we get:

Remember that Q = K0.3L0.2 so it can be sampled to Q x m0.5

Since m > 1 then m0.5 < m, an increase in inputs by the multiplier m results in a decrease in outputs. We can conclude that returns to scale decrease in this production.

## Returns to Scale - Key Takeaways

• Returns to scale occur in the long run.
• Returns to scale are the rate at which output changes due to a change in inputs.
• Decreasing or diminishing returns to scale are different from diminishing marginal returns. The former occurs in the long run, the latter in the short run.
• A change in inputs can lead to three changes in the output: remaining constant, increasing, or decreasing.
• Labour and capital are variable factors of production in the long run
• When the production function is increased, internal and external economies of scale come into play, increasing returns to scale.
• When inputs are increased, division of labour and specialisation occur.

## Returns to Scale

Diminishing returns to scale occur when a proportionate change in input is greater than the proportionate change in output.

Return to scale is a term in economics that explains the different reactions of output levels when a firm decides to increase its inputs.

The law of return to scale assumes that when inputs are increased in a production function and the output changes, the following are in place:

1. All factors of production are variable.

2. Outputs are measured in physical terms.

3. The market is perfectly competitive.

4. Technology is constant; it does not change over time.

Return to scale is calculated by multiplying each input function by a multiplier. If the result is greater than the multiplier, it increases returns to scale. If the result is less than the multiplier, then the production function will result in decreasing return to scale. If the result is the same as the multiplier, then the production function will result in constant returns to scale.

A firm’s decision to change its production function by increasing the variable factors of production causes a return to scale.

## Final Returns to Scale Quiz

Question

What is returns to scale?

Returns to scale refers to the rate at which output changes due to a change in variable factors of production such as labour and capital.

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Question

How many types of returns to scale are there?

Three

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Question

What is increasing returns to scale?

Increasing returns to scale is the rate at which a proportionate change in inputs causes a larger proportionate change in output.

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Question

What is decreasing returns to scale?

Decreasing returns to scale is the rate at which a proportionate change in inputs leads to a less than proportional change in output.

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Question

What is constant returns to scale?

Constant returns to scale is the rate at which a proportional change in inputs leads to an equal proportional change in outputs.

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Question

Is there a difference between diminishing returns to scale and diminishing marginal returns?

Yes

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Question

What is the difference between diminishing returns to scale and diminishing marginal returns?

Diminishing returns to scale occurs in the long run when both labour and capital are variable factors of production. While diminishing marginal returns occurs in the short run where labour is, the only variable factor of production and capital is fixed.

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Question

What are the assumptions of returns to scale?

1. Labor and capital are variable factors of production

2. Technology is constant

3. Outputs are measured in physical terms

4. The market is perfectly competitive

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Question

Do returns to scale occur in the long run or short run?

Long run

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Question

Let us assume firm A produces 10 units of outputs with inputs at 4, then increases inputs from 4 to 5 and the output increases from 10 to 15. However, the firm decides to increase its inputs from 6 to 7 and the output produces increases from 20 to 35. What type of returns to scale has occured?

Increasing returns to scale

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Question

Let us assume firm A produces 10 units of outputs with inputs at 4, then increases inputs from 4 to 5 and the output increases from 10 to 15 units. A further decision to increase inputs from 6 to 7 increases outputs from 20 to 25 units. What type of returns to scale has occurred?

Constant returns to scale

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Question

Let us assume firm A produces 10 units of outputs with inputs at 5, then increases inputs to 6, which increases outputs to 20 units. The firm decides to increase inputs from 6 to 7, which increases outputs to 30 units. What type of returns to scale has occurred?

Increasing returns to scale

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Question

Returns to scale is a long-run production theory. True or false?

True

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Question

Decreasing returns to scale is also referred to as diminishing returns to scale. True or false?

True

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Question

The rate at which a change in output occurs is due to a change in input is called returns to scale. True or false?

False

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