In the long-run, all factors of production are variable .

**The long-run** describes the time-period where all factors of production of a firm can be varied so that no factor of production is fixed.

In the long-run, the **law of returns to scale** applies to the production function.

The law of returns to scale refers to the effect of changes in the production scale on the units of total product.

The law of returns to scale shows the responsiveness of output to a given proportionate change in the quantities of all inputs employed in production.

The law of returns to scale essentially show returns to scale.Returns to scale are the changes in outputs that occur when all inputs are changed in the same proportion.

According to the law of returns to scale, when all production inputs are change in the same proportion, output will either change at a constant rate, a growing rate, or a decreasing rate.

Accordingly, there are three possible production functions in the long run, namely; Increasing returns to scale, decreasing returns to scale and constant returns to scale.

1. **Increasing returns to scale**: This describes a production function where the total product increases more than proportionate to the the factors used in production.

In other words, increasing returns to scale occurs when, if all factors of production are increased by a certain proportion, the the output will increases by a greater proportion.

For example, A 30% increase in the amount of labor and capital which bring about a 50% increase in the number of output is an example of increasing returns to scale.

Increasing returns to scale usually occurs when an increase in output is more than proportional to the increase in the factor inputs.

2. **Constant returns to scale**: This term refers to a production function in which the quantity produced increases proportionately to the increase in production scale.

In other words, consistent returns to scale occur when raising all production inputs by a certain proportion yields an equivalent rise in output.

A 30% increase in the quantities of input used in production, for instance, will result in a 30% increase in the quantities of output if there is constant returns to scale.

Constant returns to scale usually result when an increase in output is equally proportional to the increase in the factor inputs.

3. **Decreasing returns to scale**: This refers to a production function where the total product increases less than proportionately as the production scale increases.

To paraphrase, decreasing returns to scale describes a production function where the proportional rise in output is less than the proportional increase in the quantities of inputs used in the production

For example, a 10% rise in the amount of labor and Capital which results in a 8% rise in the outputs produced is a good example of decreasing returns to scale.

Decreasing returns to scale occurs when an increase in output is less than proportional to the increase in factors inputs of production.