# Cost Elasticity

Cost elasticity (also called cost-output elasticity) measures the responsiveness of total cost to changes in output. It is calculated by dividing the percentage change in cost with percentage change in output. A cost elasticity value of less than 1 means that economies of scale exists.

Economies of scale exist when increase in output is expected to result in a decrease in unit cost while keeping the input costs constant. Such a reduction in average cost may occur, for example, when workers are able to specialize which increases their productivity, when the firm is able to negotiate more effectively with suppliers and receive volume discounts, etc.

## Calculation

Cost elasticity is calculated by dividing percentage change in total costs by percentage change in output:

$$ \text{Cost Elasticity}\ =\ \frac{\text{%\ Change in Total Costs}}{\text{%\ Change in Output}} $$

Where ∆C is the change in total costs, percentage change in total costs equals ∆C/C. Similarly, percentage change in output is ∆Q/Q. It follows that:

$$ \text{Cost Elasticity}\ =\frac{\Delta \text{C}}{\text{C}}÷\frac{\Delta \text{Q}}{\text{Q}} $$

$$ \text{Cost Elasticity}\ =\frac{\Delta \text{C}}{\Delta \text{Q}}\times\frac{\text{Q}}{\text{C}} $$

A production process is said to exhibit economies of scale if the cost elasticity is less than 1 and diseconomies of scale when the cost elasticity is greater than 1. At a cost of elasticity of exactly 1, neither economies nor diseconomies of scale exist. A cost elasticity of less than 1 represents existence of economies of scale because it means that percentage change in costs (i.e. the numerator) is lower than the percentage change in output (the denominator). In other words, it shows that at cost elasticity of less than 1, costs increase by a lower percentage than output.

## Example

Using the data given below for three firms, advise each firm regarding production level.

Firm A | Firm B | Firm C | |
---|---|---|---|

Old output | 1,000 | 5,000 | 11,000 |

New output | 1,200 | 6,000 | 12,000 |

Old total cost ($) | 20,000 | 50,000 | 132,000 |

New total cost ($) | 22,800 | 60,000 | 168,000 |

You need to calculate cost elasticity for each firm and then see if there are economies of scale.

Let’s calculate cost elasticity for Firm A:

$$ \varepsilon _ \text{C}=\frac{\Delta \text{C}}{\Delta \text{Q}}\times\frac{\text{Q}}{\text{C}} \\=\frac{\text{\$22,800} - \text{\$20,000}}{\text{1,200} - \text{1,000}}\times\frac{\text{1,000}}{\text{\$20,000}}= \text{0.7} $$

Using the same formula, you can verify that the cost elasticities of Firm B and C are 1 and 3.

Since Firm A has a cost elasticity value of less than 1, its production process exhibits economies of scale and it should increase production. Firm B has neither economies nor diseconomies of scale while Firm C has diseconomies of scale and it should reduce production.

Written by Obaidullah Jan, ACA, CFA and last modified on