# What is a Cost Function?

Definition: A cost function is a mathematical formula used to used to chart how production expenses will change at different output levels. In other words, it estimates the total cost of production given a specific quantity produced.

## What Does Cost Function Mean?

Management uses this model to run different production scenarios and help predict what the total cost would be to produce a product at different levels of output. The cost function equation is expressed as C(x)= FC + V(x), where C equals total production cost, FC is total fixed costs, V is variable cost and x is the number of units.

Understanding a firm’s cost function is helpful in the budgeting process because it helps management understand the cost behavior of a product. This is vital to anticipate costs that will be incurred in the next operating period at the planned activity level. Also, this allows management to evaluate how efficiently the production process was at the end of the operating period.

Let’s look at an example.

## Example

The management of Duralex Companies, a manufacturer of toys, has asked for a new cost study to improve next year’s budget forecasts. They pay rent of \$300 a month and they pay an average of \$30 a month for electricity. Each toy requires \$5 in plastic and \$2 in cloth.

A. How much will it cost them to manufacture 1200 toys annually?
B. How much will it cost them to manufacture 1500 toys annually?

First thing to do is to determine which costs are fixed and which ones are variable. Remember, fixed costs are incurred whether or not we manufacture, whereas variable costs are incurred per unit of production. That means rent and electricity are fixed while plastic and cloth are variable costs.

Remember our cost function:
C(x) = FC + V(x)
Substitute the amounts.

A. At 1200
C(1,200) = \$3,960* + 1,200 (\$5 + \$2)
C(1,200) = \$ 12,360

Therefore, it would take \$11,360 to produce 1,200 toys in a year.

B. At 1500
C(1,500) = \$3,960* + 1,500 (\$5 +\$2)
C(1500)= \$14,460

Therefore, it would take \$13,460 to produce 1,500 toys in a year.

*FC = (300 +30) * 12 months (remember we are asked at an annual basis).

Thus, FC= \$ 3,960

(Notice that the fixed costs remain unchanged even at varying outputs)