Question

Give a numerical example of cost function and analyze this cost function? Discuss how is this cost function used in decision making?

Answer 1

Answer

• Cost Function is a mathematical method to determine ‘cost’ for a given level of output or various level of output.
• Cost Function is written in an equation form as Y = a + bX,
  where Y = Total Cost
  a = Total Fixed Cost
  b = variable cost per unit
  X = no. of units produced and sold, or volume of units.

Hence, Cost Function = Total Fixed Cost + (variable cost per unit x No. of units)

• Example:
  Suppose the Cost Function is this:
  Y[Total cost] = $ 20,000 + $ 2 x No. of units sold.

This means that if say 10000 units are sold, the total cost would be $ 40000 [20000 + (2 x 10000]

            Lets extend this example to a series of level of output:

Cost function: Fixed Cost + (Variable cost per unit x Units)
Fixed Cost	Variable cost per unit	Level of output	Total Cost
$20,000	$2	2,000	$24,000
$20,000	$2	4,000	$28,000
$20,000	$2	6,000	$32,000
$20,000	$2	8,000	$36,000
$20,000	$2	10,000	$40,000
$20,000	$2	12,000	$44,000
$20,000	$2	14,000	$48,000
$20,000	$2	16,000	$52,000

            As you can see, that although Fixed cost remains same in total, and Variable cost remains same per unit, the Total Cost is changing.

• How Cost Function is used in Decision Making?

The cost function is used in many ways in decision making process:
--Behaviour of cost is analysed.
--Its helps in determining contribution margin.
--Expected cost can be ascertained based on no. of expected unit.
--Break Even point calculation gets easier.
--Used in breaking down a ‘Mixed Cost’ into its Variable and Fixed elements.