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Well, you first have to look at fixed and variable costs in total as well as on a per unit basis. Fixed costs remain the constant (or fixed) in total. However, on a per unit basis they aren't constant (variable). As units produced increase (or whatever activity base) then the fixed cost per unit decreases.

Fixed example:

If rent is $8,000, then the total rent will still be $8,000 every month whether or not the company makes 100 products during the period or 1,000. However, using the 100 and 1,000 units as an example, the per unit cost decreases. When the company makes 100 units, the fixed cost per unit is $80 ($8,000/100 units). When the company makes 1,000 units, the fixed cost per unit is $8 ($8,000/1,000 units).

The opposite applies for variable costs. Variable costs, by their nature, change with the change in units produced (or again, any other activity base the company uses, such as machine hours or labor hours). Therefore, there will be a different total for 100 units produced and 1,000 units produced. However, the unit cost never changes.

Variable example:

If a product that a company produces requires a certain part, this is a variable cost. Let's say the cost of the part is $10. The total variable cost for 100 units is $1,000 ($10*100 units), and for 1,000 units it's $10,000 ($10*1,000 units). However, in each case, the variable cost per unit remained at $10.

Hope this is what you were looking for!

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Q: Why is fixed cost variable and variable cost fixed?
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