In cost accounting, fixed cost per unit will increase under which of the following circumstances?

Introduction / Context:
This question tests understanding of the behaviour of fixed costs in cost and management accounting. Fixed costs, such as rent, salaries of permanent staff and depreciation of machinery, do not change in total when production volume changes within a relevant range. However, fixed cost per unit varies depending on how many units are produced. Knowing how fixed cost per unit behaves is important for pricing decisions, break even analysis and evaluating capacity utilisation.

Given Data / Assumptions:
- Fixed costs are defined as costs that remain constant in total over a range of activity levels.
- Fixed cost per unit is calculated as total fixed cost divided by number of units produced.
- The options involve changes in variable cost and changes in production volume.
- We assume total fixed cost remains unchanged when volume changes, which is the standard assumption within the relevant range.

Concept / Approach:
The formula for fixed cost per unit is:
fixed cost per unit = total fixed cost / number of units produced If the total fixed cost stays constant and the number of units produced decreases, the denominator falls, so fixed cost per unit increases. Conversely, if the number of units produced increases, the fixed cost per unit decreases because the same total fixed cost is spread over more units. Variable cost per unit does not affect the fixed cost per unit calculation; it affects total variable cost and total cost, but not the allocation of fixed cost per unit.

Step-by-Step Solution:
Step 1: Focus on what fixed cost per unit means: total fixed cost divided by the quantity produced. Step 2: Identify the option that explicitly mentions a change in production volume while total fixed cost remains unchanged. Step 3: Recognise that a decrease in production volume will make the denominator smaller, causing the fixed cost per unit to rise. Step 4: Note that changes in variable cost per unit, mentioned in options A and C, do not enter into the fixed cost per unit formula. Step 5: Conclude that "production volume decreases while total fixed cost remains the same" is the correct condition for fixed cost per unit to increase.

Verification / Alternative check:
To verify, take an example. Suppose total fixed cost is 10,000 currency units. If the firm produces 1,000 units, fixed cost per unit is 10. If production falls to 500 units, fixed cost per unit becomes 20, clearly an increase. If instead production rises to 2,000 units, fixed cost per unit falls to 5. In all cases, changes in variable cost per unit, such as raw material prices, do not change the 10,000 total fixed cost and therefore do not directly affect fixed cost per unit.

Why Other Options Are Wrong:
Option A: A decrease in variable cost per unit affects variable and total costs but not fixed cost per unit, which depends only on total fixed cost and volume.
Option C: An increase in variable cost per unit again has no direct effect on fixed cost per unit, though it raises total variable cost.
Option D: If production volume increases while total fixed cost stays the same, fixed cost per unit will decrease, not increase, because the fixed cost is spread over more units.

Common Pitfalls:
Students sometimes confuse total fixed cost with fixed cost per unit and assume that fixed cost per unit is also constant. Another pitfall is mixing up the effects of variable and fixed costs, or focusing on changes in variable cost when the question is explicitly about fixed cost per unit. To avoid these errors, always go back to the simple formula and think about what happens when you change the numerator or the denominator while holding the other constant.

Final Answer:
Fixed cost per unit increases when production volume decreases while total fixed cost remains the same.