Regarding cost behaviour, which statement about fixed costs is correct as output volume changes?

Introduction / Context:
Understanding how costs behave with changes in activity level is crucial in managerial accounting and cost analysis. Fixed costs are costs that remain constant in total within a relevant range of activity, regardless of the number of units produced or sold. However, on a per unit basis, fixed costs behave differently. This question checks whether you know how fixed cost per unit changes as volume increases or decreases.

Given Data / Assumptions:

• Fixed costs in total (such as factory rent or manager salaries) remain constant over a relevant range of activity.
• Variable costs change in total in proportion to activity but remain constant on a per unit basis.
• We are considering changes in fixed cost per unit as volume changes, not changes in total fixed cost.
• The relevant range assumption holds, so fixed costs in total do not jump or change within the volume considered.

Concept / Approach:
Total fixed cost is constant within the relevant range, but when you spread that same amount over more or fewer units, the fixed cost per unit will change inversely with volume. Fixed cost per unit = total fixed cost / number of units. As the denominator (units) increases, the per unit fixed cost decreases. As volume falls, the per unit fixed cost rises. This behaviour is important in CVP analysis, pricing decisions, and break even calculations.

Step-by-Step Solution:
Step 1: Let total fixed cost be F. If you produce Q units, the fixed cost per unit is F / Q. Step 2: If volume increases from Q to Q2 where Q2 > Q, the new fixed cost per unit becomes F / Q2. Step 3: Because Q2 is larger, F / Q2 is smaller than F / Q, so fixed cost per unit decreases as volume increases. Step 4: If volume decreases, the denominator gets smaller, so F / Q becomes larger, meaning fixed cost per unit increases. Step 5: Compare this logic with the options: only option b correctly states that the fixed cost per unit decreases when volume increases.

Verification / Alternative check:
Assume total fixed cost is Rs 1,00,000. If the company produces 10,000 units, fixed cost per unit is 1,00,000 / 10,000 = Rs 10. If production doubles to 20,000 units, fixed cost per unit becomes 1,00,000 / 20,000 = Rs 5. Clearly, as volume increased, fixed cost per unit halved. If volume dropped to 5,000 units, fixed cost per unit would rise to Rs 20. This numerical example confirms that fixed cost per unit moves inversely with volume, while total fixed cost remains constant within the relevant range.

Why Other Options Are Wrong:
Option a is incorrect because even though fixed costs do not change in total, they are still relevant in many decisions such as pricing, capacity planning, and profitability analysis. Option c is wrong because, as shown, fixed cost per unit does change when volume changes; it does not stay constant. Option d incorrectly states that fixed cost per unit increases when volume increases, which contradicts the basic formula F / Q.

Common Pitfalls:
Many learners confuse fixed costs with variable costs and think that fixed cost per unit is constant like variable cost per unit. Others may forget that the relevant range concept limits where fixed cost assumptions hold; outside that range, total fixed cost may step up or down. To avoid confusion, always separate total cost behaviour from per unit behaviour and apply the simple formula for fixed cost per unit when volume changes.

Final Answer:
The correct statement is that the fixed cost per unit decreases when production or sales volume increases.