2 marks, −0.667MicroeconomicsCosts of productionShort-run cost curves and their relationshipsModerateabout 2 min

GATE 2023 Question 45: Costs of production

A firm in a market with perfect competition has the following total cost ( $TC$ ) function:

$TC(Q) = a + b(Q)$

where $Q$ is the quantity produced by the firm, $a$ is the fixed cost and $b(Q)$ is the variable cost. What will happen if the fixed cost increases?

Tap an option to check your answer.

Answer and worked solution

Answer: (B)

$AVC = b(Q)/Q$ depends only on the variable cost function $b(Q)$ — the fixed cost $a$ does not enter AVC at all, so a change in $a$ leaves AVC unaffected. (A) is incorrect.

$MC = \dfrac{d(TC)}{dQ} = \dfrac{d(b(Q))}{dQ}$ — since $a$ is a constant, it drops out entirely under differentiation, so MC is also unaffected by a change in fixed cost. (D) is incorrect.

$ATC = TC/Q = a/Q + b(Q)/Q = AFC + AVC$ . Since $AFC=a/Q$ rises directly with $a$ , ATC shifts upward when fixed cost increases (while AVC stays put). (B) is correct.

Higher fixed cost raises total cost without changing revenue, so profit falls, not rises — (C) is incorrect (it states the opposite of what happens).

Therefore the answer is (B).

The trap: (D) In the short-run, the firm's Marginal Cost (MC) curve will shift upwards.

Students sometimes assume that 'any cost increase must raise marginal cost,' without carefully distinguishing that fixed costs, by definition, don't vary with output and therefore vanish under differentiation — this is a common conceptual gap between 'cost' broadly and specifically 'marginal' cost.

Plain-text version

A firm in a market with perfect competition has the following total cost (TC) function: TC(Q) = a + b(Q) where Q is the quantity produced by the firm, a is the fixed cost and b(Q) is the variable cost. What will happen if the fixed cost increases? (A) In the short-run, the firm's Average Variable Cost (AVC) curve will shift upwards. (B) In the short-run, the firm's Average Total Cost (ATC) curve will shift upwards. (C) The firm will earn higher profits. (D) In the short-run, the firm's Marginal Cost (MC) curve will shift upwards.

Costs of production has come up 83 times in 7 exams since 2006.

What this question tests

This question is on Short-run cost curves and their relationships, part of Costs of production in Microeconomics.

Fixed, variable, average and marginal cost, and how marginal cost relates to average cost.

TestStop has 17 past-paper questions on this subtopic.

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Question from the GATE 2023 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.