1 markMicroeconomicsCosts of productionDeriving cost functions and cost curvesModerateabout 2 min

IIT JAM 2022 Question 45: Costs of production

The Total Variable Cost is $TVC = x^3 - bx^2$ and the Total Fixed Cost is 848. The value of $b$ for which Marginal Cost is minimum at $x = 16$ is _______ (in integer).

Answer and worked solution

Answer: 48 to 48

Marginal cost is $MC = \dfrac{d(TVC)}{dx} = 3x^2 - 2bx$ . It is minimised where $\dfrac{d(MC)}{dx} = 6x - 2b = 0$ , i.e. at $x = \dfrac{b}{3}$ .

Setting $\dfrac{b}{3} = 16$ gives $b = 48$ . The fixed cost 848 does not enter marginal cost and is a distractor. The answer is $48$ .

Plain-text version

The Total Variable Cost is TVC = x³ - bx² and the Total Fixed Cost is 848. The value of b for which Marginal Cost is minimum at x = 16 is _ (in integer).

Also written as: The Total Variable Cost is TVC = x^3 - bx^2 and the Total Fixed Cost is 848. The value of b for which Marginal Cost is minimum at x = 16 is _ (in integer).

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

What this question tests

This question is on Deriving cost functions and cost curves, part of Costs of production in Microeconomics.

Working out cost curves from a cost function, a production function or a marginal cost schedule.

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