2 marks, −0.667MicroeconomicsCosts of productionDeriving cost functions and cost curvesModerateabout 2 min

IIT JAM 2022 Question 30: Costs of production

The short-run production function is $Q = 200 + 0.2L^2 - 0.0004L^3$ . If the wage rate is Rs. 140 and labour $L = 100$ , then the Marginal Cost and Average Variable Cost, respectively, are

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Answer and worked solution

Answer: (A)

Marginal product of labour is $\dfrac{dQ}{dL} = 0.4L - 0.0012L^2$ . At $L=100$ this is $40 - 12 = 28$ , so marginal cost $= \dfrac{w}{MP_L} = \dfrac{140}{28} = 5$ .

Output at $L=100$ is $Q = 200 + 0.2(10000) - 0.0004(1{,}000{,}000) = 1800$ . Variable cost is $wL = 140\times100 = 14000$ , so $AVC = \dfrac{14000}{1800} = 7.78$ . The answer is (A).

The trap: (C) 5 and 6.68

Average variable cost divides total variable cost by total output $1800$ ; using a different output figure (for example netting out the constant 200) gives the distractor 6.68.

Plain-text version

The short-run production function is Q = 200 + 0.2L² - 0.0004L³. If the wage rate is Rs. 140 and labour L = 100, then the Marginal Cost and Average Variable Cost, respectively, are (A) 5 and 7.78 (B) 6 and 7.78 (C) 5 and 6.68 (D) 6 and 6.68

Also written as: The short-run production function is Q = 200 + 0.2L^2 - 0.0004L^3. If the wage rate is Rs. 140 and labour L = 100, then the Marginal Cost and Average Variable Cost, respectively, are

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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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