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Questions › GATE › GATE 2025 › Q51
2 marksMicroeconomics › Costs of production › Deriving cost functions and cost curvesHardabout 3 min

GATE 2025 Question 51: Costs of production

A Cobb-Douglas type short-run production function is given by q=2LKq = 2\sqrt{LK}q=2LK​, where q,L,Kq,L,Kq,L,K are the output, labour and capital, respectively. KKK is fixed at Kˉ\bar{K}Kˉ. The unit price of LLL is www and the unit price of KKK is rrr. It is given that www is 12.

Considering the above information, which of the following statements is/are CORRECT?

Select all that apply.

Answer and worked solution

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Plain-text version

A Cobb-Douglas type short-run production function is given by q = 2√LK, where q,L,K are the output, labour and capital, respectively. K is fixed at K̄. The unit price of L is w and the unit price of K is r. It is given that w is 12. Considering the above information, which of the following statements is/are CORRECT? (A) The short-run marginal cost is 6q/K̄ (B) The short-run average variable cost is 3q/K̄ (C) To produce 10 units of the output, required L is 25/K̄ (D) For K̄=3 and r=4, the total cost is 12+3q²

Also written as: A Cobb-Douglas type short-run production function is given by q = 2sqrt(LK), where q,L,K are the output, labour and capital, respectively. K is fixed at K_bar. The unit price of L is w and the unit price of K is r. It is given that w is 12. Considering the above information, which of the following statements is/are CORRECT?

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.

TestStop has 20 past-paper questions on this subtopic; the nearest in year are below.

  • GATE 2023 · Q59Consider the following short-run cost function: C(q) = 10q³-80q²+300q+50 At the minimum average variable…
  • IIT JAM 2022 · Q30The short-run production function is Q = 200 + 0.2L² - 0.0004L³. If the wage rate is Rs. 140 and labour L =…
  • IIT JAM 2022 · Q45The Total Variable Cost is TVC = x³ - bx² and the Total Fixed Cost is 848. The value of b for which Marginal…
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