2 marksMicroeconomicsFactor markets and income distributionLabour market equilibrium, minimum wages and monopsonyHardabout 3 min

IIT JAM 2022 Question 56: Factor markets and income distribution

Given the production function $Q = 6\sqrt{L}$ and the labour supply $L = \sqrt{w}$ , where $L$ is labour and $w$ the wage rate, and the unit product price is Rs. 243, the profit-maximizing value of $w$ is Rs. _______ (in integer).

Answer and worked solution

Answer: 81 to 81

With $L = \sqrt{w}$ , output is $Q = 6\sqrt{L} = 6w^{1/4}$ and the wage bill is $wL = w^{3/2}$ . Profit is $\Pi = 243\cdot6\,w^{1/4} - w^{3/2} = 1458\,w^{1/4} - w^{3/2}$ .

Setting $\dfrac{d\Pi}{dw} = 364.5\,w^{-3/4} - 1.5\,w^{1/2} = 0$ gives $w^{5/4} = 243$ , so $w = 243^{4/5} = (3^5)^{4/5} = 3^4 = 81$ . The answer is $81$ .

Plain-text version

Given the production function Q = 6√L and the labour supply L = √w, where L is labour and w the wage rate, and the unit product price is Rs. 243, the profit-maximizing value of w is Rs. _ (in integer).

Also written as: Given the production function Q = 6sqrt(L) and the labour supply L = sqrt(w), where L is labour and w the wage rate, and the unit product price is Rs. 243, the profit-maximizing value of w is Rs. _ (in integer).

Factor markets and income distribution has come up 55 times in 6 exams since 2006.

What this question tests

This question is on Labour market equilibrium, minimum wages and monopsony, part of Factor markets and income distribution in Microeconomics.

Wages and employment in competitive and single-buyer labour markets.

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