A monopolist's demand function is x = 50 - p 4 . At what level of output is marginal revenue zero ? Interpret it.

Given, demand function x = 50 - p 4 Finding p in terms of x x = 50 - p 4 x = 200 - p 4 p = 200 - 4 x Revenue function R = p x = ( 200 - 4 x ) x = 200 x - 4 x 2 Marginal revenue function M R = d d x ( R ) = d d x ( 200 x - 4 x 2 ) = 200 - 8 x When marginal revenue is zero. 200 - 8 x = 0 x = 25 Hence, M R = 0 at x = 25 . Further production leads to negative returns. So, this is the point of maximum total revenue.

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Calculate the marginal revenue function from the demand function of a monopolist which is given by $P = 2000 + 4 x + 3 x^{2}$ .

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Mathematics>Integral Calculus>Application of Calculus>Average and Marginal Revenue

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Mathematics>Integral Calculus>Application of Calculus>Average and Marginal Revenue

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Mathematics>Integral Calculus>Application of Calculus>Average and Marginal Revenue

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Mathematics>Integral Calculus>Application of Calculus>Average and Marginal Revenue

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Mathematics>Integral Calculus>Application of Calculus>Average and Marginal Revenue

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x = 50 - \frac{p}{4}

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Mathematics>Integral Calculus>Application of Calculus>Average and Marginal Revenue

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p = 1500 - 2 x - x^{2}

. Find the marginal revenue for any level of output

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when

x = 10

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The total revenue in rupees received from the sale of

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Mathematics>Integral Calculus>Application of Calculus>Average and Marginal Revenue

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Mathematics>Integral Calculus>Application of Calculus>Average and Marginal Revenue

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P (x) = 300 - x^{2}

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The demand function of a monopolist is given by

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. Calculate the marginal revenue function from the revenue function derived from the demand function.

Calculate the marginal revenue function from the demand function of a monopolist which is given by P=2000+4x+3x2.

Important Questions on Application of Calculus

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Calculate the marginal revenue function from the demand function of a monopolist which is given by $P = 2000 + 4 x + 3 x^{2}$ .