Question

calculating marginal revenue from a linear demand curve

Answer 1

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Demand curve shows the relationship between price and Quantity, So we can obtain the equation of price from it.

Total revenue = Price * Quantity

Price = Average revenue = Total revenue/Quantity (which we get from the demand curve)

Marginal revenue is the change in total revenue from sale of one additional unit. (this can be achieve by diffrentiation)

So we can obtain TR from the demand curve(price) by multipying it with quantity.

From TR curve we can find the MR by differntiating,

this is how we get MR from demand curve.

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Lets assume demand curve: Q = 10- 5P

solving for P(Average revenue), P = (10 - Q)/5

AR = P = 2 - 0.2 Q

TR = AR * Q = (2-0.2Q) * Q = 2Q - 0.2Q2

MR = 2 - 0.4 Q (diffrentiating TR to get MR)

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