a monopolist demand curve is given by p=100-2q.find his marginal revenue function .at what price is marginal revenue zero?
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price Demand curve : p = 100 - 2 q
Revenue = p q = 100 q - 2 q²
marginal revenue MR = d (revenue)/d q found by differentiating:
MR = 100 - 4 q
MR = 0 , when q = 25
Price p when quantity produced is 25, is p = 100 - 2 * 25 = 50 units.
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we can find marginal revenue function for the q th product also by:
MR = Revenue for q units produced - Revenue for q-1 units produced
MR = (100 q - 2 q²) - (100 (q-1) - 2 (q - 1)²)
= 100 - 4 q - 2
MR = 0 for , q = 98/4 = 24.5 or, when q = 25
Revenue = p q = 100 q - 2 q²
marginal revenue MR = d (revenue)/d q found by differentiating:
MR = 100 - 4 q
MR = 0 , when q = 25
Price p when quantity produced is 25, is p = 100 - 2 * 25 = 50 units.
===========================
we can find marginal revenue function for the q th product also by:
MR = Revenue for q units produced - Revenue for q-1 units produced
MR = (100 q - 2 q²) - (100 (q-1) - 2 (q - 1)²)
= 100 - 4 q - 2
MR = 0 for , q = 98/4 = 24.5 or, when q = 25
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