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  • A monopolist firm demand curve is P=100-2q. Find its marginal revenue function and at what price its marginal revenue is zero?

A monopolist firm demand curve is P=100-2q. Find its marginal revenue function and at what price its marginal revenue is zero?

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eginarrayl extDemand curve is given by\ P=100-2q\ extTotal revenue will be given by\ TR=P imes q=(100-2q) imes q=100q-2q^2\ \ ext(a) marginal revenue is the derivative of TR. So\ MR=fracdleft(TR ight)dq=fracddqleft(100q-2q^2 ight)=100-4q\ \ extSo marginal revenue is 100-4q\ \ ext(b) MR=0\ Rightarrow100-4q=0 \ Rightarrow 4q=100\ Rightarrow q=25\ extAt q=25\ TR=100q-2q^2\ =100 imes25 -2 imes25^2=2500-1250=1250\ extMarginal Revenue is 0 ext at Price 1250.endarray

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Deependra Verma

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