Find the profit-maximizing price. 80 For a monopolist’s product, the demand equation is p = 22 – 2q and the average-cost function

Question

Find the profit-maximizing price.
80
For a monopolist’s product, the demand equation is p = 22 – 2q and the average-cost function is c=2+
q
The profit-maximizing price is $

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Gerda 2 weeks 2021-07-19T06:29:49+00:00 1 Answers 0 views 0

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    2021-07-19T06:31:32+00:00

    Answer: \$11.5

    Step-by-step explanation:

    Given

    Demand function is p=22-2q

    The average cost function is c=2+q

    Total revenue is the product of demand and the price per unit.

    r=\left(22-2q\right)q

    Profit is given by the difference of the total revenue and the cost

    \Rightarrow P=r-c\\\Rightarrow P=22q-2q^2-2-q\\\Rightarrow P=-2q^2+21q-2

    Find the derivative of profit to get the maximum profit

    \Rightarrow P'=-4q+21\\\text{Put the derivative equal to 0 to get the maximum profit}\\\\\Rightarrow q=\dfrac{21}{4}

    Put q in the equation of demand to get the price

    \Rightarrow p=22-2\times \dfrac{21}{4}\\\\\Rightarrow p=22-10.5\\\Rightarrow p=\$11.5

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