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Suppose a firm faces a downward sloping demand curve givven by the equation 1=100-1/3P. The firm's cost function is given by the equation C=30+1/4Q^2. Find the profit maximizing level of output.

  • Economics -

    always always always, MC=MR.

    First rearrange the demand function to be P=f(Q). That is P=300 - 3Q
    Now then Total revenue is P*Q. So TR=300Q -3(Q^2)
    MR is the first derivitive of TR. So MR=300 - 6Q
    MC is the first derivitive of TC. So MC=(1/2)Q
    MC=MR - use algebra and solve for Q. Take it from here

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