managerial economics

posted by .

firms demand function,p=24-0.54q and the average cost function,AC=Q2-8Q+36+3/Q,calculate the level of output Q, which maximize total revenue,maximizes profits

  • managerial economics -

    But what do you need here?

    Sra

  • managerial economics -

    A) Total revenue is the product of the quantity sold and the price at which they were sold.
    (total revenue) = Q*P
    = Q*(24 - .5Q)
    = -.5Q^2 + 24Q
    This quadratic function will have a maximum at Q = -24/(2*(-.5)) = 24
    Total revenue will be maximized when Q = 24.

    B) The profit on each unit is the difference between the selling price and the cost. The total profit will be the product of the unit profit and the number of units sold.
    (total profit) = Q*(P - AC)
    = Q*((24 - .5Q) - (Q^2 - 8Q + 36 + 3/Q))
    = 24Q - .5Q^2 - Q^3 + 8Q^2 - 36Q - 3
    = -Q^3 + 7.5Q^2 - 12Q - 3
    This will be maximized when the derivative is zero.
    -3Q^2 + 15Q - 12 = 0
    Q^2 - 5Q + 4 = 0 (divide by -3)
    (Q - 1)(Q - 4) = 0
    This suggests that quantities of 1 or 4 will maximize profit. Using our equation for total profit, we find that profit for Q=1 is negative. Profit will be maximized when Q = 4.
    Here is a plot of profit versus quantity sold.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Maths

    Demand function P=50-Q Average Cost 5Q + 40 +10/Q Calculate the firm's total cost function Find the marginal cost function and evaluate it at Q=2 and Q=3 What is the total revenue function Find the firms's revenue maximising output …
  2. economics

    1. Given a firm’s demand function, P = 24 - 0.5Q and the average cost function, AC = Q2 – 8Q + 36 + 3/Q, calculate the level of output Q which a) maximizes total revenue b) maximizes profits
  3. q

    2. Given a firm’s demand function, P = 24 - 0.5Q and the average cost function, AC = Q2 – 8Q + 36 + 3/Q, calculate the level of output Q which a) maximizes total revenue b) maximizes profits
  4. managerial economics

    Given a firm’s demand function, P = 24 - 0.5Q and the average cost function, AC = Q2 – 8Q + 36 + 3/Q, calculate the level of output Q which a) maximizes total revenue b) maximizes profits
  5. economics

    2. Given a firm’s demand function, P = 24 - 0.5Q and the average cost function, AC = Q2 – 8Q + 36 + 3/Q, calculate the level of output Q which a) maximizes total revenue b) maximizes profits
  6. engineering

    Given a firm’s demand function, P = 24 - 0.5Q and the average cost function, AC = Q2 – 8Q + 36 + 3/Q, calculate the level of output Q which a) maximizes total revenue b) maximizes profits
  7. MBA

    2. Given a firm�s demand function, P = 24 - 0.5Q and the average cost function, AC = Q2 � 8Q + 36 + 3/Q, calculate the level of output Q which a) maximizes total revenue b) maximizes profits
  8. economics

    2. Given a firm’s demand function, P = 24 - 0.5Q and the average cost function, AC = Q2 – 8Q + 36 + 3/Q, calculate the level of output Q which a) maximizes total revenue b) maximizes profits
  9. ECONOMICS

    Q2) Given a firm’s demand function, P = 24 - 0.5Q and the average cost function, AC = Q2 – 8Q + 36 + 3/Q, calculate the level of output Q which: a) maximizes total revenue b) maximizes profits
  10. manaegerial economics

    iven a firm’s demand function, P = 24 - 0.5Q and the average cost function, AC = Q2 – 8Q + 36 + 3/Q, calculate the level of output Q which a) maximizes total revenue b) maximizes pr

More Similar Questions