Marginal profit, and maximizing profit & average profit

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Intros
Lessons
  1. Marginal Profit, and Maximizing Profit & Average Profit Overview:
  2. Understanding and Maximizing Marginal Profit
  3. Understanding and Maximizing Average Profit
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Examples
Lessons
  1. Marginal Profit

    Given the following information, find the marginal profit and the value of qq which maximizes the profit. Lastly, calculate the maximum profit.

    1. R(q)=−2q2+50q+6,C(q)=200+10qR(q) = -2q^{2} + 50q + 6, C(q) = 200 + 10q
    2. R(q)=−10q2+10,C(q)=2qR(q) = -\frac{10}{q^{2}} + 10, C(q) = 2q
    3. p(q)=−2q+400p(q) = -2q + 400, fixed cost is $200200, costs 4040$ per unit to make
    4. q(p)=(300−p)3q(p) = \frac{(300 - p)}{3}, fixed cost is $100100, variable cost is $2q22q^{2}
  2. Average Profit

    Given the following information, find the marginal average profit and the value of qq which maximizes the average profit:

    1. R(q)=−q2+35q,C(q)=100+5qR(q) = -q^{2} + 35q, C(q) = 100 + 5q
    2. R(q)=−100q+400,C(q)=5qR(q) = -\frac{100}{q} + 400, C(q) = 5q
    3. p(q)=−2q+50 p(q) = -2q + 50, fixed cost is $5050, costs $1010 per unit to make
    4. q(p)=400−p2q(p) = \frac{400 - p}{2}, fixed cost is $288288, variable cost is $20q20q
Topic Notes
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Marginal Profit (MP) is the additional profit that is gained when you increase the unit by one. It is also the derivative of the profit function. In other words,

MP=P′(q)=R′(q)−C′(q)MP = P'(q) = R'(q) - C'(q)

Average Profit (AP) is the amount of profit generated per unit. In other words,

AP(q)=P(q)q=R(q)−C(q)qA P(q) = \frac{P(q)}{q} = \frac{R(q) - C(q)}{q}

In this section, we would want to find the quantity qq, which maximizes profit and average profit. To maximize profit, we would want to solve for:

P′(q)=0P'(q) = 0

To maximize average profit, we would want to solve for:

AP′(q)=0A P'(q) = 0

Basic Concepts
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Related Concepts
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