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Marginal cost, and minimizing cost & average cost

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Intros
Lessons
  1. Marginal Cost, and Maximizing Cost & Average Cost Overview:
  2. Understanding and Minimizing Marginal Cost
  3. Understanding and Minimizing Average Cost
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Examples
Lessons
  1. Finding & Minimizing the Cost
    Given the following information, find the marginal cost and the value of qq which minimizes the cost:
    1. C(q)=20+70q2 C(q)=20+70q^2
    2. C(q)=250+(1+q)(q−10)2 C(q)=250+(1+q) (q-10)^2
    3. The fixed cost is $50000, and the cost to make each unit is $500
    4. The fixed cost is $25000, and the variable cost is $200q2q^2.
  2. Finding & Minimizing the Average Cost
    Given the following information, find the marginal average cost and the value of qq which minimizes the average cost:
    1. C(q)=q4−2q2+10q C(q)=q^4-2q^2+10q
    2. C(q)=100+q2 C(q)=100+q^2
    3. C(q)=q3−4q2+10q C(q)=q^3-4q^2+10q
    4. C(q)=2q C(q)=2q
Topic Notes
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Marginal Cost (MC) is the additional cost that is gained when you increase the unit by one. It is also the derivative of the cost function. In other words,
MC=C′(q)MC=C'(q)

Average Cost (AC) is the amount of cost generated per unit. In other words,
AC(q)=C(q)qAC(q)=\frac{C(q)}{q}
In this section, we would want to find the quantity qq, which minimizes cost and average cost. To minimize cost, we would want to solve for:

MC=0MC=0

To minimize average cost, we would want to solve for:

AC′(q)=0AC'(q)=0
Basic Concepts
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