# Marginal cost, and minimizing cost & average cost

### Marginal cost, and minimizing cost & average cost

#### Lessons

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,
$MC=C'(q)$

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

$MC=0$

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

$AC'(q)=0$
• Introduction
Marginal Cost, and Maximizing Cost & Average Cost Overview:
a)
Understanding and Minimizing Marginal Cost

b)
Understanding and Minimizing Average Cost

• 1.
Finding & Minimizing the Cost
Given the following information, find the marginal cost and the value of $q$ which minimizes the cost:
a)
$C(q)=20+70q^2$

b)
$C(q)=250+(1+q) (q-10)^2$

c)
The fixed cost is $50000, and the cost to make each unit is$500

d)
The fixed cost is $25000, and the variable cost is$200$q^2$.

• 2.
Finding & Minimizing the Average Cost
Given the following information, find the marginal average cost and the value of $q$ which minimizes the average cost:
a)
$C(q)=q^4-2q^2+10q$

b)
$C(q)=100+q^2$

c)
$C(q)=q^3-4q^2+10q$

d)
$C(q)=2q$