**Marginal Analysis **

Marginal analysis is the study of the rate of change of economic quantities

So in this lesson MARGINAL is the same as DERIVITIVE OF

**Marginal Cost**: the derivative of the cost function

**Marginal Revenue**: the derivative of the revenue equation

**Marginal Profit**: the derivative of the profit equation

**Cost Functions **

**To find the actual cost of the last individual product ****produced (x):**

**To find the marginal cost of the number of products ****produced (x): **

Find the derivative of the cost function

**To find the average cost per unit produced: **

**Use the notation for the average cost per unit produced:**

**Revenue Functions**

**To find the revenue:**

**To find the marginal revenue: **

Find the derivative of the revenue function

**Profit Functions**

**To find the profit:**

**To find the marginal profit:**

Find the derivative of the profit function

**Elasticity of Demand**

**To find the elasticity of demand: **

**Elastic**: if (E>1) then an increase in price will cause a decrease in revenue (revenue will react in an opposite manner from the price)

**Inelastic**: if (E<1)> then an increase in price will cause an increase in revenue (revenue will react in a similar manner as the price)

**Unitary**: if (E=1) then an increase in price will cause the revenue to stay about the same

**Example Problem**

Find the elasticity of demand from the demand equation if Sally is selling Prepstock tickets for $12:

**Step 1:** Resolve the equation in terms of x.** Step 2:** Plug in to the elasticity equation

**Step 3:** Find the elasticity of any price (p), in this case plug in 12

Here is a site with some practice problems:

http://www.math.purdue.edu/~rzhao/Courses/MA223/Lesson17.pdf

KJ, you are up next with lesson 3.5 High Order Derivatives.

"Cherish your vision and your dreams as they are the children of your soul; the blueprints of your ultimate achievements."