Blog 4

Hi class, I'm Virginia. Professor Little asked me to lead a review session about cost and revenue functions before the final exam. I've prepared a detailed handout to help with the review session.

Definitions:

• Fixed Costs: costs that do not depend on business operations (example: businesses have to pay rent, utility bills, and insurance regardless of sales)
• Variable Costs: costs that depend on business operations like volume of production (example: cost of materials and labor to produce a product)
• Marginal Costs: the cost of producing one more unit, product, or good
• Cost Function: fixed costs "a" plus variable costs "b" times quantity of units produced "q"
• C (q) = a + b * q
• Revenue Function: quantity "q" times price "p" per unit
• R (q) = p * q
• Profit Function: total revenue "r" minus total cost "c"
• P (q) = R (q) - C (q)
• Average Cost: total cost "c" divided by total quantity "q"
• A (q) = C (q) / p

Application and Example:

Imagine a company that produces any kind of product or service that you want. Now, imagine that you are the manager or owner of that company. You're presented with information about how much it costs to produce the product or service and you need to analyze it.

Consider the cost function C (q) above. 

Let's look at how to find the average cost at q = 450:

• We know that the average cost formula is A (q) = C (q) / q
• Cost at q = 450 is $2250
• Average cost = 2250/450 = 5
• This means that the average cost per unit when producing 450 units is $5 per unit
• That can be graphically represented as a linear function with the slope equal to the average cost per unit  of $5 as shown below

Next, let's figure out the marginal cost:

• We start by estimating two separate points on the function (75, 1000) and (450, 2250)

• Next, we calculate the slope between those two points as shown below

2250-1000 / 450-75

1225/375

3

• Just like we did with the average cost, we can graphically represent the marginal cost with a linear function with the slope equal to the marginal cost of $3

Thanks for having me and good luck on your exam!