Blog 4 Marek Niesiobedzki

Good Morning Class !

             My name is professor Niesiobedzki and today I will be teaching you about Average Cost .

At first, I think it is very important to know what exactly is Average cost and what it consists of. The Average Cost –Production cost per unit of output, computed by dividing the total of fixed costs and variable costs by the number of total units produced (total output). Lower average costs are a potent competitive advantage. Also called unit cost. Formula: (Fixed costs + Variable costs) ÷ Total output.

 Example -Average Cost is AC=C/x. Basically, put your cost function on the numerator and divide it by the number of machines you produce.

[2000+100(250)-0.1(250)^2]/250

which equals $83.00 per machine for the first 250 machines

Average cost is used to find out how much does it cost to produce each individual unit which includes all of the costs including factory, utilities, front costs machinery etc.

Average cost is very important to know, the reason why it is important is because if you are ever to be in the manufacturing business, it is essential to know how much it cost to produce each unit and when to stop production in order to maximize profit.

Once again, I will propose an example on how to calculate the average cost

I have a watch factory. I produce limited production watches. My costs are

            Factory - 50 thousand dollars a year

            Workers – 100 thousand dollars a year

            Materials- 25 thousand a year

            Machinery- 200 thousand

            Utilities – 50 thousand a year

Each of my watches have a selling price of 20 thousand dollars each and will produce 40 thousand units

How to calculate my average cost per unit

325 thousand for my materials and costs a year

800 thousand dollars (  40k units x 20k dollars)

 Average cost  $2,461.53 per unit

$800,000

-----------                         = 2,461.53 average cost per unit

$325,000

           

Thank you class and if you have any questions please let me know and I will do further explanations.

Have a great day.

Now please calculate the average cost for firm B which produces signature rings.

Costs-  Facilities – 60 thousand dollars a year

Materials- 70 thousand dollars a year

Workers – 100 thousand dollars a year

Utilities – 7 thousand dollars a year

Machinery – 180 thousand dollars a year

Each ring will cost 2,000 dollars each and my company will produce 300,000 units per year , please calculate the average cost of each unit .

Answer key when done and to check your work

$417,000 total costs of production

$600,000 sales revenue

$600,000/ $417,000 = Average cost per unit $1.4388

Sources :  http://www.businessdictionary.com/definition/average-cost.html#ixzz3XxYYe54O

Blog 4

Hello Class! Today we will be learning about profit and revenue functions, please see our lesson below to learn about these two great functions!

Blog 4

Hello Class!

My name is Professor Ceccarelli and I am your substitute for Professor Little. She is out rock climbing for the rest of the school year.

Today I am going to discuss how to calculate average cost.

To begin explaining the concept, we must first understand why the AC is important. Companies plan the amount they are going to produce by  fishing equilibrium between the marginal cost and marginal revenue. This way, they can calculate how to maximize profits. As the same time however, the average cost of production is vital because it tell the board if profits will be positive or negative.

The formula for AC is: a(q)= c(q)/q, where c(q) is the cost function and where q is the quantity.
Below you can see a visual to further understand what this looks like.

 Here is a worked example from my notes prepared for this class session:
c(q)=(0.01q^3)-(0.6q^2)+(13q)+1000
The function above is the cost of production cost of Under Armour running shoes.
 If you wanted to find out the avergae ocst of the shoes, you would make q=100 to find the cost.
c(100)=(0.01(100)^3)-(0.6(100)^2)+(13(100))+1000
c(100)=$6300

Now you would plug the values into the average cost formula.
      a(100)= c(100)/100
=> a(100)= 6300/100
=> a(100)= $63 per pair of shoes
That is the average cost of producing one pair of shoes.

Finally, to prepare you for the next lesson, here is what you need to know as for the relationship between marginal cost and average cost:
If MC<AC, the increasing production decreases average cost
If MC>AC, the increasing production increases average cost

Great job today class! See you next time!

Blog 4

Stacey Schwartz


Blog #4
Good evening class, my name is Professor Schwartz and tonight we're going to be learning about average cost.
Average cost is the cost per unit of producing a certain quantity.
Before we learn the actual formula for average cost it's important to know what the cost function is. The cost function, c(q), is the function to figure out how much it would cost to produce a certain quantity, q.
The formula for finding the average cost is a(q) = c(q) / q
Here's an example:
The cost of producing dresses is represented by the function below:
c(q) = 0.01q^3 - 0.6q^2 + 13q

to find out how much the average cost would be to produce 100 dresses we would put first put 100 in for q:
C(100)=.01(100)^3-.6(100)^2+13(100)+1000= $6300

so that means that the c(q) part of the average cost formula would be (6300) and the q part would be 100

to put it all together, the average cost for producing 100 dresses is represented below:

a(q) = 6300/100 

so $63 per dress

Blog 4

Profit, Revenue and Cost Functions

The purpose of this lesson is to teach students what a Profit, Cost and Revenue function are and how they are all related. Also, I will give examples to demonstrate how they are related.

Profit Function Equation

A profit function is a function that focuses on business applications. The main purpose for a business is to sell a product or service in order to make a profit. The profit is the revenue a company brings in for selling a product or service minus the cost for producing a product or service.

*The Profit function equation is made up of two main functions: the Revenue function and the Cost function.

·      Cost Function = C(q)

·      Revenue Function = R(q)

o   “q” represents the quantity

Profit Function = R(q) – C(q)

EXAMPLE:

A hot dog stand in Miami sells hot dogs for $3 each. So, his Revenue function is R(1) = 3x. His fixed cost for maintaining his hot dog stand every day is $50 and his variable cost is $2 per hot dog sold. So, his daily Cost function is C(q) = 50 + 2x.

1) How many hot dogs does the hot dog stand need to sell in order to break even (where revenue equals cost)?

• ·         To find the breakeven point, use the Profit function and equal it to 0.

o   P(q) = R(q) – C(q) = 0

o   Now, substitute the values given above into the equation and solve.

3x = 50 + 2x

x = 50

o   So, on any given day, the hot dog stand needs to sell 50 hotdogs to breakeven. Every hot dog he sells after that he will profit 1$ per hot dog sold.

o     Below is the Revenue and Cost function graphed to graphically demonstrate the breakeven point. As you can see, the Revenue function lies beneath the Cost function up until 50 hot dogs are sold, then the Revenue function lies above the Cost function representing the hot dog stand making a profit.

Blog 4 Miles VB

Hello class! I know many of you are business majors, hence why you took this course. For all this math to be useful to you, it has to applied. Revenue and profit functions are great examples of how math is useful for the business world. 

I know that the difference between revenue and profit is obvious for most of you, but it is important to understand that profit is the piece of the revenue that is left behind after costs are subtracted.

So to apply derivatives and calculus, we will be finding the marginal revenue and profit. That means the revenue or profit derived from making/selling one more unit.

So lets say someone is selling oregano. She decides that the demand function for her oregano is p=1000/√x per ounce. 

So revenue is equal to the number of ounces she sells (x) times the price (p)

So now we have to find what this means in terms of MARGINAL revenue. To do this, we find the derivative of the revenue function. So for instance when x=100: 

This all means that the revenue from selling the 101st ounce of oregano is $50. Pretty handy stuff to know in the business world.

So now lets find the marginal profits. First lets find the profit function. Well, profit (p) is revenue minus costs as I said before. So we express that mathematically by subtracting our cost function from our revenue. Lets say our cost function is C(x)= 10x + 10√x + 10,000.

So now to find the marginal profit, we must find the derivative of it at x=100

So this means that when she sells the 101st ounce of oregano, her profit is $35. This is really quite simple once you understand what is happening. The marginal profit is simply the marginal revenue minus the marginal costs. In this situation, her costs may be growing the oregano. Hope you enjoyed this lesson and have a nice night! 

Lesson on Elasticity