This section is divided in three lessons:

  1. Total Cost graphs and tables

  2. Average Cost Curves and tables

  3. Marginal Cost and tables


Lesson 1

A very important concept to begin with, the difference between explicit cost and implicit cost.  Explicit costs are visible costs that are commonly used in our daily lives such as rent, salaries, etc.  There is an actual payment that takes place, these are the costs that accountants use in their books.  Economists add implicit costs to this list, the opportunity costs.  These are costs that are not as evident, for example if a student gives up a salary of $10,000 per year to start a business the student has to consider the salary as an implicit cost.  In general any opportunity cost should be considered an implicit cost.  The sum of implicit and explicit cost gives economists the total cost of production.  By definition this cost will be higher than what the accountants would reflect.  (Accountants are not as clever as economists!  :).  The definitions in this tutorial are very brief, for a more complete definition please click on:  complete definitions  This will take you to a complete discussion of production by a firm.  It was written by a Palomar College economics teacher, Loren Lee.

The total cost curves show what the total cost of production is at any level of production.  There are three cost curves to analyze: total fixed, total variable and total cost.  Fixed cost doesn't change with production, the number of units produced doesn't affect this value.  Examples of this cost are property taxes and rent (the rent at George's Burgers remains the same regardless of the number of burgers cooked!)     In this tutorial we will deal with a firm that makes pants, our company will be called Funky Pants :)   Assume it is a poor Palomar College student, a fashion design major, who works at home and is renting a sewing machine for $36/month.  Rent is the only fixed cost :)  Furthermore assume that this analysis takes place in the Short run (a period of time when at least one input is fixed).  In our example the rent of the sewing machine remains the same throughout our analysis hence a fixed cost in the short run..

 Below is a chart with the number of units produced and next to it the graph that reflects this data. Click  here to review graphing:

Short-Run Production Costs of Producing Funky Pants

  Output: Total            
  FUNKY Fixed            
  PANTS Cost            
    (TFC) The cost of renting the sewing machine!          
  0 $36            
  1 $36            
  2 $ 36            
  3 $ 36            
  4 $ 36            
  5 $ 36            
  6 $ 36            
  7 $ 36            
  8 $ 36            
  9 $ 36            
  10 $ 36            

 

Remember that to graph the table you start with 0 pants and $36, then 1 pant and $36, etc. Since the cost doesn't change the line is horizontal. As the cost goes up or down the cost curve will also go up or down.  This is probably the simplest of all the cost curves!

 

The next cost curve is the Total Variable Cost which changes with the number of units produced, that is to say the higher the number of pants produced the larger the variable costs.  Sew more pants and you need more cloth, more zippers, more buttons, etc.  The production costs tend to be steep at first,  (for example, the period of time needed to learn the job) then as production increases costs decrease.  Economists call the former "increasing costs at an increasing rate".  Nice, ha?  Think about the first time you did a job, how efficient were you?  However as time progressed you got better at it.  This is reflected in the graph below:  the line starts steep and then flattens out a bit, ("costs increasing at a decreasing rate") then costs start increasing again. (back to "costs increasing at an increasing rate"!).  The shape of the Total Variable Cost shows this very important concept in economics, "diminishing marginal returns".  As more and more workers (variable cost) are hired to work with a machine (fixed input) the quantity and quality of production tends to decrease.  When the first units are produced, the workers are not very efficient; they are learning their respective tasks.  After a period of time the workers become very efficient and highly productive.  If production increases further they reach capacity and the costs start rising rapidly (say to buy a new machine).  This is what happens when workers start working overtime, costs are increasing rapidly.  Important to notice that the line starts at zero costs for zero units.

Output: Total
FUNKY Variable
PANTS Cost
  (TVC)  More production, more costs!
   
0 0
1 8
2 12
3 15
4 20
5 27
6 36
7 46
8 65
9 90
10 130

 

When the variable costs increase, for example if Funky Pants has to pay more for the cloth they use to produce their pants, the total variable cost curve will shift up.  Click the button and you'll see!

 

Finally we have the combination of the two cost curves above, the total cost curve.  Adding the two figures in the first table (total fixed cost plus total variable cost) we have the total cost.  See Table below:

Quantity Total Fixed Cost Total Variable Cost Total Cost Again higher costs will shift the curve up, roll your mouse over the chart and you will see the new graph with higher costs!
0
1
2
3
4
5
6
7
8
9
10

 

36
36
36
36
36
36
36
36
36
36
36

 

0
8
12
15
20
27
36
46
65
90
130

 

36
44
48
51
56
63
72
82
101
126
166

 

Place your mouse on top of the picture below and the graph shows the same effect as as above with the new costs (red numbers) reflected on the table:

Summary

The total cost tables and curves provide information regarding fixed costs, variable costs and the combination: total cost of production.  The fixed cost  remains the same over a period of time, it does not change with production such as rent.  Variable costs increase as more production takes place, however the rate of increase changes given the number of machines and the productivity of the workers, an example of this is the quantity of clothing used in making pants.  Graphically the fixed cost is a horizontal line, while the variable cost changes slope according to the rate of increase in the cost function.  Those students that have taken calculus may think in terms of derivatives as the rate of change in the costs of production.  The combination of fixed cost and variable cost result in the the total cost, graphically it is represented by a curve similar to the variable cost with the fixed cost added to it.  This results in a parallel shift upwards of the total variable cost. 

Total Fixed cost Total Variable Cost Total cost

Have you learned all there is to know about the total cost curves?  Check your knowledge with the worksheets below:

1) Complete the table below by calculating the missing data:

Quantity Total Fixed Cost Total Variable Cost Total Cost
0   0 300
1 300 75  
2   150 450
3     600
4 300 500  

2) Graph the cost curves for the table above.

3) Explain what would happen if fixed cost went up by $100.

4) Explain what would happen if variable cost went up by $25 at every level of production starting with unit 1.

5) Graph the total variable cost and total cost curves from number 4 above.

Yeahoo!  This is the end of the total cost curves tutorial.

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Lesson 2

 

This section discusses the cost per unit function, how much does every unit cost?

The Average Fixed Cost is the first cost per unit curve that we shall analyze.  As the name implies it is calculated by using the total fixed cost discussed previously and determining the average cost per unit.  Since we start with  the total fixed cost and spread this number amongst an increasing number of units, the AFC becomes smaller and smaller.  The formula takes the Total Fixed Cost and divides by the number of units, (Formula AFC = TFC/Q) no AFC when you produce zero units, hence the first coordinate is at 1 unit!  Below is a table and a graph of the AFC:

 

Short-Run Production Costs of Producing Funky Pants
A B F          
Output: Total Average          
FUNKY Fixed Fixed          
PANTS Cost Cost          
  (TFC) (AFC)          
    TFC/Q          
0 36 --          
1 36 36          
2 36 18          
3 36 12          
4 36 9          
5 36 7.2          
6 36 6          
7 36 5.14          
8 36 4.5          
9 36 4          
10 36 3.6          

 

As you can see from the graph above, the larger the number of units the lower the average cost per unit.  Check column F!  Starts at $36 at 1 unit (there are no averages at 0 units) and goes to $3.60 at the 10th unit.  Visualize what would happen if you produce a million units!  (The cost becomes very, very small) Suppose the cost goes up?  What do you think would happen?  Try to sketch it in a piece of paper or in your mind, and then compare with the animation below.

 

Click on the button below and you can see how the AFC curve moves up, showing that costs have increased.

The next cost curve is the Average Variable Cost, again as the name implies these data is obtained by taking the Total Variable Cost and dividing by the number of units.  Average Variable Costs start high, go down and after added production go back up, almost like a smile!  As production starts the work is not very efficient, after a while workers get better at their jobs and costs go down, eventually as production increases the costs of production increase, hence the shape of the curve. Remember no costs at Zero units, so the Average Variable Cost curve starts at one unit and continues at two units, three units, etc.  (Formula AVC = TVC/Q). Below is the table for the Total Variable Cost with an added column to reflect the Average Variable cost:

Output:
FUNKY
PANTS
 
 
 
0
1
2
3
4
5
6
7
8
9
10

 

Total
Variable
Cost
(TVC)
 
 
0
8
12
15
20
27
36
46
65
90
130

 

Short-Run
Average
Variable Cost
(AVC)
 
=TVC/Q
--
8
6
5
5
5.4
6
6.57
8.13
10
13

 

The same process works when the costs increase, the line will shift up to reflect the higher costs.  Click the button below and you will get the animation for higher Average Variable Costs:

Now that we analyzed Average Fixed Cost and Average Variable Cost we combine them to build the Average Total Cost, the combination of total fixed and variable, just like we did with the Total Fixed and Total Variable Costs.  There are two methods to obtain the Average Total Cost, the first one simple takes the AFC and AVC added together, the second one takes the Total Cost figures and divides by the quantity as we did before for the AFC and AVC.   (Formula ATC = AFC + AVC)  ) OR (Formula ATC = TC/Q).  Both methods are displayed below, notice the end result is exactly the same!

 

Short-Run Production Costs of Producing Funky Pants
A F G H  
Output: Average Short-Run Short-Run  
FUNKY Fixed Average Average  
PANTS Cost Variable Cost Total Cost  
  (AFC) (AVC) (ATC)  
     

 AFC+AVC

 
         
0 -- -- --  
1 36 8 44  
2 18 6 24  
3 12 5 17  
4 9 5 14  
5 7.2 5.4 12.6  
6 6 6 12  
7 5.14 6.57 11.71  
8 4.5 8.13 12.63  
9 4 10 14  
10 3.6 13 16.6  
 
     
A D H
Output: Short-Run Short-Run
FUNKY Total Cost Average
PANTS (STC) Total Cost
    (ATC)
   

 TC/Q

0 36 --
1 44 44
2 48 24
3 51 17
4 56 14
5 63 12.6
6 72 12
7 82 11.71
8 101 12.63
9 126 14
10 166 16.6
 
Drawing the chart shows some of the same patterns as before, costs start high, decrease and then start increasing again.  (Recall the concept of diminishing returns) 

Have you learned all there is to know about the cost per unit tables and curves?  Check your knowledge with the worksheets below:

1) Complete the table below by calculating the missing data:

Quantity Total Fixed Cost Total Variable Cost Total Cost Average Fixed Cost Average Variable Cost Average Total Cost
0 300 0 300 --- --- ---
1 300 75 375   75  
2 300 150 450 150    
3 300 300 600   100  
4 300 500 875      

2) Graph the per unit (last three columns) cost curves for the table above.

3) Explain what would happen to the per unit cost tables if fixed cost went up by $50.

4) Explain what would happen if variable cost went up by $30 at every level of production starting with unit 1.

5) Graph the average cost and average variable cost curves from number 4 above.

Yeahoo!  This is the end of the cost per unit curves tutorial.

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Lesson 3

Now we get into the most interesting and important cost curve, the Marginal Cost Curve. It is the additional cost of producing one more unit and later on will allow us to maximize profits.  Yeahoo!  I love profits $$$!  As the production of pants increase, determining the additional cost of producing one more pant is crucial since that information will help us decide whether to produce or not that particular pair.  In order to calculate the  Marginal Cost we calculate Total Cost between the previous unit and the current unit.  The table below calculates the Marginal Cost for Funky Pants:

 
A D E
Output: Short-Run Short-Run Marginal
FUNKY Total Cost Cost
PANTS (STC) (SMC)
     

 

The calculations start with the first unit, as the cost went from $36 to $44, the marginal cost of producing the first unit is $8 ($44-$36), for the second unit the cost is $4, and so on.  The arrows illustrate that the marginal cost is the additional cost of producing one more unit.  Suppose someone offers you $25 for the eight pair of pants, would you sell it at $25?  How much did it cost you to sew that particular pair? ($17, so sell!)  The graph below shows why the Marginal Cost is more challenging to understand, notice that the coordinates are not exactly at 1,2,3..units, they are graphed at 0.5,1.5,2.5, etc.  This is because the MC starts increasing as you start producing the units.  In this case imagine you got your cloth and you add a zipper, costs have increased yet you are not finished with the pair of pants.  In order to reflect that graphically economists graph the MC at mid point to account for the transition.  This is a bit confusing yet useful in drawing accurate graphs and arriving at accurate conclusions! 

 

 

As mentioned above graphing the marginal cost accurately is very important because this will help us determine important stages in production costs:

When the additional cost of producing one more unit (Marginal Cost) reaches its lowest point, the Average Total Cost is at its lowest also, hence graphically the intersection of MC and ATC reflect the lowest cost per unit that may be achieved with the present production structure at Funky Pants.  As stated earlier the intersection of MC and ATC reflect the lowest point of production, play animation. Let's review a complete set of numbers for the per unit cost of production:

Short-Run Production Costs of Producing Funky Pants
A E F G H      
Output: Short-Run Average Short-Run Short-Run      
FUNKY Marginal Fixed Average Average      
PANTS Cost Cost Variable Cost Total Cost      
  (MC) (AFC) (AVC) (ATC)      
0 -- -- -- --      
1 8 36 8 44      
2 4 18 6 24      
3 3 12 5 17      
4 5 9 5 14      
5 7 7.2 5.4 12.6      
6 9 6 6 12      
7 10 5.14 6.57 11.71      
8 17 4.5 8.13 12.63      
9 25 4 10 14      
10 40 3.6 13 16.6      

 

Notice the bold numbers highlight the fact that when producing 7 units, the Average Total Cost per unit is at its lowest point, Funky Pants should produce seven pants if they want to produce at the lowest possible cost!

Combining all per unit cost curves in one graph is very important and the results appear below, notice the intersections of Marginal Cost and both Average Total Cost and Average Variable Cost,  they represent very important production stages.

The intersection of Marginal Cost and Average Total Cost curve happens at 7 units, which tells us that the lowest cost of production is 7 pants, this would be the most efficient level of production at this stage of Funky Pants!  Notice in the table $11.71 is the lowest average cost of production at a level of  seven units. This is a very important rule: the intersection of the marginal cost curve and average total cost curve represent the lowest cost of production! Does this imply that we should stop production at this level to maximize profits?  Not necessarily!  This will be discussed in the profit maximization section of Microeconomics.  Another intersection that is very relevant for future discussions of profits is the intersection of Average Variable Cost and Marginal Cost Curves.  Again this discussion will be expanded in the next section of Microeconomics!

Practice your knowledge of the Marginal Cost Curve:

1. If the Total Cost of producing 98 burgers at "Junk-in-the-Bag" is $68, and the cost of producing 99 burgers is $68.95, what is the marginal cost of the 99th burger?  Why?

2. Complete the table below:

 Costs of Producing Snowboards

Output: Total Total Short-Run Short-Run
BOARDS Fixed Variable Total Cost Marginal
  Cost Cost (STC) Cost
  (TFC) (TVC)   (SMC)
0  $       1,000 0  $       1,000  
1  $       1,000  $            78  $       1,078  
2  $       1,000  $          128  $       1,128  
3  $       1,000  $          150  $       1,150  
4  $       1,000  $          200  $       1,200  $          50
5  $       1,000  $          259  $       1,259  
6  $       1,000  $          360  $       1,360  
7  $       1,000  $          480  $       1,480  
8  $       1,000  $          650  $       1,650  
9  $       1,000  $          900  $       1,900  
10  $       1,000  $       1,500  $       2,300  
       

 

3. Graph the Marginal Cost from number 2 above.

4. Given the graph below, estimate the lowest cost of production and the number of units produced at this cost:

 

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