Copyright © 1985-2000 Samuel L. Baker

This tutorial introduces economics concepts of total cost, fixed cost, variable cost, and marginal cost.

Firms and institutions, whether for-profit or non-profit, use these cost concepts for pricing and output decisions. These concepts form the basis for much of cost accounting.

We'll use for illustration an imaginary firm, Joan's Home Care Services, which uses nurses, supplies, and machinery to maintain patients with a certain ailment. As a starting point, we assume that Joan's already knows what their total cost would be for maintaining any number of patients for a year.

In practice, developing that cost information requires considerable work. We assume that this work has been done.

- Total Cost
- is what it costs to operate at some particular rate of output.
- Total Cost
- is not the cost per item. That's the average cost, which we'll discuss in another tutorial.
- Fixed Cost
- Fixed Cost is the part of the budget that stays the same regardless of whether you produce a lot, a little bit, or even if you produce zero. Overhead, rent on buildings, and interest on loans are in fixed cost.
- Variable Cost
- is the rest of total cost, the part that varies as you produce more or less. Producing more adds to Variable Cost. Producing less reduces it.

Total cost can be divided into two portions: Fixed Cost and Variable Cost.

For those of you who like graphs, here is a graph
illustrating total, variable, and fixed cost for Joan's Home Care. In
this tutorial, we will be working with the numbers in this graph.

Which costs are fixed and which costs are variable depends on your time horizon. In what economists call the "short run," labor cost (staffing) might be fixed. A lab may have a certain number of technicians, for example. From day to day, its cost for materials might vary, depending on how many tests it does, but the labor cost is fixed. In the "longer run," labor costs might be variable, as the lab adjusts staffing to the demand for its tests, but costs for its facility (space and major equipment) would be fixed. In the "long run," the lab can change its space and equipment. No costs would be fixed in the long run.

For Joan's, we'll imagine an intermediate run, where labor and materials are variable costs, but overhead is not. (The cost numbers in the following tables are made up for illustrative purpose. They are not represented as realistic.)

Suppose that Joan's has done its accounting work, and has come up with these figures for what it costs Joan's Home Care to maintain various numbers of patients for a year. (Assume that patients sign one year contracts, so we don't have to bother with fractions of patients. This makes things simpler.)

Number of Patients Total Cost

0 $ 1000

1 $ 4500

2 $ 7500

3 $ 10000

4 $ 12000

5 $ 14500

6 $ 17500

7 $ 21000

8 $ 25000

9 $ 30000

How much is the fixed cost?

Now let's do variable cost. The variable cost is that portion of total cost that varies when the rate of output varies. In the table below, fill in the variable cost column.

To do this, click on a box in the Variable Cost column. Type a number, with no $ sign. Then press Enter. I'll let you know if you're right.

If you need hints, just enter a number that you know is wrong.

Do at least three of these, to be sure you have the idea.

That should be plenty about fixed and variable cost.

In practice, a firm would probably proceed in the reverse order from the way we did. It would understand that total cost is made up of fixed cost and variable cost. It would figure out what its fixed cost is and what its variable costs are at different rates of output. Then it would add the fixed and variable cost to get the total cost.

Here's the top part of the cost table, with a column added for marginal cost. I've left spaces between the lines for the marginal costs. This emphasizes that marginal cost is the difference in total cost between one output rate and another.

Click on an answer box. Type a number, with no $ sign. Then press Enter.

If you need hints, just enter a number that you know is wrong.

The Law of Diminishing Returns is an economics classic. It says: As you repeat doing something, each repetition becomes harder and/or less rewarding. The "returns" to your extra efforts "diminish," In our context here, diminishing returns would mean that marginal cost increases as Joan's adds more patients in a year. That's the opposite of what we have so far. So far, the "Law" of Diminishing Returns doesn't apply to Joan's. Instead, we have increasing returns.

Things change, though, in the next part of the cost table:

Please fill in these marginal costs.

By the way, when you figure the marginal cost, do you take the difference between the total costs or the variable costs?

Here's the table with all the variable and marginal costs:

You can reason through the answer to this one using words or using algebra.In words:

The marginal cost of changing from one rate of output to another is how much total cost increases when the output rate goes up. When the output rate changes, the fixed cost doesn't change. That's why it's called "fixed." The variable cost is what changes, so the difference in total cost is just the difference in the variable cost.

This means that marginal cost equals marginal variable cost. For example, suppose part of Joan's fixed cost is the cost of an advertisement in the Yellow Pages. That cost doesn't change when her company adds one more patient.In algebra:

This equation is true by the definitions of Total Cost, Fixed Cost, and Variable Cost:

i is the output rate. TotalCost(i) means the total cost at an output rate of i per unit of time.

TotalCost(i) = FixedCost + VarableCost(i) This equation is also true by definition. It has "i+1" where the above equation has "i":

TotalCost(i+1) = FixedCost + VariableCost(i+1) Subtract the first equation from the second, to get:.

In the subtraction, the FixedCost terms cancel each other out.

TotalCost(i+1) - TotalCost(i) = VariableCost(i+1) - VariableCost(i) Define MarginalCost(i+1) to mean TotalCost(i+1)-TotalCost(i). This is OK because the marginal cost is supposed to be the cost of adding 1 to the output rate.

Define MarginalVariableCost(i+1) similarly.

We can then rewrite the above equation as:

MarginalCost(i+1) = MarginalVariableCost(i+1) This equation says that marginal cost = marginal variable cost, which is what we sought to prove.

Number ofHere are those cost data in a graph.

Patients Total Cost Variable Cost Marginal Cost

0 $ 1000 $ 0

$ 3500

1 $ 4500 $ 3500

$ 3000

2 $ 7500 $ 6500

$ 2500

3 $ 10000 $ 9000

$ 2000

4 $ 12000 $ 11000

$ 2500

5 $ 14500 $ 13500

$ 3000

6 $ 17500 $ 16500

$ 3500

7 $ 21000 $ 20000

$ 4000

8 $ 25000 $ 24000

$ 5000

9 $ 30000 $ 29000

Total cost and variable cost are cumulative. That's why their graph lines go up and up. Fixed cost is not cumulative because it's -- well -- fixed at $1000, regardless of the output rate. Its line does not go up. Variable cost parallels total cost, always below it by $1000. Marginal cost on this graph is the difference in cost between the given output rate and the next lower one. Marginal cost dips for the first few patients, indicating increasing returns to scale. ("Scale" means size, which here means output rate.) After the fourth patient, diminishing returns to scale set in, and marginal cost per added patient rises. The total cost curve bends down a bit for output rates from 0 to 4, because the marginal cost is falling. For output rates from 4 to 9, marginal cost is increasing, so the total cost curve bends up a bit.

That's all for now. Thanks for participating!

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