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.
Total cost can be divided into
two portions: Fixed Cost and Variable Cost.
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.
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?
If
your answer is $1000, you
are right! The fixed cost is the cost you
have even if you produce
nothing.
Total
cost at 0 is $1000.
The fixed cost is therefore
$1000.
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, note the values of Fixed
Cost and
Variable Cost for the present example.
| Number
of Patients |
Total
Cost |
Fixed
Cost |
Variable
Cost |
| 0
|
1000
|
1000
|
0
|
| 1
|
4500
|
1000
|
3500
|
| 2
|
7500
|
1000
|
6500
|
| 3
|
10000
|
1000
|
9000
|
| 4
|
12000
|
1000
|
11000
|
| 5
|
14500
|
1000
|
13500
|
| 6
|
17500
|
1000
|
16500
|
| 7
|
21000
|
1000
|
20000
|
| 8
|
25000
|
1000
|
24000
|
| 9
|
30000
|
1000
|
29000
|
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.
Marginal Cost: Now
let's introduce marginal
cost. Marginal cost is the difference
in total cost between one rate of output
and another. Usually, unless stated otherwise, the marginal cost
is the change
in cost that results from changing the output by one unit.
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.
Just
do a mental calculation
for the values of Marginal Cost in the shaded boxes in the table below
(& check your answers
in this table):
| Number
of patients |
Total
Cost |
Variable
Cost |
Marginal
Cost |
| 0
|
1000
|
0
|
|
|
|
|
|
|
| 1
|
4500
|
3500
|
|
|
|
|
|
|
| 2
|
7500
|
6500
|
|
|
|
|
|
|
| 3
|
10000
|
9000
|
|
|
|
|
|
|
| 4
|
12000
|
11000
|
|
Check your answers in this
table:
| Number
of 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
|
|
Interlude on the Law
of
Diminishing Returns:
So
far, the marginal cost has
been falling as output has been rising. The fourth patient added in a
year
costs Joan's much less than the first patient. Does this illustrate the Law of
Diminishing Returns?
Answer in “Yes” or
“No”…….
If your answer is
“No”, you are
Correct! - Marginal cost is falling, not
rising. The return from more effort is
increasing.
If your answer is
“Yes”, you
are Wrong! - Marginal cost is falling,
not rising. The return from more effort
is not diminishing.
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:
Just
do a mental calculation
for the values of Marginal Cost in the shaded boxes in the table below
(& check your answers
in this table):
| Number
of patients |
Total
Cost |
Variable
Cost |
Marginal
Cost |
| 3
|
10000
|
9000
|
|
|
|
|
|
|
| 4
|
12000
|
11000
|
|
|
|
|
|
|
| 5
|
14500
|
13500
|
|
|
|
|
|
|
| 6
|
17500
|
16500
|
|
|
|
|
|
|
| 7
|
21000
|
20000
|
|
Check your answers in this
table
:
| Number
of patients |
Total
Cost |
Variable
Cost |
Marginal
Cost |
| 3
|
10000
|
9000
|
|
|
|
|
|
2000
|
| 4
|
12000
|
11000
|
|
|
|
|
|
2500
|
| 5
|
14500
|
13500
|
|
|
|
|
|
3000
|
| 6
|
17500
|
16500
|
|
|
|
|
|
3500
|
| 7
|
21000
|
20000
|
|
Second Interlude on
the Law of
Diminishing Returns:
The
seventh patient in a year
adds more to Joan's costs than the fourth one did. Does this illustrate
the Law
of Diminishing Returns?
Answer in “Yes” or
“No”…….
If your answer is
“Yes”, you
are Correct! - We had increasing returns
at first.
Now
we have diminishing
returns.
Increasing
marginal cost =
Decreasing returns.
Decreasing marginal cost =
Increasing returns
If
your
answer is “No”, you are
Wrong!-
Increasing
marginal cost = Decreasing returns.
Decreasing marginal cost =
Increasing returns
By the way, when you figure the
Marginal Cost, do you take the difference between the Total Costs or
the Variable Costs?: 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.
Here's
the table with all the Variable and Marginal Costs:
| Number
of 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
|
|
Here
are those cost data in a
graph.
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!
|