Central Carolina Technical College Fixed and Variable Costs Questions Before addressing this question, but sure to have read Lecture 7a: Short-Run Unit Cos

Central Carolina Technical College Fixed and Variable Costs Questions Before addressing this question, but sure to have read Lecture 7a: Short-Run Unit Cost

Instructions:

1. Provide an example of a real or hypothetical business. (US Based Business)

2. Give examples of fixed costs and variable costs for this business.

Please answer in at least 3 or more paragraphs. This is a discussion board type post. See the Lecture 7a attached Average Total Cost (ATC) is found by dividing total costs by the number of units
of output. ATC = TC / Q = AFC + AVC
Marginal Cost (MC) is the extra cost associated with producing one more unit of
output. Marginal cost is found as the change in total cost for a given change in
output. MC = TC / Q
UNIT COSTS
AFC, AVC, ATC and MC are all examples of “unit costs”. That is, these are
different ways of calculating the cost of one unit of output. We will spend the
most time with ATC and MC, because these measures of unit cost are of the
most interest to firm’s decisions. We’ll also use AVC in a couple of applications.
We want to be able to characterize the way unit costs change with the level of output
produced. This will move us toward a better understanding of how profits change with
output.
Similar to the way we used graphs to illustrate total product, marginal product and
average product in the last unit, we can create graphs to illustrate how total, marginal
and average costs change with output.
Example:
Let’s assume that we have 2 inputs: labor (the variable input) and capital (the fixed
input).
Our monthly fixed cost (FC) is $200 (call this “rent”).
Our labor cost (VC) is $60 per worker per day
—
On the next page there is a table of numbers showing the relationship between Labor
units (L) and total output produced (Q). Use these numbers to calculate the values in the
missing columns.
You will notice that this table of numbers incorporates the principle of diminishing
marginal product that we learned in the last unit. If you are unfamiliar with this principle,
you should go back and read lecture 6 part 3 before reading further.
2
Using the definitions for each type of cost and the assumptions noted above, fill in
the missing data for the short-run costs of this firm.
L
0
1
2
3
4
5
6
7
Q FC VC TC AFC AVC ATC
0
5
12
21
28
30
30
28
TC
Q MC
The answers are on the next page… please try this on your own first!
Also, notice that the principle of diminishing marginal product is incorporated into the
first two columns!
You can quiz yourself on this principle:
Calculate the marginal product for each unit of labor.
What can we say about hiring here?
3
Completed cost table for our hypothetical firm:
L
0
1
2
3
4
5
6
7
Q
0
5
12
21
28
30
30
28
FC
200
200
200
200
200
200
200
200
VC
0
60
120
180
240
300
360
420
TC
200
260
320
380
440
500
560
620
AFC
40
16.67
9.52
7.14
6.67
6.67
7.14
AVC
12
10
8.57
8.57
10
12
15
ATC
52
26.66
18.09
15.71
16.67
18.67
22.14
TC
60
60
60
60
60
60
60
Q
5
7
9
7
2
0
-2
MC
12
8.57
6.67
8.57
30
There are a few things to notice about the data.
First, notice that the VC and TC increase as we produce more output. This should make
sense… we must spend more to produce more.
Next, notice that ATC, AVC and MC (3 unit cost measures) all first decrease and then
increase.
Why does this happen?
While you’re thinking about this, let’s see what this data would look like graphically…
4
First, plot TC, VC, and FC as a function of output.
Notice that since TC = FC + VC, to graph
the TC curve, all we have to do is add
$200 (FC) to each point on the VC curve.
Costs ($)
500
TC
400
VC
300
FC
200
100
0
5
10
12
15
20
21
28 30
25
units of output (Q)
Next, plot ATC, AVC and MC:
Notice that the point of
diminishing marginal product
corresponds to the minimum
point on the MC curve
Costs ($)
MC
ATC
AVC
0
5
0
1
10
12
2
15
20 21
3
25
28 30
units of output (Q)
4
5
units of labor (L)
5
Note: The graphs above are a bit smoothed out to show the relationships that we’re
interested in.
Hopefully you see that the “U-Shape” of the average cost curves is a result of the
principle of diminishing marginal product.
Unit costs are inversely related to productivity because rising productivity (i.e. when APL
or MPL are rising) means we’re getting more and more output for a given wage. This
implies lower costs per unit. When productivity is falling (i.e. when APL or MPL are
falling) we’re getting less and less output for a given wage. This implies higher costs per
unit.
Unit costs will be falling if productivity is rising and unit costs will be rising if productivity
is falling.
Specifically,
When MPL is rising MC is falling
When APL is rising AVC is falling
When MPL is falling MC is rising
When APL is falling AVC is rising
This inverse relationship can also be seen in the definition of Marginal Costs (MC):
MC = TC/ Q
Notice from the data above that Q = the change in output when labor changes by one
unit = MPL
Also notice that TC = how total costs change. Only variable costs change, hence TC =
the change in variable costs for a one-unit change in labor, which is equal to the wage
rate per worker ($60 in our example).
Hence, MC can be written as: MC = TC/ Q = wage/MPL
Because the wage is constant, if MPL is rising (before the point of diminishing marginal
product) then MC is falling. If MPL is falling (after the point of diminishing marginal
product) then MC is rising.
6
Summary of short-run unit cost curves:
MC, AVC, and ATC are “U-Shaped”.
The U-shape of short-run cost curves reflects the law of diminishing marginal product.
That is, unit cost curves are U-shaped because productivity curves are shaped like upsidedown U’s
Graphically, the relationship between unit costs and productivity looks like this:
output (Q)
Productivity
APL
MPL
0
1
2
3
4
5 Labor (L)
costs ($)
MC
0
1
2
3
4
AVC
Unit costs
5 Output (Q)
The maximum of MPL corresponds with the minimum of MC.
The maximum of the APL corresponds with the minimum of AVC.
The intersection of MPL and APL corresponds with the intersection of the MC and AVC
curves.
When productivity is rising (before the point of diminishing marginal product) then unit
costs are falling. When productivity is falling (after the point of diminishing marginal
product) then unit costs are rising.
** next we’re going to discuss long-run cost curves, and we’re going to see that they are
U-shaped also, but for a different reason.
7
Topics in this lecture:
1. Categories of costs
2. The relationship between productivity and unit costs
3. The shape of short-run unit cost curves
To figure out the best (i.e. profit-maximizing) quantity of a good or service to produce,
we need to understand how revenue and costs change with output. Our goal for this
unit is to explore how costs change with output.
Let’s start with some definitions:
Fixed Costs (FC) are also known as “overhead”. These are the costs associated
with running a firm that do not change with the level of output. Fixed costs are
the costs associated with fixed inputs. Examples of fixed costs include rent and
management salaries.
Variable Costs (VC) are costs that do change with the level of output. Variable
costs are the costs associated with variable inputs. Examples of variable costs
are fuel, electricity, labor costs, and materials costs.
Total Cost (TC) is the sum of all costs, both fixed and variable. TC = FC + VC
Total Cost = Fixed Costs + Variables Costs
Average Fixed Cost (AFC) is the fixed costs divided by the number of units of
output. AFC = FC/Q
Average Variable Cost (AVC) is variable costs divided by the number of units of
output. AVC = VC/Q
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