Production Costs Worksheet
Coretta leases a workshop, in which she weaves rugs from marsh grass she gathers
(for free) from a nearby riverside. She finds that if she works alone for a day, she can
weave two rugs. If she hires one additional worker, together they can weave 5 rugs
in a day, each specializing in some of the tasks. Adding a third worker also allows for
more specialization, bringing production up to 8 rugs. Adding a fourth worker adds
only 2 rugs to production, because there are no more gains from specialization to be
had. Hiring a fifth worker adds only one additional rug to daily production, because
now the workshop space is getting crowded.
a. What is the output in this example? What is the fixed input? What is the variable
input?
b. Complete columns (1) to (3) of this table, showing how number of workers is
related to the total and marginal number of rugs produced:
(1)
Quantity of
Labor
(Number of
Worker-Days)
0
1
2
3
4
5
(2)
Quantity of
Output
(Number of
Rugs)
(3)
Marginal
Return to an
Additional
Worker-Day
(Number of
Rugs)
(4)
Fixed
Cost ($)
(5)
Variable
Cost ($)
(6)
Total
Cost
($)
(7)
Cost of an
Additional
WorkerDay ($)
(8)
Marginal
Cost of
Production ($
per Rug)
--
--
--
c. On the graphing worksheet , sketch Coretta’s total product curve for rugs.
d. Find the slope (“=rise/run”) of the total product curve along each of the following
line segments:
from 0 to 1 worker:_____
from 1 to 2 workers:_____
from 2 to 3 workers:_____
from 3 to 4 workers:_____
from 4 to 5 workers:_____
Note that these numbers are the same as “marginal return.”
e. Are there ranges of production characterized by increasing returns? Constant
returns? Diminishing returns? Mark these on your graph.
f. Suppose that rent for the workshop space costs Coretta $50 per day (whether she
produces anything or not). Her cost for labor (including the opportunity cost of
“hiring” herself!) is $80 per worker per day. Complete columns (4) through (6) in
the table above, showing her fixed, variable, and total costs of producing various
numbers of rugs.
g. On the graphing worksheet , sketch Coretta’s total cost curve for rugs.
h. Find the slope (“=rise/run”) of the total cost curve along each of the following line
segments:
from 0 to 2 rugs:_____
from 2 to 5 rugs:_____
from 5 to 8 rugs:______
from 8 to 10 rugs:_____
from 10 to 11 rugs:_____
These numbers represent Coretta’s marginal cost of production, at each level of rug
production. Since it is the daily cost of employing one additional worker divided by
amount the additional worker contributes to daily production, you could also find
these by filling in Column (7) with the cost of each additional worker-day, and filling
in Column (8) by dividing Column (7) by Column (3).
i. On the graphing worksheet, sketch Coretta’s marginal cost curve for rugs.
(Technical Note: Plot the points on the segments between the horizontal axis values.
For example, the marginal cost of going from zero rugs to two rugs should be
graphed above an “x-value” halfway between zero rugs and two rugs--that is, 1 rug.
Likewise, the marginal cost of going from 2 rugs to 5 rugs should be graphed above
an “x-value” of 3.5 rugs.)