Production Costs Worksheet--Answer Notes

Production Costs Worksheet--Answer Notes

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? Rugs. The workshop space. Labor.

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:

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:__rise/run = 2/1 =2

from 1 to 2 workers:___3

from 2 to 3 workers:___3

from 3 to 4 workers:___2

from 4 to 5 workers:___1

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. From zero to 2 workers. From 2 to 3 workers. From 3 to 4, and from 4 to 5 workers.

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:___ $ 80/2= $ 40

from 2 to 5 rugs:___ $ 80/3=$ 26.67

from 5 to 8 rugs:___$ 80/3 = $ 26.67

from 8 to 10 rugs:___$ 80/2 = $ 40

from 10 to 11 rugs:___$ 80/ 1 =$ 80

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.)