A Fun Look at Economics and the Parabola
Goal: Students will simulate a factory that has the ability to add workers but can not add capital resources. Students will create a product called Nutterflutters in the class. The production process of the product will be analyzed mathematically.
Background information for the teacher: All CTE areas include an element of business and how to be successful in the world of work. In business, seldom are all of your resources unlimited and usually small changes are put into place to increase production (profits). If the marginal benefits (profits) are greater than the marginal (additional) costs, then the change was successful. Some resources such as additional labor can be added (temporary or long term) easily (relatively inexpensive investment) while other resources take planning and substantial ongoing expense. For example, expensive modifications/additions to floor space in a factory or additional production machinery may be cost prohibitive or may require extensive long range planning. We will be looking at The Law of Diminishing Marginal Returns which predicts that labor productivity will eventually fall as you add additional (marginal) workers to the production process, while keeping other resources fixed.
Materials needed: 1 large jar of peanut butter, 1 large jar of marshmallow cream, 1 box of graham crackers, 2 plastic knives, paper plates, and a roll of paper towels.
Time to complete activity: 45 minutes
Process:
1. Let students know that you are going to examine the Law of Diminishing Marginal Returns from economics and how it affects business decisions. Model at a desk/table how to make the Nutterflutter snack (I have heard them called peanut smores, flutternutters, etc). Let them know they will be eating the products at the end of the activity.
2. How to make a snack: Spread out 2 – 4 paper towels on the table. The paper towels represent the work area (factory space) and the work can not be on the bare table (health codes). Break a large graham cracker into fourths (small rectangles). Spread peanut butter on a graham cracker using a knife (must use a knife). Spread marshmallow cream on the other graham cracker using the other knife (must use a knife for “health codes”). Stack the 2 rectangle graham crackers to make a sandwich and then place it on the paper plate (represents your warehouse).
3. Choose a student (or two) to be quality control inspectors. Discuss what is a “good” snack and what would be rejected. Choose another student to be the timekeeper.
4. Select a student to be the worker at the factory. He/she will be making the snacks. He/she is to make as many complete snacks as possible in 1 minute. When the time is up, the inspector(s) will inspect the products to decide if they pass quality control. Count the number of completed snacks that pass inspection and record in the production table. Unacceptable ones are not to be counted. Marginal output is the number of additional products produced because another worker has been added. See the table below for an example of how to calculate marginal output.
Production Table
# workers.....# snacks produced.........................Marginal Output
.......0............................0............................................... N/A
.......1..................3 as an example..............................3 as an example
.......2..................7 as an example............................. 4 as an example
.......3
.......5
.......8
......etc
Your second worker added 4 more Nutterflutters, called the marginal output.
5. Select an additional student to join the already employed student (there are now 2 people on the production line). Remove the previous snacks made and replace with an empty paper plate. Students can not expand the work area (can not add paper towels), or use additional knives….remember the resources are fixed…the only variable is the number of workers. They are to repeat step 4 above by adding another worker.
6. Continue adding workers, being sure not to increase work area (paper towels represent the floor of the factory) and do not increase the number of knives or supplies. Continue adding students until the marginal output begins to drop or perhaps even go negative.
7. Graph the number of workers and marginal output. This should approximate a parabola. If your data is poor, be ready to adjust as needed. Extensions include writing the equation of a parabola, predicting using your equation, and general terminology.
8. Questions: How did specialization/division of labor/assembly line affect the production? Were the additional workers lazy? In this example, when would the factory hire and when would they quit hiring?
This activity has been around for a long time….done differently with different products produced. So, if you have done something similar, I do not want you to think I am taking credit for the creation of this activity. It is a lot of fun, and gives a real life example of the use of quadratics.
