Applying the Law of Diminishing Marginal Productivity
Introduction:
The importance of marginal analysis to economic reasoning cannot be overstated. While students often intuitively understand the diminishing satisfaction a consumer may derive from acquiring more and more of the same good or service, they may have more difficulty understanding how marginal analysis is equally important in production decisions such as hiring workers or buying additional resources, or in large scale consumption decisions like how much pollution clean up we, as a society, are willing to purchase.
Concepts:
- opportunity cost
- marginal cost
- marginal benefit
- diminishing marginal productivity
Economic Content Standard:
Standard 2 - Effective decision making requires comparing the additional costs of alternatives with the additional benefits. Most choices involve doing a little more or a little less of something; few choices are all-or-nothing decisions.
Lesson Description:
In this paper-and-pencil exercise, students take the role of a farmer who must decide how many times to spray a strawberry crop. In the process, they learn to apply marginal analysis, and discover the law of diminishing marginal productivity - often referred to in conversation as the "law of diminishing returns."
Time Required: 1/2 class period
Materials:
overhead transparencies
student handout - "Spraying Strawberries" chart
Procedure:
- After teaching a lesson on
diminishing marginal utility, ask students to hypothesize other
ways in which marginal analysis might be used. (Hint: Help to
guide the discussion by reminding students that marginal deals
with "the next unit," or "more of something,"
or "an additional amount."
- Encourage students to think of examples in which a producer, rather than a consumer, must think about "more" - i.e. how does the restaurant manager know whether to hire another waiter or waitress?
- Display Overhead #1 and ask students how they would solve the farmer's problem. (Accept several answers and list them as hypotheses.)
- Distribute "Spraying Strawberries" chart handout to individual students or pairs of students. Demonstrate how to fill out the marginal benefit and marginal cost columns by doing the first two entries. Then let students complete the columns on their own.
- Review the results and then ask how many hires the farmer should pay for. (Accept several answers and require that students give reasons to support their answers. Insist that they use "marginal" in their explanations.)
- Using the overhead, direct students to the MB-MC column. Ask students to explain what this column tells us. (The additional income the farmer earns because his willingness to pay for the spraying increases the productivity of his strawberry field. Value of the extra strawberries produced - cost of the hire.)
- Ask students to fill in the column and to use the results to decide which of the hypotheses in question #4 is correct.
- Review with students the Law of Diminishing Marginal Productivity.
- Extensions: Change the parameters
of the problem so that students can practice applying the principle.
- Suppose the plane owner charges $75 per 5 passes? (2 hires - on the third, the farmer would lose $5)
- Suppose the plane owner charges $50 to show up and $50 per 5 passes; now how many passes should the farmer pay for? (The maximum benefit doesn't change, it's still at 5 hires, but the farmer's gains are only $80.)
- Transfer: Ask students to
apply the Law of Diminishing Marginal Productivity to other
situations. For each example, identify:
- the marginal benefits,
- the marginal costs,
- the point at which MB=MC
- Insulation in the attic
- Bombing in VVWII
- Face Lifts
- Seat Belts
- Proof-reading
- Pollution Clean-up
(Sample acceptable answer: The marginal benefit is measured in the savings on the heating bill for each additional unit of insulation. The marginal cost is the price of the unit of insulation. MB=MC at which the electricity savings equals the cost of the unit of insulation. Beyond that point, it is not worthwhile to buy more insulation.)
overhead transparency
Spraying Strawberries:
A Producer Uses Marginal Analysis
A strawberry farmer plans to spray his fields to reduce mildew.
Here is the information the farmer has:
- Area: the farmer has 100 acres planted in strawberries
- Mildew kills strawberries; aerial spraying reduces or eliminates mildew
- The local crop duster makes 5 spraying passes per hire
- Each hire costs $50
How many hires should the farmer pay for? How do you know?
What other information might the farmer want to have to help him make his decision?
overhead transparency and student handout
Spraying Strawberries Chart
|
Number of Hires |
Total Benefits (TB) value of crops saved |
Marginal Benefits (MB) value of additional crops saved |
Marginal Cost (MC) cost of an additional hire |
MB-MC |
|
1 |
$100 |
$100 |
||
|
2 |
$200 |
|||
|
3 |
$270 |
|||
|
4 |
$330 |
|||
|
5 |
$382 |
|||
|
6 |
$420 |
|||
|
7 |
$450 |
|||
|
8 |
$460 |
|||
|
9 |
$460 |
|||
|
10 |
$455 |
teacher guide to Spraying Strawberries chart
|
Number of Hires |
Total Benefits (TB) value of crops saved |
Marginal Benefits (MB) value of additional crops saved |
Marginal Cost (MC) cost of an additional hire |
MB-MC |
|
1 |
$100 |
$100 |
$50 |
$50 |
|
2 |
$200 |
$100 |
$50 |
$50 |
|
3 |
$270 |
$70 |
$50 |
$20 |
|
4 |
$330 |
$60 |
$50 |
$10 |
|
5 |
$382 |
$50 |
$50 |
$2** |
|
6 |
$420 |
$38 |
$50 |
($12) |
|
7 |
$450 |
$30 |
$50 |
($20) |
|
8 |
$460 |
$10 |
$50 |
($40) |
|
9 |
$460 |
$0 |
$50 |
($50) |
|
10 |
$455 |
($5) |
$50 |
($55) |
** Total of MB-MC = $132 (point of profit maximization)
overhead transparency
Applying the Law of Diminishing Marginal Productivity.
For each example, identify:
- the marginal benefits
- the marginal costs
- the point at which MC=MC
- Insulation in the attic
- Bombing in W.W.II
- Face Lifts
- Seat Belts
- Proof-reading
- Pollution Clean-up
Copyright © 1999 Foundation
for Teaching Economics
Permission granted to copy for classroom use.