krugman_mods_3e_irm_micro_econ_mod21

Module
21
The Production Function
Module Objectives
Students will learn in this module:
• The importance of the firm’s production function, the relationship between
quantity of inputs and quantity of output.
• Why production is often subject to diminishing returns to inputs.
Module Outline
Opening Example: The example describes why European farmers are more productive
than U.S. farmers in producing wheat: European government policies provide incentives
for using more inputs, and with more inputs comes increased productivity.
I.The Production Function
A.Definition: A production function is the relationship between the quantity of
inputs a firm uses and the quantity of output it produces.
B.Inputs and outputs
1. Definition: A fixed input is an input whose quantity is fixed for a period and cannot be varied.
2. Definition: A variable input is an input whose quantity the firm can vary
at any time.
3. Definition: The long run is the time period in which all inputs can be
varied.
4. Definition: The short run is the time period in which at least one input is
fixed.
5. Definition: The total product curve shows how the quantity of output
depends on the quantity of the variable input, for a given amount of the
fixed input.
6. The slope of the total product curve is not constant. The slope of the total
product curve is equal to the marginal product of the variable input.
a.Definition: The marginal product of an input is the additional quantity of output that is produced by using one more unit of that input.
b. Marginal product of labor
or
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=
Change in quantity of output
Changge in quantity of labor
MPL = ∆Q/∆L
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the production function
7. Definition: There are diminishing returns to an input when an increase
in the quantity of that input, holding the levels of all other inputs fixed,
leads to a decline in the marginal product of that input.
a.Diminishing returns only holds if the quantity of all other inputs is
fixed.
Teaching Tips
The Production Function
Creating Student Interest
A good starting point is to talk about the costs of owning a car. Assume that the car is a
fixed input while it is in the garage and a variable input when you drive it. Ask students
to think about the fixed cost of owning a car (as it sits in the garage) and the variable
costs of owning a car (as you drive the car). The fixed costs are depreciation and registration fees, and the variable expenses are gasoline and maintenance.
Ask students to brainstorm the fixed and variable inputs used at a fast-food restaurant
or at the student bookstore. List them on the board.
Presenting the Material
Use this example of a fast-food restaurant to illustrate the concept of a production function.
Use the size of the store as the fixed input and the number of workers as the variable input.
Quantity of labor (workers)
0
1
2
3
4
5
6
Total production of hamburgers per hour
Marginal product
of labor
0
5555
12065
19070
23040
24010
2455
This example of a production function shows the total output of hamburgers given the
addition of workers. Diminishing marginal product occurs after the third worker. The
total production function rises at an increasing rate through the third worker and rises
at a slower rate after the third worker. Explain that this happens due to crowding. Plot
the total product curve and the marginal product curves on two separate graphs.
Common Student Pitfalls
• What’s a Unit? Students can be confused about how to measure a unit of labor.
For example, labor can be measured in hours, days, weeks, or years or as the number of workers. Make sure students understand that the units used to measure
labor do not affect the analysis—as long as you are consistent in the units you
select.
• Marginal versus total product and diminishing returns. Make clear to the
students the distinction between declining marginal product and declining total
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the production function
product. Diminishing returns sets in when there is a decrease in the rate at which
total product increases (not a decrease in total product). So, total product may continue to rise with diminishing returns. It just rises more slowly.
Case Studies in the Text
Economics in Action
The Mythical Man-Month—The title of this EIA is also the title of a book published in
1975. The book applies the concept of diminishing returns to the writing of computer
software.
Ask students the following questions:
1. How does the law of diminishing marginal product apply to the writing
of software? (It was found that doubling the number of programmers did
not proportionately reduce the time necessary to complete a project.)
2. How did the title of the book The Mythical Man-Month originate? (It was
found that a project that was possible for one programmer to produce
in 12 months could not be accomplished by 12 programmers in one
month.)
3. How does the nature of programming lead to diminishing returns?
(Programmers must coordinate their work with all the other programmers: A greater quantity of programmers leads to an increase in the time
spent communicating with everyone instead of writing code.)
Activities
Producing Successful College Students (3–5 minutes)
Pair students or form into teams of four. Ask them to list all the inputs on a college
campus which are used to “produce” successful college students. In the “short run,”
which inputs are “fixed”? which inputs are “variable”? (Plant size, such as the number
of classrooms, is the fixed input. As the number of registered students increases, the
number of instructors needed—a variable input—increases.)
Production at a Fast-Food Restaurant (3–5 minutes)
Ask students to list the fixed and variable inputs at a typical fast-food restaurant.
How has the company attempted to produce efficiently during busy times of the day? What
technological changes has the company added to achieve a more efficient production? For a
follow-up assignment ask students to interview a manager of a fast-food restaurant and ask
what production problems occur. Ask the manager what amount of ham­burger production
is efficient and what quantity would be highly inefficient to produce.
“Grow Rice on a Chalkboard” (10–20 minutes)
(Adapted from Classroom Activities by Charles Stull, Dryden Press, 2001.)
“Grow Rice on a Chalkboard” is a short simulation that illustrates the principle of
diminishing marginal product. On the board, draw two rectangles, 2 × 3 feet each. Select
two volunteers to act as farm managers and draw two equal-sized rectangular areas on
the chalkboard, approximately 2 × 3 feet. These rectangles are the farm on which they
will “grow” rice by writing the word RICE. Before they start producing, they must run to
the back of the class to get a slip of paper from you that says LOAN on it. They then run
to the board and start writing RICE in the same size, in a 30-second period. In the next
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the production function
round, the managers can hire one worker from the class. The game is played repeatedly,
adding another student each period. Track total output and the quantity of labor on the
board as the game proceeds. It becomes increasingly too crowded to produce the rice
efficiently. A typical result might be as follows:
Labor
Total Output
00
13
215
325
432
533
Have the class calculate the marginal product and determine when diminishing marginal
product began.
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