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The
Importance of Money and Prices with a Brief History of the Calculation Debate |
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Three
Dimensional Look at The Production Function and Isoquants |
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Production
Explaining the Production Process
Salvatore Schiavo‑Campo, Economic Research Services
Ask if anyone has a pencil to give you, and make a great show of asking whether the student can spare it. Then visibly break the pencil in half, return the half with the point still on it to the student, hold up the other half, and ask "What is this?" To the answer: "A broken pencil", the rejoinder is: "It is more useful to think of this object as materials, wood, lead, etc." Go on to point out that eventual production of a pencil is impossible without materials, and proceed to discuss natural resources as a factor of production.
Next, place the object on the desk and say: "Let us conduct a brief experiment. For the next 30 seconds everyone focus on this object, concentrate very hard, and `think pencil.’” Those 30 seconds will go by slowly, with titters, bored looks and shifting of chairs, but will lastingly emphasize the simple fact that‑‑as you will say to your students: "Production does not occur by thinking very hard, by prayer, government decree, or divine intervention. Production requires the conscious application of human effort to resources of various types."
You may then, with whatever embroidery is suitable to your temperament and your students, point out the necessity of human effort and use that as an opening to discuss labor as a factor of production. Then point out that‑‑while teeth and nails might sharpen the object sufficiently to write with it‑‑a pencil sharpener shortens that process and makes it enormously more efficient, and go on to discussing the economic meaning of capital. Finally, note that only by accident would an infant succeed in producing a pencil and a pencil sharpener from the materials at hand, no matter how much "labor" he put into it. And use this as the opening to introduce the subject of technology. (The simplest conclusion is to return to the unfortunate student, with an appropriate flourish and with thanks, the useless broken half of the pencil, provided that the student has a sense of humor.)
Diminishing Marginal Productivity in Basketball
Sharon K. Carson,
Basketball is very popular in this area of the country. A number of my students played basketball in high school and/or are playing it in college. I told the class to suppose that our college had a basketball game in which our coach was allowed to add an extra player while the other team was limited to the usual five players. Since our team would have six players to their five, we would probably score more baskets. Now suppose that our coach added another, and another, and another. Up to a point, each player would help us score more points (more than just five players could score.) As more and more players were added, however, we would benefit less and less. The basketball floor would become overcrowded. Players would fall over each other and eventually the total number of baskets scored would diminish.
The Law of Diminishing Returns
Daryl Gruver,
To introduce the law of diminishing returns, the professor asks for three student volunteers to begin a game in which each person attempts to raise the most corn. Each student is assigned a 3'x3' section of chalkboard and seven pieces of chalk (about 1" long). They are told that the chalkboard represents their land area and that they raise corn by simply writing the word corn on the chalkboard. The word corn must be legible to the other members of the class. The students are given 15 seconds to raise as much corn as possible. At the end of the 15 second growing season, the corn is counted and recorded for each country. Then the population of each country is doubled by adding a second person. The process is repeated. The game continues with the doubling of the population to four and then to eight. The law of diminishing returns usually begins to be experienced at this time. The land area becomes crowded and the chalk supply is inadequate, illustrating what happens when additional units of a variable resource are added to fixed resources.
Ralph O. Gunderson, University of Wisconsin-Oskosh
This is a variation of the "Too many cooks spoil the broth" story that is frequently told to illustrate the law of diminishing marginal returns. With some not‑too‑difficult‑to‑do pantomime, I manage to perk up student attention and even evoke some laughter if I'm having a good day.
The object of the pantomime is to pretend to be "making up my bed" in the morning. I begin by telling my students to think of fixed factors. The number of people making up the bed is the variable factor of production. The desk or table that is in the front of the classroom is my simulated bed. I then pretend to make up the bed by myself (one unit of labor). I demonstrate with some silly motions all the different little tasks that I must complete, such as fluffing the pillows, pulling up the covers, running around the foot‑end of the bed to straighten out a wrinkle on the other side, making sure the bedspread hangs evenly, etc., to make the bed.
Once finished, I announce that it took, for example, 4 minutes to complete the job. I then "hire" a phantom worker to help me do this job again. Through pantomime it is demonstrated that this second worker makes it possible to make the bed in 1 minute thus saving 3 minutes. A third worker reduces work time to 30 seconds thus saving 30 seconds. However, when a fourth worker is hired, pantomime pillow fights break out among the workers and required time increases.
This activity is designed to illustrate the advantages of specialization of labor and the accompanying ranges of increasing and then diminishing returns to a variable factor of production which is employed in different combinations with a set of fixed factors of production.
McDonald's and the Law of Diminishing Marginal Returns
Daniel P. Schwallie,
When introducing diminishing marginal returns, I find it most fruitful to use an example familiar to nearly all students: a McDonald's hamburger outlet. The facility itself, with its tables, parking lot, cash registers, grills, and fryers is the short‑run fixed plant and equipment. The long‑run is the time it would take to expand the facility or move it to a new location. To these fixed factors, McDonald's must add workers before it can produce hamburgers. The number of labor hours used can be readily changed to produce different quantities of hamburgers, so it is quite clear to students that labor is the variable factor of production. (I usually note that the all‑beef patties, pickles, sauce and sesame‑seed buns are also inputs into producing hamburgers to make the example realistic. However, I assume the McDonald's franchise has unlimited access to these inputs at constant per‑unit costs.)
Besides the fact that students are generally very familiar with the details of a McDonald's franchise, this example is particularly well suited to explaining diminishing returns because the labor used is quite homogeneous and the labor market is reasonably close to being purely competitive. Students quickly grasp that diminishing returns result, not because of varying labor quality, but because of the increasing mismatch between the quantities of fixed and variable factors as the quantity of labor employed is increased. I begin by supposing there is only one worker doing all the jobs: taking orders, cooking, packing and making change. I then point out there are initially increasing returns from hiring a second worker due to specialization of labor which is then possible. I continue to discuss the specialization of additional workers until it is clear that the marginal product of additional workers must be declining and diminishing returns have set in. Additionally, the instructor can discuss negative marginal productivity if the number of workers is continually increased until they are tripping over one another. The instructor can also introduce the idea of capacity by explaining that the McDonald's facility is designed to optimally employ a specific number of workers. I use a numerical example of the short‑run production function in terms of hamburgers per hour to construct total product, marginal product and average product schedules. These are then used to derive U‑shaped marginal cost and average variable cost schedules.
Athletes On Steroids and The Law of Diminishing Returns
By Gregg Davis,
Why do some apparently successful athletes, such as sprinters, football players and body builders, resort to illegal steroid use?
In all areas of athletic endeavor, training during the early stages can significantly enhance athletic performance, whether through speed, strength, or a psychological edge. Weight lifting, for example, allows one to significantly increase muscle mass and weight lifting abilities just months after initial training begins. The rewards are obvious--bigger muscles and more weight lifted. But continued training eventually contributes less and less to overall performance. The muscles cannot grow forever, and limits to weight lifted begin to emerge. Athletes have now entered the economic range of athletic training called diminishing returns. Additional training only marginally contributes to enhanced athletic performance.
In a futile attempt to defy the law of diminishing returns, some athletes turn to pharmaceutical supplements, such as steroids. Steroids initially, but only temporarily, afford athletes an opportunity to again reap the rewards of continued training (if they are able to pass drug tests and avoid the growing legal pitfalls of using these substances.) But eventually, diminishing returns set in once again, only now there are no escape routes left for the athletes to increase their performance. Continued steroid often eventually pushes athletes into a region of negative returns, where severe damage to the body manifests itself (e.g., Lyle Alzado).
Diminishing Marginal Productivity
Ralph T. Byrns
To illustrate how marginal products of labor diminish, suggest that if the last worker hired makes the beer run, the resulting popularity with coworkers may not be reflected in much extra production. Any number of activities show how problems of congestion emerge as more and more workers are hired: too many cooks in a kitchen, finishers at a car wash, or shovel wielders in a ditch. And imagine the problems if more and more lecturers tried to simultaneously spread their pearls of wisdom before a single audience.
The Law of Diminishing Returns: A Simple Demonstration
Terry D. McCraney,
I use a simple example to explain the law of diminishing returns to students‑‑sweeping the classroom floor. I usually start by stating the law as simply as possible. Then I tell the class that we have the job of sweeping the floor. All students agree that they are interchangeable when it comes to sweeping. They can all sweep and all can sweep equally well. I ask them how to measure our efficiency, if all sweep equally well. The general response is that we can measure efficiency in terms of time. Then I explain that we have four brooms and I will choose people to serve as sweepers. I choose the first sweeper and tell him it will take 60 minutes to do the job. The use of 60 minutes is for easy division. If you must, you can remind the students that the job was never done before so we have no idea how long it will take to complete the job. A second student is chosen and I ask how long it will take with two sweepers. The response is thirty minutes. Questions may be asked to explain the thirty minute time. After a third sweeper is added the time falls to twenty minutes. A fourth sweeper brings the time to fifteen minutes. Then I add a fifth sweeper and ask for the time. Twelve minutes will be given as the logical answer. Now I explain that twelve minutes is incorrect, and that it will take twenty‑four minutes. I ask the students to explain why it took longer with five sweepers than with four. Most of the class will quickly point out that we only have four brooms. Then I restate the law of diminishing returns stressing that sweepers are inputs, brooms are the fixed factors, and the amount of time reflects marginal returns.
The newly learned concept can now be reinforced by standard analysis, production examples, and graphing.
Production Principles and "Mock" Tests
Roger H. Goldberg,
To provide my students with hands‑on experience with the principles of specialization and division‑of‑labor, I divide the class into groups A and B for one class period with the following instructions: to make‑up a mock examination consisting equally of multiple‑choice, matching, true‑false and fill‑in the blank type questions. Question content must draw from both microeconomics and macroeconomics. Students in Group A must work alone; each student individually develops a complete examination. Students in Group B are told that they may coordinate their production efforts by dividing into smaller groups to specialize on question formats and area. The "mock" tests are then collected after a fixed time and the output and quality of questions compared. In addition to highlighting the desired production principles, students have enjoyed the review opportunity!
The Importance of Money and Prices with a Brief History of the Calculation Debate
Jim M. Cox,
After giving the students sample data in which they calculate average product and marginal product from the quantity of inputs and total product, and then graph TP, AP, and MP, I ask the students which quantity of output should be produced. A number of responses are usually forthcoming--the greatest output level, the output with the highest marginal product, the output with the highest average product, etc.
This set of responses gives the instructor the opening to bring forth the fact that a rational answer cannot be made. A physical relationship between input units and output units is meaningless without knowing the relative values of the inputs and outputs. Therefore, in an economy with an absence of money and prices to guide decision makers, rational calculation is lost.
Then bring in the fact that the original socialist theories included abolishing money and prices and that this set off the calculation debate between Mises and Hayek and the socialist theoreticians in the 1920s and 1930s. This also allows the instructor to make the point that we are seeing socialist societies confirm this theory in their practice of encouraging more reliance on market prices and less on centralized planning.
Diminishing Returns and Fixed Inputs
Joseph E. Pluta, St. Edward's University
As a variable resource (say labor) is added to a fixed resource (say land), total product eventually increases by smaller amounts. This familiar definition of the law of diminishing marginal returns, when illustrated with appropriate examples, is easily grasped by most students. Questions often arise, however, about timing. Why, for example, do diminishing returns appear to set in at lower levels of output in some production processes than in others? Detailed discussion of relative input mix and stages of production may be useful in answering such questions, but I have found it instructive to focus on the size of the fixed input. Traditional examples include adding workers to an acre of land or the impossibility of growing the world's food supply in a flower pot. In both cases, diminishing returns occur relatively early because the fixed input is small. (The "why does it take three students from (your school's chief rival) to change a light bulb? One to hold the bulb and two to turn the ladder" story is also applicable).
Then I relate a conversation with a Navy Admiral who refused to accept the diminishing returns concept. His argument: "If you give me 20 ships, I can patrol the oceans with a certain degree of effectiveness. Give me 40 ships and I will double effectiveness. So much for diminishing returns." Two things may be learned from this argument. First, it may be difficult to convince some Admirals (or other persons with vested interests) that it is ever possible to have too many ships. Second, and more importantly, the size of the fixed factor strongly influences when diminishing returns occur. This may be when a second worker begins cultivating the flower pot or the 200th ship is launched but, so long as one factor is fixed, diminishing returns are inevitable. (Consider an astronaut discussing rocket ships as variable inputs and outer space as the fixed input!)
Similarly, diminishing returns occurs at much higher levels of output at a General Motors or Exxon plant than at Kate's Country Kitchen or Andy's Lumber Store. This is not because GM is more efficient than smaller firms, but because it utilizes more fixed input.
Diminishing Marginal Productivity in Class
Rose M. Rubin,
To convey the concept of diminishing marginal product, I set up a participatory experience in which the class develops the numerical example for discussion. The materials which I take to class for this are a stack of colored paper, two markers or heavy felt tip pens of different colors, and a stop watch. At the beginning of the class period, I set up the tabular framework on the blackboard for the data to be generated: Number of Workers, Total Product, Average Product and Marginal Product.
The announcement is made that the class is setting up a firm to produce greeting cards. A name for this firm may be developed. The distinction between fixed and variable inputs having been previously made, I explain that the firm's fixed inputs are the materials brought and a classroom desk; and the variable input is labor to be provided by students. Then, one student is designated as accountant for the firm to record production, and another is designated production timekeeper. The production process is described: a) the workers are to produce greeting cards by folding a sheet of the colored paper twice to form each card; b) then, it is to be "decorated" with a red triangle on the front and a purple square on the back (or any similar two‑step, specific decoration); c) next, the cards are to be piled in stacks of 5 for packaging.
The first student "worker" is selected to begin operations for a specified time period of 1 to 2 minutes, timed by the timekeeper, and his/her production is recorded on the board. Then a second worker is added, followed by a third, fourth, etc., with the entire process repeated with each additional worker. The students immediately recognize the advantage of setting up an assembly‑line process and the class tends to cheer the "workers" on. By the time the sixth, seventh or eighth worker is added, the students clearly see the constraint of fixed inputs with a small workspace and, especially, only two marking pens. At about this point, marginal product of greeting cards will begin to decline, demonstrating the major point. The instructor can also institute a "quality control" measure, which generally causes marginal product to decline more rapidly. Thus, the class generates an example of the Law of Diminishing Returns.
You can extend this example with wage and price information so that marginal revenue product, marginal cost, average variable cost and other concepts can be related to your class's productivity.
Josef M. Broder,
One difficult concept to teach in production economics is the relationship between marginal product and average product. Lacking practical experience in production decision making, many students lack an intuitive understanding of marginal and average product.
To illustrate the relationship between marginal and average product, I use the process of pledge selection by Greek social fraternities and sororities. First, I ask the class to assume that the university offers an annual award to the social fraternity with the highest average grade point average (GPA). During rush week of each semester, fraternities and sororities select and initiate new pledge classes. The impact of the pledge class on the fraternity's GPA can be used to explain relationships between marginal and average product.
Assume that our fraternity has a GPA of 2.50 and that the GPA's of potential pledges ranges from 2.00 to 3.00. Assume also that our fraternity's chances of winning the award are good, that grade point average is a major factor in selecting this year's pledge class, and that pledges are selected incrementally by the brothers. How might the selection process be analyzed in a production function context?
Consider the GPA of the fraternity as the average production in a production process. To this production process we add pledges whose GPA's are defined as marginal products. As long as the pledges' GPA exceed the fraternity's GPA, then the pledge improves the fraternity's GPA or the average product increases. When the pledges' GPA is equal to the fraternity's, the average product is equal to the marginal product. When pledges' GPA fall below the fraternity's average, the marginal product is below the average product and the average product or GPA will decline. At this point the fraternity must choose between pursuing the award and accepting pledges with "other" talents.
Single Variable Production Function
Bette Polkinghorn,
In the small African country of
Three Dimensional Look at The Production Function and Isoquants
Tantatape Brahmasrene, Purdue University North Central
To provide my students with a visual aid to more fully understand the production function and isoquants, I do the followings:
1. I cut a large funnel into three layers (please see enclosed photographs) and paint each layer with a different color.
2. Draw two axes on a white poster board and label them as "Quantity of Labor" and "Quantity of Capital."
3. Place the funnel on a white poster board
from step (2) which serves as a floor plane and draw three isoquants parallel
to each layer of the funnel with corresponding color. These curves show various combinations of inputs
that can produce 50, 100 and 150 units of output.
4. Fold the second sheet of a white poster board in half. This provides two sides of the vertical plane. Then draw a production function on each side and label each side as "Total Output."
Now, I am ready to present to my students. The surface of a funnel represents the production surface. The height of a particular point on this surface denotes total output. Dropping a perpendicular down from that point to the floor plane allows us to determine how far the resulting point is from the labor and capital axes which in turn indicates amount of inputs required to produce that level of output. If we want to find the isoquant pertaining to a total output of 100 units (the red level), we just cut the production surface at that red level parallel to the base plane and drop perpendiculars to the floor plane. This results in an isoquant that includes all efficient combinations of labor and capital that can produce 100 units of output. Other details can be added to this model by inserting the new floor plane.
Isoquants in production theory play a similar role as indifference curves in consumer theory. Therefore, this funnel model can be used to explain indifference curves and total utility by simply relabeling with post-it notes.
I have found that students enjoy the demonstration and are able to comprehend the otherwise abstract concept of three dimensional modeling.
Figure 23-1
How Different Technologies Yield Similar Products
Ralph T. Byrns
Many students seem to believe that most production requires fixed coefficients between capital and labor. Examples to dispel this idea include using Mason jars for home canning versus the mass production in a Libby's plant, or collecting garbage with a few workers and automated equipment versus using many trash collectors all pushing wheelbarrows. An analogy from consumption that seems to work is the suggestion that just as a well balanced diet can be derived from an incredible variety of foods with huge variations in the portions that are placed on one's plate, so too almost any form of output can be generated with a variety of inputs (e.g., chemists have produced imitation `silk' purses from sow's ears, bananas can be grown under artificial lights in Alaska, electricity can be generated by water power, solar conversion, atomic energy, or combustion of wood, natural gas, fuel oil, etc.)
Emphasize that different technologies are available over different production periods, and that these periods are defined by the range of possible adjustments, not by time per se. Long run adjustments in one industry (e.g., entry and exit of children's lemonade stands) may absorb much less time than short run adjustments in another industry (e.g., for steel producers.)
Production Costs
Gary M. Galles,
To emphasize that sunk costs are irrelevant to current actions, I have found an example about guilt feelings to be both close enough to home and off beat enough to effectively get the point across.
I begin by asking if my students ever feel guilty (of course they do), and then ask what it means to feel guilty. Someone will eventually respond guilt involves current feelings about things that happened in the past, and which therefore cannot be changed. I point out that guilt is therefore remorse over a sunk (fixed) cost and ask whether that means guilt feelings have no use at all. This question usually puts students into shock temporarily, so I continue by saying that guilt feelings that only involve the past and have no positive effect on your present or future acts are worse than useless‑‑they involve a cost with no corresponding benefit. I then ask whether that statement suggests a use for guilt feelings, getting the students to see that if guilt feelings lead to improved present or future behavior (perhaps including apologies to the offended, but necessarily including attempts to translate these guilt feelings into positive changes altering future behavior and/or avoid future guilt over the same thing), then it has a use. (Ask here why students' parents sometimes try to make them feel guilty‑‑to get the students' behavior to conform more closely to what parents think it should). Once guilt had led to a change for the present or future, however, it involves a sunk cost and it has no more useful function. Guilt can be helpful as a motivator for the only thing we can change‑‑our present and future actions‑‑but if it involves fretting over the past with no effect on current behavior it is just an example of falling into the sunk cost fallacy. I conclude with some sort of joke about whether economists should be allowed to practice psychiatry.
Ben Collier,
David Friedman in his textbook Price Theory: An Intermediate Text has an excellent illustration of sunk cost: "When, as a very small child, I quarreled with my sister and then locked myself into my room, my father would come to the door and say, 'Making a mistake and not admitting it is only hurting yourself twice.' When I got a little older, he changed it to 'Sunk costs are sunk costs.'"
After telling this story and pointing out that David Friedman's father was Milton Friedman I go on to make the case that a knowledge of economic principles isn't just applicable to business decisions or those involving "money" but it is also extremely useful for everyday life situations, such as parenting. I may not convince students of this latter point, but this story makes a wonderful economic example.
Fixed Rental Payments and Decision Making
Norman Knaub,
The following analogy provides a simplified personal example of when firms should continue to produce even though they have losses and the role of fixed and variable costs in the production decision.
You sign a 12 month lease for an apartment. The rent is $300 per month, and you must pay the utility bill, regardless of who is actually in the apartment. If the apartment is unoccupied the utility bill is zero, but the utility bill is $80 per month when the apartment is occupied. You will not be using your apartment this summer. The best offer you have received to sublet your apartment is $200 per month for the summer. Should you accept this offer? As an alternative, what would you do with your apartment if the best offer you received was $50 per month? Since you have signed the lease, the $300 per month rent is a fixed cost. If the apartment is empty, you will receive no income from the apartment and have a loss of $300 per month. By renting the apartment, you will reduce your loss to $180 per month with the $200 per month sublet. With the $50 per month sublet the lowest cost alternative is to leave the apartment empty during the summer since the rent during the sublet does not cover all of the additional utility costs and the loss from renting the apartment in this case is $330 per month. If the rent was $600 per month but the utility bill and best sublet offers are unchanged, would the decisions to sublet be different?
This example illustrates that once the lease is signed the rent becomes a fixed cost and should not influence the decision to sublet. The utility bill, however, is a variable cost and will influence the sublet decision. The decision rules for a firm to produce or not in the short‑run follow naturally from this example.
University Fixed and Variable Costs
Eric Steger,
I've found that using our universe as an example is useful in communicating fixed and variable costs concepts. I explain that several years ago we faced a serious budget crisis. That is, we had to reduce expenditures. I asked the class "What costs could we cut at our university?" Salaries were mentioned but I explained that typically salaries were "untouchable" during an academic contract year. i explained that at our university 87% of the total cost of operation was due to salaries and wages. I then explained that we cut utilities expenses, travel, postage costs, telephone bill costs, books and periodicals, membership dues, equipment, data processing expenses, supplies and materials, and printing and binding. The categories were variable costs.
The MC and AC of Late Arrivals at Small Parties
Frederick S. Weaver,
How can the marginal cost curve start rising before the average cost curve does? Why does the marginal cost curve always intersect the average cost curve as its minimum point? These are simply arithmetic relationships, but they do confuse students and are sufficiently important to the theory of the firm that they warrant some special attention. An example that works for me is to ask students to imagine a small gathering of, say, ten people, and the average height of those at the party is 5'7". But some people are still arriving, and a latecomer who is 5'2" tall arrives at the party. What does this marginal guest do to the average height of those at the party (i.e., what direction does it change)? Another person, who is 5'3" arrives, and the average height of the roomful of revelers is pulled down a bit more. Yet another character drifts in, and her height is 5'6". The average height again declines (to 5'7"), as it has consistently even though the successive marginal changes have been getting larger. So as long as the increments are below the average, the average declines. Anyway, back to the party: when a person who is 5'7" joins the party, the average is unch