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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 unchanged, and when someone 5'8" tall finally manages to get there, the average height rises. So when a person of average height joints the festivities, the average does not change, but when someone above average height appears on the scene, the average height rises. Ergo, the marginal curve intersects the average curve at the average curve's minimum point.
Only directions of change rather than the particular numbers matter, but from experience, it pays to have a clear numerical example worked out before class. Initial confusion may facilitate understanding of some analytical issues, but this is not one of them!
Decisions about Variable Costs and Fixed Costs
John T. Ying, Rose‑Hulman Institute of Technology
Due to current business circumstances, XYZ Corporation is operating at a very low rate of output. The president of the company argues that it is inefficient to employ the two existing plants‑‑each operating at half its customary output. Instead, he asserts that production should be concentrated in one plant, which can generate output at a normal level. On the other hand, the plant managers argue that the company should continue to use both existing plants to save production costs. Since both plants have U‑shaped average cost curves and increasing marginal costs, it is more efficient to continue operations at the two plants. With whom do you agree? Explain your answer.
Optimum Input Mixes Depend on Relative Factor Prices
William C. Lee, Saint Mary's
When I was going for my regular jog on a bike trail which parallels, a creek, I passed an unusual sight‑‑over 200 live goats. At first I thought I was experiencing some sort of runner's high because I had never seen goats there before. Later in the jog I approached the person who appeared to be in charge of the "operation" and asked what the goats were doing. He told me they were clearing the poison oak and brush from the creek bed. We joked that the goats probably did not get paid too much nor did they need health insurance, retirement benefits or a paid vacation. The economics lesson here is that although there are probably a lot of "high tech" machines or tools that could do this job, the economically efficient (least cost) input mix (200 goats, 1 dog and 1 goatherd) is probably the same one that would have been used thousands of years ago.
Computerizing Production and Costs on a Spreadsheet
Edward C. Koziara,
In the past two years Drexel has been using the Macintosh personal computer in teaching economics. Students are assigned homework, receive disks with classroom examples, and view a screen which is used as an electronic blackboard. Templates have been developed for the basic courses and the following is one of the simplest and most useful. I use Microsoft Multiplan, but any spreadsheet could be used.
Production Methods is a decision analysis tool in which the costs of four different methods of making the same number of product units are compared to determine which method will cost less. The sheet looks like:
Production Methods I
II III IV
Tools 135 100 300 400
Labor 345 178 500 100
Material 90 100 30 600
Machines 2,000 456 20 100
Cost Of Tools Labor Material Machines
(dollars) $700 $100 $500 $500
Cost Of Methods I II III IV
(dollars) $1,174,000 365,800 $285,000 640,000
Least
Cost Method $285,000 . . . Method III
chosen.
All four methods require different amounts of the same four inputs: tools, men, material and machines. The Production Method section of the sheet illustrates the four methods, I, II, III and IV, and the requirements of each. Some processes are more capital intensive, such as Method I, and some are more labor intensive such as Method III. Under the Cost Of section of the sheet the costs in dollars contains the cost per unit of input. A tool costs $700, a man costs $100, a unit of material costs $500 and a machine costs $500. The costs of methods is shown in the Cost Of Methods section. Each of the prices of the components is multiplied by the amount needed to give the cost of employing the different methods. Method I, $1,174,000 is the most expensive method and method III, 285,000 is the least expensive method. The final section of the sheet gives the total cost of the low cost method ($285,000), the name of the method (III), and states that method has been chosen. To test for the least expensive method of production, this sheet uses the IF statement coupled with the MIN (minimum) function. The MIN function returns the minimum value in a series of values. Here the MIN function acts on the Cost Of Methods section and returns the minimum cost method. The IF function stipulates that IF the method is the least expensive print that method as the least cost method.
The sheet is mathematically simple. Major calculations involve only addition and multiplication. At the same time it is a powerful analytic tool because it allows the cost per unit or the production method to be changed and gives the low cost method after changes have been made. Although this example is for four methods it can be expanded to a greater number. For basic courses, four is probably sufficient.
Explaining the Shapes of Average Cost Curves
Keith Sherony, University of Wisconsin-La Crosse
I use the following method to illustrate the shapes of average cost curves to first year micro students. The illustration builds on the story line that if politicians can use "voodoo economics" it's ok for economists to use "voodoo mathematics". The method does not require the calculation and concomitant plotting of values. I assign those activities as out-of-class exercises. The method does require student understanding of relationships that increase at a decreasing rate ( @ ¯) and those that increase at an increasing rate ( @ ).
The presentation takes place immediately after completing the discussion of total fixed (TFC), total variable (TVC), and total cost (TC). While referring to a diagram that includes the three total curves I define and develop, one at a time, the corresponding average cost. Additionally, I tell the students that we are going to use what we learned about the respective total relationship to derive the shape of the average curve.
We try the easy one first. I give the definition of average fixed cost (AFC = TFC/Q). Then I ask the students to consider what happens in the numerator as I begin production, increasing output (Q) from 0 to 1 to 2 to 3 units etc., i.e., increasing the denominator at a constant rate ( @ ®). Since we had learned that TFC is constant we have:
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indicating that AFC declines over the entire production range.
Next we take on the tougher challenge. Given the definition of average variable cost (AVC = TVC/Q), I ask the same question--- what happens in the numerator as I increase the denominator at a constant rate? Having learned that during the early stage of production TVC increases at a decreasing rate we have:
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Now voodoo mathematics comes into play. Since the up pointing arrow in the numerator cancels with the up pointing arrow in the denominator we're left with a declining numerator divided by a constant denominator. The conclusion is that AVC is decreasing. Of course eventually, as TVC begins to rise at an increasing rate, when you voodoo the up-pointing arrows you're left with a numerator that is becoming larger. The conclusion now is that AVC rising. If you draw the corresponding segment of an AVC curve as each voodoo operation is completed, the traditional U-shaped figure unfolds. Finally, the same treatment of average total cost (ATC = TC/Q) gives an U-shaped curve too.
Transitions From Production to Cost Theory
J. Michael Swint, The
University of
These two devices will enable students to see the monotonic transformations between short‑run production and cost theories. (Naturally, you can use simpler language in your principles classes.)
Figure 23‑2
1. Given a total product curve Q = f(L), with K = K (Panel A of Figure 23‑2), then TVC = w(L). Since TVC is linearly related to output, multiplying the horizontal axis of the total product curve by the wage rate, w, yields total variable cost, or w(L), with output, Q, inconveniently measured along the vertical axis. Now rotate Panel A 90 degrees clockwise and then turn over the paper upon which it is drawn. What you then see are the lines of Panel A through the sheet as Panel B. Because of the 90‑degree rotation the axes are reversed as you would want; i.e., in production theory the dependent variable is Q and should be on the vertical axis; in cost theory costs are dependent and belong on the vertical axis.
2. Similar relationships exist between marginal product (MP), and average product (AP) (Panel A of Figure 23‑3) and marginal cost (MC) and average variable cost (AVC) (Panel B). Since AVC = w/AP and MC = w/MP, the symmetry of the relationship can be seen by turning Panel A over and upside down; MC and AVC appear through the sheet as Panel B. With both of these sets of graphs, you will need to emphasize the role played by the wage rate, but the fundamental symmetry of production and costs comes through loud and clear.
Figure 23‑3
The Costs of Short‑Run Production: A Textbook Illustration
Roy B. Levy,
The exercise below provides for derivations of cost information from production information. I form the hypothetical Textbook Transport Company (TTC). TTC operates to minimize the cost of transporting textbooks from point A to point B. Opposite ends of the classroom serve as points of origin and destination. The company pays a user costs of $.10 to employ a narrow band of classroom space, i.e., the capital input. TTC hires student employees at a wage of $.04 per labor second. I act as the self‑appointed president of the company, earning a salary of $.50.
One can catalog output and labor information from several iterations of the productions process. At each iteration, TTC transports an additional textbook and employs an additional student. With the use of a watch, I record the total seconds used at each iteration. Given a judicious rounding of labor time, one can obtain an economically consistent set of output/labor combinations. Table 23‑1 contains data from recent operations of TTC.
Output 0 1 2 3 4 5
Labor 0 3 5 9 16 25
Table 23‑1
I instruct all students to compute the various costs that TTC incurs at each level of output. (Table 22‑2)
Table 23‑2
An instructor may use this exercise as an introduction to cost theory. One might then entertain discussions of the law of diminishing marginal returns and the properties of short‑run cost functions.
The Choice of Production Methods
Yung‑Ping Chen,
Profit‑maximizing firms strive to operate efficiently. Economic efficiency is determined by the least cost of production. The cost of production under various methods can be determined by comparing the dollar value of the output with the dollar value of the input.
Suppose there are four alternative methods for producing 100 units of the product per month. These methods require different amounts of capital and labor, as follows:
Method Capital Required Labor
Required
A 6 units 200 units
B 40 units 50 units
C 10 units 150 units
D 10 units 250 units
Which method should be used? All four methods can produce 100 units of the product, but they can result in different costs. Method D can be rejected because it used the same amount of capital as does Method C but more labor. Thus, Method D is obviously more costly than Method C and, therefore, less economically efficient. To choose the most efficient of methods A, B and C, however, we must have the relevant cost data. Let us assume that three different cost conditions could exist.
Per
Unit Cost of
Cost Conditions Capital Labor
I $50 $3
II 20 5
III 15 5
Then, the comparative costs of Methods A, B, and C are:
Cost
Conditions Method A Method B Method C
I $900 $2150 $950
II 1120 1050 950
III 1090 850 950
Therefore, the least cost or the most efficient method depends on cost conditions. Under Cost Condition I, Method A is the best; under Cost Condition II, Method C is the best; under Cost Condition III, Method B is the best. The most economically efficient method of production depends on the relative costs of labor versus capital.
We could draw some interesting and useful implications from this illustrative discussion. Suppose we currently employ Method A because it results in the least cost of production as compared with other methods. That is, we have Cost Condition I. If the cost condition changes to that of II, our present method is no longer the best (that is , the least cost). We will want to switch to some other method of production.
Changing conditions of resource availability can change the relative cost of labor and capital. These changes in relative costs of inputs may require changes in the methods of production, which mean changes in the usage of different resources. The development of new technology can lead to new production methods which may even use different resources to produce the same product.
For
example, the Industrial Revolution may be viewed as a process of coping with
the resource constraints which began to constrict economic growth. In
Due to
abundant timber resources, the
In the mid‑19th century, relative timber prices began to rise. As a result, a shift toward coal occurred, in some cases rather rapidly. For example, at the beginning of the Civil War, cord wood supplied the energy needs of the railroads, but twenty years later, railroads were using twenty times as much coal as wood.
These examples show that as the relative price of the resource currently in use increases, other resources become more economically attractive alternatives. Technology develops to exploit these abundant and relatively inexpensive alternative resources. Entrepreneurs apply the new technology to find new production methods with lower costs than the method that had once seemed the best choice.
Weights and Relationships Between AVC, ATC, and MC
John W. Reifel,
Students frequently have difficulty grasping why a firm's marginal cost curve must pass through the minimum points of the average variable cost and the average total cost curves and why average variable cost achieves its minimum point at a lower level of output than where average total cost reaches its minimum point. A weighing analogy can aid in an understanding of the relationship.
To explain why the MC curve must
pass through the minimum point of AVC, relate the following analogy. If the
parents of a sizable family whose children range from pre‑school age to
teen age stand on a large scale at the same time, the average human weight
(ABW2) can be calculated by dividing the weight reading (W2) on the scale by
the number of people (2) standing on the scale. Now, successively add the
children, one at a time in order of increasing weight, to the group already
standing on the scale. Take weight totals as each heavier child steps onto the
scale and compute the resulting average human weights. Students readily grasp
that as long as the children who successively step onto the scale weigh less
than the average human weight of the group already on the scale, the resulting
new average human weight will fall. But, as the heavier children step on the
scale, at some point they will start weighing more than the average human
weight of the group already on the scale and so the resulting average human
weight will begin to rise.
The analogy of the weighing example to the firm's cost curves can be drawn by letting people on the scale be units of output, the weight reading be variable cost, average human weight be average variable cost, and the weight of the last child to step on the scale be marginal cost (the change in variable cost). Thus, as output increases one unit (another child steps on the scale), the new average variable cost (the new average human weight) will be smaller, the same, or larger depending on if the marginal cost (the weight of the last child to step on the scale) is less than, the same as, or greater than the preceding average variable cost (the preceding average human weight).
To explain
why the marginal cost curve must pass through the minimum point of average
total cost, relate the following extension of the preceding analogy. Assume the
head of the family is blind and has a seeing eye dog which accompanies him
everywhere and is therefore considered his appendage. If the seeing eye dog and
the parents stand on the scale at the same time,. the average total weight (ATW2)
can be calculated by dividing the weight reading (W2' = W2 + weight of seeing
eye dog) on the scale by the number of people (2) standing on the scale.
Successively add the children, one at a time in order of increasing weight, to
the group already standing on the scale. Take weight totals as each heavier
child steps onto the scale and compute the resulting average total weights.
Students readily grasp that as long as the children who successively step onto
the scale weigh less than the average total weight of the group already on the
scale, the resulting new average total weight will fall. But as the heavier
children step on the scale, at some point they will start weighing more than
the average total weight of the group already on the scale and so the resulting
average total weight will begin to rise.
The analogy of this second weighing example to the firm's cost curves can be drawn by letting people on the scale by units of output, the weight of the seeing eye dog be fixed cost, the weight of the people on the scale be variable cost, the weight reading on the scale be total cost, average total weight be average total cost, and the weight of the last child to step on the scale be marginal cost (the change in total cost). Thus, as output increases one unit (another child steps on the scale), the new average total cost (the new average total weight) will be smaller, the same, or larger depending on if the marginal cost (the weight of the last child to step on the scale) is less than, the same as, or greater than the preceding average total cost (the preceding average total weight).
Note also that average total weight will reach its minimum point at a larger number of family members than where average human weight reaches it minimum point because where average human weight is at a minimum, it equals the weight of the last child added but is less than average total weight (including the dog's weight) and so average total weight must still be declining. By analogy, average variable cost must reach its minimum point at a smaller level of output than where average total cost reaches its minimum point.
Relationships between Marginal and Average
David J. Jobson,
In explaining why marginal cost intersects average total and average variable costs at the latters' minimum points, the following analogy has proved useful.
First, the three cost curves are sketched on the blackboard and students are led to observe that when the marginal is below the average, the average is falling; when the marginal is above the average, the average is rising; when the marginal equals the average (intersection point), the average is unchanged.
At this point, when asked, students are commonly unable to explain why these relationships exist. Students are then asked to guess the average weight of all students currently in the class. After various guesses, we agree that the average is about a certain amount say 130 pounds.
Then I propose that a new (additional or marginal) student weighing 95 pounds enters the class. What must happen to the average weight of students in the class? Why? Then I propose that a new student weighing 300 pounds (sumo wrestler?) enters the class. What must happen to the average weight of students in the class? Why? Finally, it is proposed that the new student weigh an amount equal to the current class average. Will the average change? Why not?
Marginal and Average Relationships
Thomas J. Shea,
Marginal/average relationships are among the most difficult concepts for mathephobic students to master. One way to get this idea across is to ask students to suppose that they were given 10 quizzes during the term and that they had to keep a "graph log" of the results of each quiz as well as their average. Ask what would happen if they got 100 in the first quiz and 80 in the second. Their marginal result (80) was below their average. What happened to the average? Then tell them that their next quiz result was a 0. What happened to the average? In the next quiz they received a 90. Now what happens to the average? And so on. Students are very adept at figuring their average and can easily grasp the idea that "when the margin is less than the average, the average decreases and when the margin is greater than the average the average increases." Homework requiring graphs paralleling these results also reinforces this concept.
Relationships between Marginal and Average Costs
Gary M. Greene, Sr.,
Many students find it very difficult to understand the relationship between the marginal and average cost curves and how one moves in relation to the other. The examples that I have used can be explained very simply and readily understood by any economics student. Consider the average weight of ten skinny men to be 100 pounds. Along comes a fat lady who weights 200 pounds. The fat lady is the extra or marginal person to be considered. Now, what is the average? Does the average increase? When the marginal cost curve (the fat lady) is greater than the average cost curve (the ten skinny men), the average cost curve (the total of the ten skinny men and the fat lady) must rise. The case of the skinny man and ten fat women will explain why the average cost curve will fall. It does not matter what example one uses: whether it is a large dog or small cat, large football player or small football player. The relationship will always hold true.
Decomposing the Linkages from TC to MC
Jim Vincent,
Most students who lack a good background in calculus find it difficult to interpret and use the concept of the slope of a nonlinear function. In micro principles classes, this poses a major problem in teaching about the relationship between a total cost curve (or total variable cost curve) and the marginal cost curve. The result is that many students complete beginning micro with big gaps in their comprehension of the linkages between cost functions and production functions.
Instructors often try to motivate the idea that the MC curve reflects the slope of the TC by referencing a "textbook‑style" total cost curve such as that illustrated in Figure 23‑4. This involves explaining that the MC curve is downward sloping over the range of output for which the TC curve is decreasing and upward sloping over the range of output for which the TC curve has increasing slope. In my experience, there are many students for whom this type of explanation, however clear, is inadequate. I have been using an extension of this approach that has proven to be quite successful.
Figure 23‑4
After going through the preceding explanation, I find that many students memorize the relationship in Figure 23‑4, but cannot generalize the fundamental concepts. To extend this standard explanation, I decompose the approach into the two panels shown in Figure 23‑5. I first draw the top part of Panel A, but do not even hint that this is simply the portion of the TC curve in Figure 23‑4 that is to the left of the inflection point. Upon being asked what the MC curve associated with this TC curve might look like, very few students are able to respond. I then present them with the TC in the top part of Panel B, again without mentioning that it is the portion of the TC curve in Figure 23‑4 to the right of the inflection point. Most students still draw a blank.
After their minimal responses, I draw the MC curves (at the bottoms of Panels A and B of Figure 23‑5) associated with both of these partial TC curves while describing the related effects on output (e.g., . . . and in Panel A, the MC falls because increasing amounts of output are produced as each extra worker is added to the production process, but each worker adds only a constant amount [the wage rate] to total cost . . .). Then the fact that these TC curves are just parts of the original is revealed, and there is much groaning and a recognition by most students of how simple the concept really is. I have received numerous comments from students that this exercise provided a major breakthrough in their understanding of the relationship between a total and a marginal function. A similar step‑by‑step approach is useful in clarifying many economic concepts that involve lengthy and intricate linkages.
Figure 23-5
Notes: