. Paper Presentation on Marginal Revenue Product And Optimal Employment Level: A
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Paper Presentation on Marginal Revenue Product
And Optimal Employment Level:
An Illustration of Student Involvement
Dr. Eugene Steadman, Jr.
Averett University
7Th Annual Economics Teaching Conference
Gulf States Economic Association
New Orleans, Louisiana
October 27, 2011
Background
Many students have trouble grasping how marginal revenue product (MRP) and marginal cost (MC) concepts relate in hiring the optimal number of employees, under differing sets of employment conditions. From my experience, when students become personally involved in applications of these concepts and have a stake in the outcome, they understand better the concepts. On end-of-course final exams where these concepts are tested, the students perform quite well in critically thinking their way to correct answers.
In order to help achieve the desired student learning outcomes from economic courses, I create a hypothetical holiday wreath business, for which I am the owner. In the classroom, I point out an area where I have purchased and installed a wire-bending machine that processes and welds the wreath assembly support structure. From the assembly of materials and the processing of welded support structures for the holiday wreaths, the assembly of a wreath goes through another eight workstations to attain the final product. In total, there are 10 workstations, each of which has to be performed by student workers that I will employ from the class. The ten workstations are shown in Figure I.
I presume that my students know what a holiday wreath is, and have little trouble envisioning it. I explain that it has pine cones, ribbons, bows, berries, and frosted parts from spraying glitter paint on parts of the wreath. Quality control, assembly, and shipping to the customer are briefly reviewed in the description of my business.
Then, starting with the first student as my first employee, I ask the class how many wreaths do they think the first student can make, based on an eight-hour workday. Over many classes, the consensus is that a total of six wreaths could be completed. Essentially, this entails over an eight-hour period, the performance of 10 X 6 = 60 workstation tasks; about one and one-third hours, on average, for each wreath to be completed and shipped.
Starting with the second student, they are asked about how many wreaths two students can complete in one day. Some students express the view that it must be 2 X 6 = 12 wreaths, based on the first student’s performance; but in general, most students grasp the fact that the two students can divide the 10 workstations into 5 stations each, and thus become more proficient at each of the five workstations. Thus, the majority of the class “sense” that more than 12 wreaths can be produced by the two students. Over several classes, 14 wreaths has proven to be a good number that all class members can agree on. Given that the students intuitively realize that something is happening between the two workers—that the second worker, at the margin, produces eight additional wreaths, while the first student only produced six wreaths—some suggest that the second student must be more productive than the first. Again, the majority of the class does not agree, and seize on the fact that the students have divided the work, and thus have become more efficient at their individual tasks.
Law of Diminishing (Marginal) Returns
Before proceeding further, the law of diminishing returns (or, the law of diminishing marginal returns) is examined, and explained in some detail. Basically, Figure II reflects this law, and the students are pushed to understand its importance, particularly from the fact that this law is the basis for variable costs, as a function of output, for all known goods and services companies, anywhere in the world today.
Main points emphasized are:
During the stage of increasing returns, the line slope is positive and increasing, up to an inflection point where the curve, while still positive in slope, becomes less so. The curve represents the effects from the division of labor and specialization of tasks in producing products, and is covered by most microeconomics textbooks.
Total output continues to increase, even during the stage of diminishing returns, up to the point where marginal productivity is zero, when the curve becomes perfectly elastic (a horizontal slope of 0). Past that point, the product output declines as more of the variable input factor is employed, and the slope of the line becomes negative.
A key in the analysis, that is reinforced with students, is the reason that the curve changes slope, i.e., the reason the marginal productivity begins to decline. Simply put, according to the law itself, the variable input factor is beginning to “overwhelm” the fixed factors of production. In this case, as the number of students are increased (the variable input factor), the number of tasks each has to do becomes less, and they become quicker/more efficient at doing each of their assigned tasks. But, back at the front end in this case, the machine (the fixed factor) can only operate at a certain speed, and can only turn out so much wreath support structures, so that the increase in the productivity begins to diminish for additional employees as they are added. This is reached at the inflection point on the curve. Finally, in the area where the diminishing returns turns into negative returns, not only is the fixed machine not turning out enough frames to supply to all the student workers that are now only doing two work stations, as an example, the students are beginning to “stand around” and get in each other’s way, talking instead of working, so that the variable factor in and of itself begins to be an impediment. Thus, output reverses, and actually begins to fall. Sometimes, the illustration is used that if I cram 1,000 students into the classroom with the one fixed machine, we may not be able to turn out a single, completed wreath. We’ve really gone backwards using the variable input factor of student workers!
After this explanation, with the textbook as a reinforcement, we quickly proceed around the room, considering up to the first eight students to work on wreaths. Depending on the size of the class, the students can be picked contiguously, or randomly. The random approach can serve to keep the students “on their feet and alert,” if required. Figure III is shown as the final production numbers from each student being hired.
This point is stressed: all known production systems for goods or services, anywhere in the world, follow this law. If a student plans on going into business, either for themselves or to work for an employer, it’s very wise to understand and appreciate the importance of this law.
Marginal Returns and Marginal Revenue Product
Students understand that they have to pay a price for any good or service. So, for this business, the price of each holiday wreath is set at $25 each, no matter how many wreaths are produced. Thus, each wreath sold has a marginal revenue of $25, and the average revenue is also $25. Although it’s very easy to make a classroom case for lowering the price of the wreaths as the quantity is increased (that is, to follow the law of demand whereby the demand curve is downward sloping), I defer this aspect to a later part of the course, where I demonstrate the concept of economies of scale. Basically at that point, I inform the class that demand is so strong that we are knocking down the wall to the adjourning classroom, doubling the space, adding another machine, and actually increasing the scale of the operation by 100%. Then, the question is whether we have achieved an increasing, decreasing, or constant returns to scale operation. Based on the answer, if it is decided that we have achieved an increased economy of scale, I then lower the prices for the holiday wreath. But, regardless, since the focus of this paper is on marginal revenue from a single variable factor of production, rather than considering all factors to be variable as is the case in considering economies of scale, the product price is assumed to remain constant at $25.
Given the assumption of a constant price, the students quickly see that the marginal revenue is, indeed, $25--each wreath sold brings in $25. From that point, the focus is on each student’s financial contribution to the business: given the number of students that might be employed, is each one creating enough revenue to cover their employment costs? To “get at” that answer, each of the student employees is asked how much revenue have they brought in for the company? Intuitively, again, they recognize that the amount of money they’ve each brought in must be the price of each wreath ($25), multiplied by the number of wreaths they produced, at the margin, during the eight-hour shift. For the first student that produced only six wreaths, the income brought in was 6 X $25, or $150. This finding is then used to reinforce the concept of marginal revenue product (MRP): MRP = MR X MP, or marginal revenue product equals marginal revenue times marginal productivity. This process is then repeated for all of the eight students considered in the production of holiday wreaths. As shown in Figure IV, without any labor costs yet considered and due only to the law of diminishing returns, the optimal employment of students is at six. Hiring more or less than that number will lower the “profit” of $975 per day, or $234,000 per year, as shown on the chart.
At this point in achieving learning outcomes, the students have grasped well the law of diminishing returns, the concept of marginal revenue, and the concept of marginal revenue product.
Marginal Cost
At this point, it now becomes appropriate to ask each student what they would like to make, given the nature of the tasks involved in making holiday wreaths. Again, over many classes, the generally agreed wage is $7 per hour. For an eight-hour day, the marginal cost to me as the employer becomes $56 per day. I assume no part-time workers, no sick leave, no paid vacation, and no benefits whatsoever. Simply, each additional worker, at the margin, costs $56 per day. Given this new piece of information so critical to running a successful business, that is, the variable cost, the question becomes, how many students should we now hire? At first, most students do not deduce how to arrive at the correct answer, based on economic reasoning. When I then ask how much money they must “bring in” to cover their employment costs, given that my goal is to maximize profits (that is, I won’t hire them if they cost me more than they can create in revenue), they begin to see that, as an employer, I will not hire any more students than those that can cover their employment costs, through the sale of holiday wreaths that they helped manufacture, at the margin. Using Figure V as a guide, the students quickly realize that, given the labor costs I now am incurring, I would not as a logical and rational employer, hire any more than five of them. They realize that one of the “free” volunteers is no longer going to be able to remain a part of the holiday wreath business. In other words, the student “Karl” cannot cover, at his marginal productivity, his costs of employment to me.
The students then focus on the fact that profits have declined from the old figure of $234,000, down to $154,800. This reflects the added costs of $56 per day for five students, for 240 workdays, plus the loss of $12,000 in revenue from the sixth student that is no longer working in the company.
To reinforce the learning that a “wise” employer will always hire employees up to the point where the marginal revenue product covers each employee’s marginal cost in order to maximize profits, benefits costs are now added to the analysis. The students demand health care and a 401-K benefit plan, for an additional cost of $40 per day for each employed student. Again, the students are asked to determine how many students should I hire, given these new costs?
Using Figure VI, it again becomes clear that the optimal level of employment remains at five students. No one loses their job, but it is pointed out that the profit drops further, from the original $234,000 down to the earlier $154,800, and now down to a new level of $106,800. The latter difference is accounted for from the additional cost of $40 per student per day, for 240 days.
At this point, the students have achieved critical thinking such that they know, for a business to succeed, its variable cost factors (such as student labor in this case) must be covered from revenue generation by that factor, or the decision to employ that variable factor of production will not be a good decision.
Minimum Wage Impacts
This illustration becomes quite a learning experience for many students. Most students, at least in the beginning of explaining the impacts from raises in the minimum wage, believe that increases are a good thing, either for themselves or for someone they know (e.g., a friend or relative). For many, working in a fast-food restaurant or similar business is an underpaid experience, and increases in the minimum wage are believed to be justified and indeed, deserved. After the economics are traced through, the students really begin to understand, ceteris paribus, that jobs are lost somewhere in the economic system as a result. This, of course, presumes nothing else is changed; there is no additional training or education to economically justify an increased wage.
Using Figure VII to illustrate this principle, the assumption is made that the minimum wage is increased from the current $7 per hour, to $13 per hour, with the benefits unchanged. One can always argue with the size of the increase in the wage, but that is really not relevant to the purpose: any increase in the minimum wage, without some economic justification, means that somewhere (maintaining profit margins and so forth), some costs have to be reduced, and that can only come from the variable factor that has the increased cost. Thus, jobs are lost. Further, for the wreath business, profits really fall, from $106,800 in the prior case, all the way down to $53,760. Besides having less workers, this has really eroded my capability or incentive to invent in expanding my business, or doing research on how better to make holiday wreaths. In the area of “welfare economics,” this has clearly been a shift from producer surplus (from the employer), to consumer surplus (the employees).
Figure VII shows that we incur a 20% reduction in the workforce. This is a hefty price to pay for a minimum wage increase, but in my holiday wreath business, I am left with no choice. Students can argue about getting a more efficient machine, or training the workers to perform better, or installing a better computerized way to track demand and materials inventories, but all of those violate the basic premise: ceteris paribus. On its face, simply put, “there is no free lunch” and within the economic system, someone’s gain is another’s loss. Thus, while Renee, Emily, David, and Zack get nice pay raises, it’s too bad that Malika loses her job.
Students really begin to see the import of raising the minimum wage from this example. When they do, they usually begin to ask why government decision makers don’t understand this. Why is this done at all? Why would any policy maker do something that causes people to lose their jobs? I point out that, in many cases, our public policy makers are not economists. And, additionally, politics can involve many powerful groups, and some groups such as labor unions may well be in favor of a raise in the minimum wage. Why? Simply put, it gives those groups more leverage to fight for increases in the wage rates for their own specific constituency.
A final, but most important point is made here. To economically justify an increase in the minimum wage, workers need to be able to produce more in order to offset the increased costs. This ability to produce more, in terms of better quality or more quantities, or perhaps a higher level of goods and services, can only come from training and education. In the final analysis, then, by getting an undergraduate degree or a graduate degree, college graduates have an economic basis for earning more than a high school graduate. Essentially, salaries should increase, consistent with the additional education earned.
Impacts from Illegal Immigration
Compared to the minimum wage increase whereby job losses are incurred (for mostly lower level wage earners), the opposite extreme is now demonstrated to the class, again using the holiday wreath business. Ignoring the ethical implications, the question is asked of the class, what will be the impact if I, as the business owner, can employ illegal immigrants at a wage rate of $4 per hour, with no benefits?
Given the assumption of identical productivity levels, that is, illegal immigrants can make holiday wreaths just as well as college students, no better or worse, Figure VIII reflects that I should hire six immigrants. This means I can add two workers, a 50% increase in my workforce, compared to the previous situation of just having four student employees.
Further, looking at the profit level, I have increased from $53,760, all the way up to $187,920. This is over a tripling of profit! Given that I am in the business of maximizing profits, there is little doubt that I will “lay off” all of the student employees, and hire the illegal immigrants, again ignoring any ethical implications and, of course, ceteris paribus.
Summary
At this point, due to the personal involvement of the class, the students “get it.” They have grasped marginal productivity, marginal revenue, marginal revenue product, marginal cost, minimum wage increases and the impacts, and see the illegal immigration issue as it impacts employment in this country. I find that by involving each of them in this hypothetical holiday wreath business, it has gotten “personal” for them. Consequently, they become empowered in the process, and are forced to understand better these concepts for their betterment.
It should be noted that this author is in the process of building a “custom textbook,” working with Cengage Publishing, for a course in Managerial Economics. The contents of this paper will be included in that textbook, which should be completed in time for Fall, 2011, classes.
· Do you think the diminishing returns principle (from the law of diminishing marginal productivity) is applicable to the company/firm where you work? Why or why not?
Explanation / Answer
Diminishing marginal productivity is experienced in my organization, it is evident and recognized by the management. It is because of this reason that the number of people hired at the same role decreases with the increase in the hierarchy. The law of diminishing marginal productivity states that the marginal increase in total output declines with the increase in additional units of labor after a certain point of time. It is observed that the increase in the quantity of work done is not directly proportional to the increase in the person employed.
For example, there are three analysts that are hired by the company to keep the track of the shares of a certain company in the various market. The firm is a hedge fund company and requires constant monitoring of the share. If one more person is employed to do the same job, he may not lead to an increase in the productivity of the company as much as employing the first three did. As three people are enough to monitor the fluctuations in the rate of the shares of a single company, employing more will be futile.
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