Category Archives: Production Theory

Questions for Classroom Discussion on PRODUCTION THEORY

After reading about a real-world application of diminishing marginal returns, consider the following:

  • What could explain diminishing marginal returns with respect to school inputs, such as class size and teacher education?
  • Can you argue that marginal returns to school inputs should be positive?
  • Why should those not entering educated-related careers care about the evidence regarding diminishing marginal returns in education?

Our classroom discussion will likely take place on March 6. I am looking forward to your participation!

Posted by Prof. C-S

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Production Theory

Discussion on the abstract for “Diminishing Marginal Returns and the Production of Education: An International Analysis,” by Douglas N. Harris (Education Economics, 2007).

 Summary

According to Harris’ article, the Law of Diminishing Marginal Returns (DMR) may explain a wide range of findings within the educational research field. The author suggests that the concept of DMR may apply to the respective effects of class size and teacher education level on the “production” of education. According to the Law of DMR, this implies, for example, that the benefits of decreasing a class size will initially increase educational production (or learning) at an increasing rate; however, at some point a decrease in the number of students per class will begin to result in progressively less learning as a result of crowding-out effects.

Harris also indicates that, although the Law of DMR may apply in this context, educational data typically doesn’t conform to the requirements of a traditional DMR test. Within the article, Harris proposes a new DMR test and applies it to educational data from 36 countries. Harris further concludes that, in many cases within the education literature, the marginal effects of school inputs (like class size and teacher education) are negative, which makes the Law of DMR impossible to apply. However, Harris’ model does give some indication that the Law of DMR may apply in those cases when the marginal effects of school inputs are positive.

This article is relevant to our classroom discussion of production theory, because the Law of DMR explains the predictable pattern of a firm’s short-run output, in which an increase in the variable input yields progressively less output as a result of crowding out effects.

 Commentary

Education and success in the classroom is a product of the inputs that make up the entire educational experience.  Across the world education is of important value to everyone.  However, in certain parts of the world resources are more available than in other.  It is these resources that help to create the output of education.  When comparing the returns of the education in developed countries like U.S. to developing countries like African, South American, or Asian countries, the returns of the two is expected to be different.

Schools in the U.S. and other developed countries experience diminishing returns as a result of the already high levels of resources committed to education.  While increased inputs allow for advanced and high quality education, the developed nations have reached a point in their production output that each additional input does not generate the same level of return as the previous input.  It is a result from the years of continuous growth and development of education in these nations. 

However, looking at developing nations, the inputs for education only further increases the marginal returns.  The developing nations are still early enough in their output function that each unit produces higher return.  The developing countries have significant room for growth and development, which allows for this increasing marginal return.  Since so few resources have been committed to the education systems in these developing nations they have the opportunity to grow and expand.  As more resources are committed to education in these developing nations the marginal return is likely to start decreasing.  However, for the time being it is still early enough in the life cycle that each input will lead to a greater marginal return.

 Real World Application

Perhaps the most important concept from production theory is diminishing marginal returns. One way to better understand this idea is to consider a pizza restaurant.  The first worker at the restaurant is only able to produce two pizzas an hour. He must work in the kitchen while also handling the cash register and miscellaneous duties. Once a second worker is hired, they are able to produce five total pizzas together. This is a marginal increase of three pizzas. One worker is able to work in the kitchen while the other handles customers. When a third worker is hired the company is able to produce three more pizzas per hour. It is starting to get a little crowded in the kitchen, and the workers are now working slightly below their optimum efficiency. When a fourth worker is added only one more pizza per hour can be produced. Efficiency is becoming a serious issue and more space is needed. Theoretically, the diminishing marginal returns would continue in this scenario to the point where additional workers actually caused a decrease in pizzas produced per hour.

Posted by Sarah, Dan and Ted (Section 4)

Discussion on the abstract for “Diminishing Marginal Returns and the Production of Education: An International Analysis,” by Douglas N. Harris (Education Economics, 2007).

Marginal return is the amount of benefit that is added by adding one additional input. Diminishing marginal return (DMR) is the hypothesis that each additional input has a smaller effect than the previous one. The article Diminishing Marginal Returns and the Production of Education: An International Analysis looks at the role that DMR plays on education. Specifically, the article states that class size and the educational level of teachers have DMR. The article then takes this a step farther and states that DMR has actually reached such a degree where the marginal return is negative. Finally the article challenges the Heyneman-Loxley hypothesis, which believes that school inputs are the primary drivers of success in schools, and has shaped the role of governments aiding schools.

This challenge raises the obvious question, “At what point does the marginal return begin to be negative?” In order to look at this question, let us imagine two countries, America, a developed nation, and Afghanistan, a developing nation. Also, let us define that the marginal return we are measuring is the overall knowledge of the entire population. Furthermore, let us first isolate the event to look at only one input at a time. First, we will look at class size. A larger class size in America is likely to have a negative marginal return, as each additional student means every individual student is getting less attention from the teacher. In Afghanistan, however, a larger class size would increase the overall knowledge of the country as more students are being educated. Because the education level is lower in the developing country, the greater the input of students, the greater the overall increase of knowledge.

Let’s now look at a second input, technology in the classroom. The diminishing marginal return for students in America would become evident much quicker than in Afghanistan. In America, there is much less to learn with each additional input of technology, as many people are already accustomed to it. However, in Afghanistan, the additional inputs would have much greater marginal returns, as there is more information to be learned.

In conclusion, diminishing marginal returns have a greater effect on developed nations than they do on developing nations.

Another real world application of diminishing marginal returns in production theory is the classic example of fast food restaurant employees. Say the first worker you hire to work the grill in the kitchen has a marginal return of 15 hamburgers an hour. When a second employee is hired s/he adds a marginal return of 10 hamburgers an hour. Following the same pattern, the third employee hired only adds a marginal return of 5 hamburgers. The reason for these diminishing returns is that the more employees at the grill, the more crowded the area becomes and the lower their utilization and marginal return. This principle could generally apply to many different small businesses because it reflects the logic that early inputs yield the highest return while later inputs yield lower returns due to limited resources and over utilization.

Posted by Addison, Conor and Conor (Section 3)

Production Theory

Discussion on the abstract for “Diminishing Marginal Returns and the Production of Education: An International Analysis,” by Douglas N. Harris (Education Economics, 2007).

Diminishing Marginal Returns is the decrease in marginal output as the amount of one factor of production is increased, holding all other production factors constant. Adding more of this one factor of production, while holding all other factors constant, will eventually bring about lower per-unit returns.

In the article Diminishing Marginal Returns and the Production of Education: An International Analysis, author Douglas N. Harris researched the effects of increased school inputs on the production of education across 36 countries. Previous studies have shown that increased school inputs such as class size and teacher education play a significant role in the production of education in developing countries and among minorities within developing countries. The goal of this article was to use a new test with functional forms that allow for Diminishing Marginal Returns (DMR). The test concluded that there is little evidence for DMR within countries, and no evidence of DMR in total inputs in the United States, as suggested by other studies. The evidence is more supportive of DMR across countries; however, there is not enough evidence to be able to reject the possibility of constant returns. Previous data has shown the marginal effects of school inputs is frequently negative. However, in those places with positive marginal effects, there is some evidence of DMR. The Heyneman-Loxley hypothesis has suggested that “school inputs are the ‘predominant influence’ on achievement in developing nations.” The article reinterprets the hypothesis and shows that this may no longer be the case by including such variables as school and non-school inputs as well as national income.

The article also examined the differences in the marginal return of school inputs between developed and developing nations. We expected that there would be a significant difference between the two categories of countries. Specifically, we expected that the marginal gains of school inputs would be greater in developing countries than in developed countries. We hypothesised this to be true because of the disparity of resources between the two types of countries. In developed countries, educational systems already have access to inputs such as quality teachers and good facilities, so one would expect that adding more of these items would not yield high marginal returns. However, to the contrary, educational systems in developing countries most likely do not have access to many educational inputs. Thus, when these inputs are added, one would expect the marginal returns to be high due to the influx of new types of resources. Essentially, developed nations are inputting more of what they already have so the marginal gains are not as high, whereas developing nations are putting in place new inputs so the marginal gains are higher. As we expected, the article found this relationship to be true.

Another real-world application of these concepts of Production Theory has to do with adding fertilizer to farms and gardens. This fertilizer will increase crop production, but only to a certain extent. If the farmer or gardener adds more and more fertilizer, at some point, the increase in yield per unit of fertilizer used will begin to decrease. Also, in the case of adding too much fertilizer, total yield could also be affected negatively. For example, if tomatoes are given too much nitrogen, they will grow more leaves, and less tomatoes, decreasing total yield because of the addition of too much fertilizer. This is referred to as negative marginal returns.

Negative Marginal Returns

Posted by George, Phil and Drew (Section 2)

Resources:

http://www.detroitnews.com/article/20090612/OPINION03/906120305

Production Theory

Discussion on the abstract for “Diminishing Marginal Returns and the Production of Education: An International Analysis,” by Douglas N. Harris (Education Economics, 2007).

Summary

Douglas N. Harris’s article describes how there are diminishing marginal returns (DMR) with respect to school inputs, such as class size and teacher education level, for production of education in developing nations and for minority students in developed nations. Although popular literature and previous research findings claim that there is no DMR with respect to school inputs and education results and few tests looking for DMR appear invalid, Harris thinks differently. A new test was performed with 36 different countries for data, and as commonly found in popular literature the marginal effects of school inputs are frequently negative, predicting no DMR. But there were cases with positive marginal effects, offering signs of DMR. Harris also discusses a reinterpretation of the Heyneman-Loxley hypothesis about school input effects, which has helped international governments and aid agencies with educational investments.

 Commentary

Diminishing marginal returns is an economic law that claims that the marginal output of a production process decreases as the amount of a single factor of production is increased, holding the other factors of production constant. In other words, it claims that adding one more factor of production, holding all others constant, will lower returns at some point in time. Pertaining to our article, this would mean that marginal education results decrease as the amount of school inputs is increased.

While there will be a difference between the marginal returns to school inputs in developed vs. developing countries, we believe there would still be DMR in both types of countries. We believe the difference in marginal returns would result because of the current amount of technology in developed countries.

More specifically, we believe that since developed countries have ready access to technology and are more likely to have updated, thorough textbooks, increasing inputs would in turn increase their education results, but not by very much. There is only so much an updated textbook can achieve with respect to education levels. Likewise, teachers with higher education levels in developed countries are likely to boost education results because of their experience in their field of study, but not so much comparatively to undeveloped countries.

Contrarily, the developing countries are not as likely to have access to current technology, thus their education levels will not be as strong as the developed countries. Moreover, developing countries are not as likely to have updated and current textbooks, so that could hinder their education results as well. But, any increase in resource in developing countries would significantly increase the educational results more than in developed countries. The developing countries are able to utilize the extra resource more than the developed countries because of their lack of prior resources.

This is where the difference in marginal returns exists. More specifically, if an extra computer were added to Notre Dame’s campus, the educational results would not be significant. Yet if a computer were given to an undeveloped country, the educational results would be significantly increased. The developed countries can be seen as the “overcrowded” factories, when one more factor of production is added (educational input), the marginal output begins to decrease (education levels). Contrastingly, the undeveloped countries can be seen as a factory that does not have many workers, so adding one more worker (educational input) will increase their output (education levels) even more.

 Real-World Application

Diminishing marginal returns is a potential problem in every form of production, from manufacturing to farming. Managers must make decisions concerning the types and amounts of inputs involved in the process, in order to optimize the final output. At Stryker, a manufacturing company involved in the production of medical equipment, a manager would have to decide how many factory workers to hire to make each piece of equipment. For example, starting with 20 workers the company can produce 200 machines in a day. By hiring an additional worker, the daily production would increase to 210 machines. However, due to space constraints, when hiring another worker the company’s production would only increase by 8, to 218. When additional workers are hired, the increase in total production continues to grow smaller due to diminishing marginal returns.

A similar example can be found in farming, where crop yields are carefully monitored. Crop yields can be affected by many different variables, such as moisture, minerals, and sunlight, and plants must compete for the resources. Due to the competition, planting more seeds does not necessarily lead to an increase in production.  As shown in the graph below, while planting more seeds increases the net yield initially, the flattening of the slope of the graph clearly illustrates the effects of diminishing marginal returns.

  Graph

Posted by Matt, Chris and Allison (Section 1)

Resources:

http://www.investopedia.com/terms/l/lawofdiminishingmarginalreturn.asp#axzz1nXHsIJjA

http://en.wikipedia.org/wiki/Diminishing_returns#cite_note-1