A Critical Analysis of the Malthusian and Alternative Principles Underlying One Scientific Article's Model of Population Capacity as Controlled by Biophysical Limitations.

A critical analysis of the Malthusian and alternative principles underlying one scientific article’s model of population capacity as controlled by biophysical limitations.

Abstract
With natural resource depletion and the human population at all time highs, both economists and ecologists alike are asking, “How much further can our population continue to grow.” At a historical glance, this question has been gone unscaved, as mans thirst for growth has always been regulated by high mortality rates (due to diseases and inadequate medical practices). However, better health care and social improvements have increased longevity since 1800 and, consequently, the human population has seemingly grown without bound up until 1970. Now, with the world population exceeding 6 billion people, for the first time mankind is beginning to breach the capacity limitations set by the biosphere.
Thomas R. Malthus, leading innovator in the debate over biophysical limits to economic growth, argues that economic activity cannot be expected to grow indefinitely unless the rates of population growth and the rates of resource utilization are effectively controlled. Modeling population dynamics and economic growth as competing species: An application to CO2 global emissions , from the journal Ecological Economics, utilizes Malthusian theory to provide a set of ordinary differential equations which model population growth as a complex interrelated function of natural resource depletion. Our Principles of Environmental Economics course explicitly examined this issue as we searched for an answer to the aforementioned question from Malthusian, Neoclassical, and purely ecological viewpoints. The following final project will incorporate the teachings we’ve developed in class, with a primary focus on Malthusian theory, and apply them towards a critical analysis of this article and its results; in addition to addressing the question posed at the beginning of this section to come up with a thorough understanding of this topic, once and for all.
Malthusian Theory: Our Primary Focus Malthusian theory dictates that human resources are finite and, therefore, will eventually limit the progress of the human economy. There are three basic postulates of the Malthusian doctrine as it applies to population limitation and growth. First, there are a finite number of resources available as dictated by the biosphere. This means that while technology can increase our efficiency of extracting and using these resources, the amount of resources available for extraction is finite. Second, if uncontrolled, the tendency for human populations is to grow exponentially. And lastly, technology cannot be perceived as the ultimate escape from resources scarcity. It follows then that under these postulate economic activity cannot be expected to grow indefinitely unless the rates of population growth or the rates of resource utilization are effectively controlled. Malthus most criticized proposition was that population growth, if left unchecked, would lead to the eventual decline of living standards to a level barely sufficient for survival. This has been called the dismal doctrine or the Iron Law of Wages because of its dismal vice tactics. The law of diminishing marginal product supports this suggestion because since resources are assumed to be fixed in supply, more labor applied to extracting a resource will yield a proportionately smaller return.
A good example is a family farm with one acre of land (a limited resource). If a farmer has a family of 5 which he is expected to provide for he can easily cultivate the land to allow his family to feast lavishly. However, if his wife continues to have more children, the farmer will have to yield more crops as he hopes to feed 8, 9, or 10 family members. The farmer is limited in the amount of food he can yield off of his one acre so that as he has 9, 10, 11 mouths to feed, each additional child means less food for everyone. Malthusian theory states that with each successive mouth to feed, the marginal product for each family member would decrease given the limited amount of land available to all.
This microscopic example holds true at the macro level as well, as Malthus used this logic to explain how economic efficiency is limited at the world level as the human population begins to over extract its available resources. This interdependence between population growth and natural resource limitations will serve as the primary basis for understanding the population model given in the article as will be depicted later in the paper. Before moving forward into the article’s application of Malthus’s work, it is important to acknowledge some important dissertation of the Malthusian theory which will impact our article. First, Malthusian theory ignores the institutional factors that induce humans to check their own population growth under adverse conditions. Second, it simply overlooks the important role technology plays in ameliorating resource scarcity. For example with our family farm, if new farming methods allowed the farmer to produce a higher yield on his land, diminishing marginal product could be offset. And third, Malthus’s model is considered to be ecologically naïve because it does not recognize the existence of absolute limits to natural ecosystems and therefore fails to explain the effect of economic growth on natural ecosystems and their inhabitants. Thus, Malthusian theory on population and resources is incomplete from economic, technological and ecological perspectives which we will attempt to correct using complex variables in our model.

A Neoclassical Perspective: A Brief Discussion Although our article contains a Malthusian focus, it is important to briefly acknowledge the neoclassical take on natural resource limitations. Neoclassical advocators do not differ entirely from Malthusians concept of finite resources; however they do reject that this fact implies economic growth will be limited. They believe that technology will ameliorate natural resource scarcity to avoid its limitations. Neoclassical economists believe that through finding substitutes, increasing efficiency or resource utilization, and the discovery of new resources, the human population can continue to grow without natural resources as a burden. They view resource scarcity as being specific, rather than general, so that any scarcity issue in a specific resource can be avoided through one of the three processes just mentioned. This theory also postulates that population, rather than becoming the problem with resource scarcity (as is the Malthusian belief), is actually the solution. Increased population also increases the number of bright minds capable of coming up with new technological advancements, in their eyes the more the merrier. Neoclassical economists look at the past results to support their future beliefs. This support they argue provides “proven” backing that technology can solve resource scarcity problems as it has done so many times in the past. The primary dissertations for this belief are that past trends are too unreliable as predictors of the future and that technology itself is too unpredictable to be so heavily relied upon as the cure.
In spite of these arguments, neoclassical theorists believe that any shortcoming in technology will be avoided by the demographic transition effect. This theory is based on an empirical generalization which claims that, as countries develop, they eventually reach a point where the birth rate falls. There are a number of psychological explanations for this phenomenon. The following historical example provides the primary basis for the demographic transition effect and its derivation.
The world population’s growth rate first showed significant increases in the latter half of the nineteenth and better part of the twentieth century. This effect has been the result of significant advances in technology during that period (examples include vapor machines in industry, the discovery of penicillin, and advances in theoretical physics to name a few) which increased life expectancy, reduced mortality rates and boosted economic growth. The world was transforming from a labor-intensive agro-rural economy to a more urban industrial one. But the introduction of computation and automation reduced the need for manual activities, replacing the demand for human labor for fewer but highly trained personnel, leading to a steady decline in population growth for the first time in over a century. Given the lowered mortality rates is combination with decrease in demand for labor, there simple were fewer reasons to have kids, and statistics strongly support these propositions. While the demographic transition experienced in the 20th century is relevant to any discussions of population capacity, it was not the primary focus of this article. It should be noted, however, that a scrupulous amount of historical statistics when in to helping determine the coefficients for our model. So while the theory of demographic transition is ignored in our model, its effects through the twentieth century did play a role in determining our results.

The Model: Relating GPD to Population Growth
The journal article references the aforementioned Malthusian theory in addition to some alternative concepts in order to derive its model. One of its primary assertions is the idea of Gross Domestic Product being used as measurement of natural resource extraction because of its direct correlation as a factor of production. As it serves, if the GDP level doubles, the natural resources required to facilitate this production should in turn double in a linearly organized fashion. This article chooses to acknowledge both the “exogenous” and “endogenous” theories for relating population growth to GDP. The methodology is irrelevant to the authors, because rather than concern themselves with which theory is best they choose to simply allow them to acknowledge the close correlation between GPD and population growth which has also been established in the text. Then, rather than choose one theory explicitly, it chooses a dynamic modeling system which allows for the aforementioned postulates of the Malthusian theory and its shortcomings to be accounted for, then uses the best possible historical data to derive values for the constants. In doing so the authors were able to achieve comparable results to leading world agencies such as the United Nations.
Before we reveal equations the article used we should discuss briefly an explanation for why the author chose to use ordinary differential equations to model the carrying capacity. Population growth can be modeled using a variety of different functional relations, the most basic of which is an exponential function. Exponential growth occurs often in nature (especially at the microscopic level) provided there are no limiting factors. It also was an applicable model for the population expansion which occurred from the early 19th century up until about 1970 (this concept will be further expanded upon in a moment). A more practical method for population modeling, however, is the idea of using logistic formulas because they incorporate the idea of a carrying capacity. This allows us to account for many of the limiting factors that more often arise in nature (i.e. limited space, food, or predator species), making logistic modeling a popular way to model real world problems. The human population capacity could be also be fitted to a logistic curve, however, pinpointing a carrying capacity would be difficult to estimate and it would ignore the complex relationship between population growth and GDP the article intends to focus on. Clearly a more dynamic modeling approach is required.
Using GDP as a proxy for natural resource depletion we are able to describe a more complex relationship between the growth rate of the human population and GDP. The authors chose to use the popularized Lotka-Volterra Relations modeling system to find a more dynamic solution to relate our two variables. Originally developed to describe predator-prey relations, the passage shows how the LVR system can effectively be applied to describe the our model by viewing world population as the predator and GDP as the prey (the article includes a disclaimer which explains how it is irrelevant which variable you select as the predator or prey which I chose not to include because it is irrelevant to our discussion).
The following is the set of differential equations the authors used to model the relationship between population size (p) and gross domestic product (g): Focusing on the first equation for population growth, it logically follows that population growth would otherwise grow exponentially if it were not for the limitations set by the biosphere (i.e. finite natural resources), as represented by α1. This falls in line with what we learned in class in that without some limiting mechanism population growth would be exponential. Malthusian theory, however, explains gives us this limiting factor (a finite deposit of resources) because as the population size increases, marginal benefit from natural resources diminishes, placing downward pressure on population growth. This downward pressure is a direct result of the positive checks which will ultimately suppress the reproductive power of a population to a level consistent with the means of subsistence (the Iron Law of Wages). The coefficient α2 represents this effect.
The second equation explicitly defines GDP as a function of both itself and the current population level. It begs no detailed explanation that β1 represents the natural growth rate of GDP over time if it were independent of the population size. The more interesting component is the coefficient β2, which represents the diminishing effect an overwhelming population has on GDP. Malthusian theory explains how as a population lowers the GDP level both directly and indirectly, which can be more clearly explained using an example such as oil. Direct implications can be seen by the increased population resulting in a greater labor force which will diminish the oil supply while indirectly the increased population will have a greater demand for oil consumption, leading to more oil being depleted. This effect will put downward pressure on GDP as result of resource depletion likely per capita damage.
The α3k1 coefficient is a modifier of the α1 growth rate and represents the most uncertain future variable, technology. One of the main criticisms of Malthusian theory is that technology is often overlooked, so this coefficient plays a crucial role in the modeling outcome as a whole. This coefficient is difficult (and some would argue impossible) to predict, so determining this coefficient properly has a dramatic effect on our results. To best reflect the technology component, the authors collected historical data from over 20 different international databases dating back to 1850 to achieve the most accurate interpretation of this coefficient as possible. The article dictates how although empirical evidence was used to derive this technology component, it is very possible that at some point in the next decades a new excitation may boost again the economy leading to a new phase of population growth, or some other unforeseeable solution.
The Results: In Conclusion

Thanks to our Malthusian principles which gave base to our Lokta-Volterra modeling system and allowing for an extensive collection of historical data to determine our coefficient values. The results were as follows: According to the proposed coefficients, the population will have a slow growth (α1) of about 0.3% per year (typical value for population growth prior to 1900), and it is boosted through the per capita growth rate increase present in the functional response α3k1 (used as a proxy function to represent the technological and cultural changes). But the same GDP growth will limit the population growth expressed by negative sign of α2. On the other side, the mean growth of GDP (β1) at a high rate of 3.1% is controlled by the population growth β2. The end result is new stabilization phase (what neoclassical followers could argue as a new demographic transition) by about 2070 to 2080 of about 10 billion inhabitants. Thus, through an in depth analysis of this scientific article, we have reviewed some of the more prominent theories which are pertinent to any population capacity discussion, and moreover, received at least one guestimate to the aforementioned question which we hoped to discover.