Water and Food for 9 Billion People in 2040

November 7, 2013 • John Vandivier

Malnutrition is defined as poor nutrition caused by insufficient, over-sufficient, or poorly balanced diet or by a medical condition (“Malnutrition”). This means that every person requires a certain amount of certain nutrients on a regular basis. Nutrients include both caloric and noncaloric nutrients such as water, vitamins, minerals and others (“Schaffer”). If a person lacks nutrient enough and succumbs to malnutrition the results are dire. Malnourishment will attack the immune system, eventually leading nearly inevitably, although usually indirectly, to death by infection or otherwise. This means that feeding and providing water for 9 billion or more people after the year 2040 is an important question to answer if we seek to maximize the welfare and safety of the future world population. I will look at past and present data on producing food and water and will extrapolate the growth patterns found into the future in order to attempt effective forecasting of how the world situation will look at that time. I will give special attention to technological innovation including what innovations have been made in these fields, how often innovations are made in these fields, and whether or not we should expect future innovations and what those future technologies might look like. Based on these findings I will argue that the world will easily be able to produce enough nutrient to feed 9 billion people in the year 2040, but that it is likely that hunger and malnourishment, even deadly malnourishment, will still exist to some degree despite increased availability of nutrient.

The World Food Problem records that the US Census Bureau projects world population to be about 9.54 billion by the year 2050 (“Foster”). Population projections are a tricky thing and vary somewhat widely. Exxon Mobile still uses the once common projection that, “By 2040, there will be nearly 9 billion people on the planet, up from about 7 billion today” (“Global Fundamentals”). In that article Exxon Mobile goes on to mention that while developing countries

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and third world countries are expected to explode and then level off in population growth, OECD countries are expected to have little population growth or even some population decline. Exxon Mobile argues that this will contribute to a major decrease in demand for energy sometime soon after 2040. I will argue later in this paper that the situation with regard to nutrition is similar. Debate over time-lines for population growth do not only vary from organization to organization. Some organizations have multiple different projections depending on various factors in order to develop a more robust understanding. The UN, for example, has developed 5 different estimates based on systematic differences in assumption or calculations behind population replacement rates (“Figure 1.”). The population replacement rate is a better tool for calculating population than simply the population growth rate because the replacement rate accounts for the death rate as well, a key feature in our present age of rapid medical advance. A graphical illustration of the UN's estimates is attached on Addendum A, the page after the bibliography. In the highest rate of growth projection the population of the world hits 9 billion not in 2040, but in 2035. Perhaps more surprising, in the low growth rate projection the world population never comes near the 9 billion mark, topping out at about 8 billion around 2045. The average of the various projections, however, do approximately support the idea of a population around 9 billion in about 2040. Providing food for 9 billion people in 2040 and providing water for 9 billion people in 2040 are not exactly equivalent goals. In general the problems and solutions are the same, but the way those goals will be achieved are different enough to warrant note. Both dehydration and lack of food result in the general thing called malnourishment or malnutrition and they both contribute indirectly to death or otherwise lowered quality of life by allowing the immune system to weaken or via other means. However, one significant difference

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exists on the production side. As we will discuss later, the marginal cost of producing additional clean and drinkable water for one more person is much more costly than the marginal cost of producing additional food for one more person. Additional differences include the fact that water is a more widely used nutrient across the human body and therefore more is required than is required of other nutrients or else the negative impact to the immune system will more often be more rapid and severe, and finally the fact that increases to water supply and improvement to water production technologies vary at a systematically and significantly different way than do those same factors with regard to food. It is this last noted difference which is most significant to our computational efforts.

The reason that the rate of change of water production technology is of supreme calculative interest is because the causes of malnutrition can be broken into three very general parts, and one of those parts can be readily addressed by a simple calculation. The three very general issues are lack of supply, logistical problems and medical problems. We can calculate whether a lack of supply exists relatively simply using several growth rates and one of them is the rate of change of water production technology. The other two issues we will have to deal with separately. Very simply, if the growth of production outpaces the growth of demand then in the long run we will be able to eliminate hunger due to a lack of supply. We can take demand per for water and demand for food and assume that they grow at the same rate as population based on the principle that there is a static level of nutrition which will allow people to escape malnutrition. We will take the estimated growth rate of population, as provided by UN estimates, and use this as a proxy measurement for the growth rate of demand of water and food. As previously mentioned there were several different growth scenarios offered by the UN. We also

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noted that by taking the average of those estimates we can roughly confirm the common wisdom, or common estimate anyway, that population will be near 9 billion in about 2040. However the growth rates behind those estimates vary widely and for various different theoretical reasons (“Figure 1.”). One model, for example, assumes that fertility is constant, one model assumes that population maintains “instant replacement,” and the other models project varying degrees of fertility. Because these models are so theoretically different, we have no reason in theory to justify the averaging of their various growth rates. Instead of simply averaging the very different assumptions behind these models, I will select and use the growth rate behind only one model. Because we roughly confirmed the 9 billion people in 2040 figure from various sources we will simply use the growth rate of that UN growth model which most nearly predicted that population would hit 9 billion people in 2040. As shown in the figure from the Addendum A the model which made the prediction most nearly is the model called “Medium Fertility Varient.” It also happens to be one of the models which makes less odd or extreme assumptions, as it is built using moderate expectations of fertility. The growth rate of population for that model is revealed to be variable in another UN article (“Figure 6”). That article had an illustration as well and that is included at the end of this paper as Addendum B.

Not only is the growth rate variable under UN projections, it is subject to nonlinear variation, making it very hard to back into the numbers they use. Neither do they publish the values they use, although the raw data from individual countries can be obtained on their website. On the other hand, for the particular model we have chosen the growth rate decreases at a nearly perfectly linear rate over the time period of interest, from 2010-2050. The data shows that from 2010-2015 the annual rate of change of total world population is about +1.15% while

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the annual rate of change of total world population from 2045-2050 is estimated at about +0.5%. Using these figures the projected rate of change of the annual rate of change is (-1.1%) / (40 years) = -.0275% per year. Because this number is negative we have an indication that the rate of growth of the world population is expected to decrease over our time period of interest. Furthermore, as shown by the figure in Addendum B, this slowing of growth is expected to continue on outside our period of interest, and in some models the growth rate of world population is expected to turn negative over time. To simplify calculations we will allow for world population growth to maintain a 1.2% growth rate per year. This is a more conservative than estimated value and therefore if food and water can keep pace with this rate than they can also keep pace with our real estimated values, however the 1.2% value is easier to work with because it is a static value and includes fewer decimal places. In order to establish whether or not food and water can keep pace with increased demands by the population we must obtain values for the growth rate of food and water production. Chapter 14 of The World Food Problem is called “Increasing Yields” (“Foster”). Early in the chapter a table reports wheat yields in Britain over the time period from the years 1450-2000. In 1450 wheat yield was at 500 kilograms per hectare. In 2000 it was about 8000 kg/hectare. This calculates to (8000/500) x (100%) increase over 550 years. This is = (1600/550) = about 3% per year increase. Not only is this a fairly time-robust figure, being drawn from a period of hundreds of years, it also easily outpaces the increasing demand figure of 1.2% by over double. However, this is only for one crop and one geographical area. Fortunately, the same chapter of the same book has other robust studies which reinforce the idea that food will outpace increased demand. A meta-study by Pingali and Heisley is discussed in the chapter which covers TFP estimates from fifteen separate studies which

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involve thirty two countries over a variety of time periods. That study concluded that total calories produced worldwide increased on average by 2.24% per year from 1961-2001, showing that food production increase is not limited to wheat or Britain, and that production increases, while slowing, are still dealing handily with population increases. The chapter also points out that there are numerous advances going on and that food production technology still has plenty of untapped potential. Specifically the chapter mentions reduction of environmental degradation as a particular concern.

Before we try to find similar calculations for water, I would point out one particularly sad, but effective argument showing that hunger is not a world threatening problem. Economics of Agricultural Development also discusses the importance of reducing environmental degradation, but it does so in a very different context (“Norton”). In Chapter 9 which covers “Resource Use and Sustainability,” the authors note that, “The poorest countries...have the potential of being the most vulnerable to environmental degradation,” and that, “The poorest people within these countries usually suffer the most.” What is uncovered here is the fact that risks of hunger and malnutrition are not evenly spread over the globe, they are systematic. This is very sad in one sense but sickly positive in another light. It is sad because the poor suffer an increased risk of malnourishment for which they are not always directly responsible. However this unequal distribution is positive in the sense that if one day the amount of nutrient available were to fail and fall below the nutrient needed by the world population, that would not imply that the whole world would starve. Rather, some of the poor would starve. Again, this is sad, but it is also strangely beneficial. The poor contribute to the rate of technological increase at a disproportionately low share, while the rich, who would not be starving, contribute to innovation

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at a higher rate. Finally, it is the poor who have a dramatically higher birth rate on average. For example the USA and Europe are responsible for more innovation than Africa or most of the Middle East. What this implies is that if a “hunger shock” were to occur it would not threaten the whole world and it would not be a “game-changer.” Rather, it would lower the rate of population growth, drive up the average literacy rate, and lower the demand for nutrient more than it would lower the supply.

According to World Bank the world is on track to cut the number of people without access to good drinking water in half from the period from 2000-2015 (“Water Supply.”) This number is tricky to convert into growth rate, but it does represent an absolute reduction in the number of people suffering from lack of good water. If this rate would keep up then we would be safe despite increases to population growth. However, there are some problems here. That is because most of this water is from nonrenewable sources. This means that, some time or another, we will run out of that water. According to an article from The Economist magazine, the problem has been the fact that renewable sources of water drinking water are rare (“Tapping the Oceans”). However that article notes various improvements to drinking water technologies. While it includes no information on growth rates, it does mention the fact that there is technology which can be used to desalinate the oceans, producing a virtually limitless supply of water. The issue here is more of an economic one because this technology is very expensive. The article states that in 1965 small reverse osmosis plants were used to filter water, but not yet for sea or ocean water. Even if the world could only tap freshwater it would still be able to support a significant population, but whether it would be able to support 9 billion is questionable because, as the article states, less than 3% of the world's water is freshwater, and of that freshwater much is

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frozen in polar ice caps. However the article states that starting in the 1970s, reverse osmosis plants began to be used for desalination, but they used huge amounts of energy. Finally we get into some information we can use when the article notes that:

“Economies of scale, better membranes and improved energy-recovery have helped to bring down the cost of reverse-osmosis seawater-desalination. Although the cost of desalination plants and their water depends on where they are, as well as the local costs of capital and operations, prices decreased from roughly $1.50 a cubic metre in the early 1990s to around 50 cents in 2003.”

The article notes that increased energy prices since 2003 have meant a bounce-back to about $.75 per cubic meter of water, but that technologies which hold promise are still being researched and that as energy costs in general decline the process will cheapen (“Tapping the Oceans”). Using the most conservative numbers of a decrease in price from $1.50 in 1990 until $.75 in 2008, the year that the article was written, we find a growth rate in supply of 100/18 = 5.6% increase per year. Technically this is a reduction in cost by 5.6% per year, but I think this is the best proxy measurement for a growth rate of water supply that we will find. This number, as well as the evidence from the World Bank development numbers, signal that we will at least be able to keep water production in excess of water demand until our nonrenewable sources run out, but then the game may change.

Now that we have addressed the question of supply and demand growth rates for food and water a disclaimer must be made. The relative outpacing of growth rates ensures that there should be no issue of supply only if we assume that such supply can be effectively transported to

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the those people who demand it, and that no unusual “shocks” occur. It is quite possible that logistical issues may arise in the future, or that some unexpected shock to supply or demand may occur, any of which would render our analysis either less useful or completely worthless. A research paper by the organization Microcon claims that war has been identified as a main cause for poverty in the world (“Justino”). War causes infrastructure damage and can impede free trade between supplies and those who demand them. Natural disasters can function in similar fashion, as was noticed during Hurricanes Sandy, Ike, and Isaac amongst other major storms. Finally, poor governance or economic policy such as prevention of free trade or free flow of information can distort the results we would expect under normal capitalist free market conditions. Supply and demand shocks are another entity which could negatively impact forecasts. These are much trickier to anticipate. In fact, according to one website's definition of supply or demand shocks, “In the context of economic markets, anything that unpredictably affects the market in a large manner is considered a shock” (“Supply and Demand Shocks.”) Under this definition shocks cannot be anticipated or foreknown necessarily, or else they would not be considered shocks. Yet time and time again we have documented cases of supply and demand shocks occurring such as during the oil shock of the 1980s. If there is a take-home message for policymakers which we can deduce from the historical existence of shocks it is that we should act conservatively with our valued assets by anticipating more risk than our average predictions allow for, and that we should also value adaptivity because we recognize that absolute catastrophe is not a rarity nor a possibility but an inevitability, and therefore we should be prepared to quickly adapt and bounce back when, not if, danger strikes.

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In conclusion we have only discussed relative growth rates, not actual supply and demand. The results of the analysis showed that supply growth rate of food and water will handily outpace the growth rate of demand due to increased population by most reasonable forecasts. However the outpacing of growth rates by no means indicates that hunger and malnourishment will be eliminated. The outpacing only indicates that we will have lower rates of hunger and malnourishment than we do in our present time, ceteris paribus. These gains would possibly be thrown off due to things such as bad governance, war, natural disaster, an unforeseen outbreak of disease, or any other number of interesting and dangerous events. On the other hand, as one economics website points out, there can be positive shocks as well (“Supply and Demand Shocks.”) Perhaps a new technology or resource deposit discovery is made and it might just happen that these tings we consider so dangerous now may be shortly and miraculously resolved. However, even if the bad shocks occur while the good shocks do not, and the world finds itself unable to feed the global population, it still does not indicate that worldwide malnutrition will ensue because the nature of exposure to malnutrition is unevenly distributed. Instead of a worldwide famine in such a case we would see only part of the world exposed to famine. Of course that would be a grievously bad thing, but it would only be temporary, and humanity would still find a way to carry on.

Bibliography

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Norton, George W., Jeffrey R. Alwang, and William A. Masters. Economics of Agricultural Development: World Food Systems and Resource Use. 2nd ed. New York: Routledge, 2006. Print.

Foster, Phillips, and Howard Leathers. The World Food Problem: Tackling the Causes of Undernutrition in the Third World. 5th ed. Boulder, CO: Lynne Rienner, 1992. Print.

Schaffer, Catherine. "Effects of Malnutrition on the Body." Livestrong.com. N.p., n.d. Web. 04 Dec. 2012. <http://www.livestrong.com/article/491403-effects-of-malnutrition-on-the-body/>.

"Figure 1." World Population Prospects, the 2010 Revision. United Nations, Department of Economic and Social Affairs, n.d. Web. 04 Dec. 2012. <http://esa.un.org/unpd/wpp/Analytical-Figures/htm/fig_1.htm>.

"Figure 6." World Population Prospects, the 2010 Revision. United Nations, Department of Economic and Social Affairs, n.d. Web. 04 Dec. 2012. <http://esa.un.org/unpd/wpp/Analytical-Figures/htm/fig_6.htm>.

"Global Fundamentals." Global Fundamentals. ExxonMobil, n.d. Web. 04 Dec. 2012. <http://www.exxonmobil.com/Corporate/energy_outlook_evolution.aspx>.

"Malnutrition." The American Heritage Stedman's Medical Dictionary. Houghton Mifflin Company. 03 Dec. 2012. <Dictionary.com<a href="http://dictionary.reference.com/browse/malnutrition">http://dictionary.reference.com/browse/malnutrition>.

"Water Supply." Water. The World Bank, n.d. Web. 04 Dec. 2012. <http://water.worldbank.org/topics/water-supply>.

"Tapping the Oceans." The Economist. The Economist Newspaper, 05 June 2008. Web. 04 Dec. 2012. <http://www.economist.com/node/11484059>.

Justino, P., 2010. War and Poverty. MICROCON Research Working Paper 32, Brighton: Microcon. Web. 04 Dec. 2012. <http://www.microconflict.eu/publications/RWP32_PJ.pdf>

"Supply and Demand Shocks." EconPort. Experimental Economics Center, 2006. Web. 04 Dec. 2012. <http://www.econport.org/content/handbook/Equilibrium/shocks.html>.

Addendum A

Estimated and projected world population according to different variants

$\"un-population-projections\"$

1950-2100 (billions)

Source: (“Figure 1.”)

Addendum B

Estimated Annual Change to World Population Growth Rate by Time Period as a Percentage

$\"249d2fc9a6e58d4092ad5fbb5dfde53bd3a92494\"$

Source: (“Figure 6.”)