High Population Considered Necessary but not Sufficient for Poverty

A lot of water has passed under the bridge since my last blog entry. “Where in the world,” some asked, “is Atanu and why is he not writing stuff anymore?” For better or for worse, I am back from a brief round-the-world trip. Among the exotic far off places of the world, I was in Helsinki, Paris, London, Boston MA, New York NY, the San Francisco Bay area, Los Angeles, San Diego, and Seoul Korea. I flew Air France (which I call ‘Air Chance’), Delta (don’t ever make the mistake of flying Delta), and Korean Air. Met lots of interesting people and heard lots of great stories. One of these days I will write about them. But for now, it is back to the usual business.

So my obsession is with the population problem and as it happens, a member of the Deeshaa yahoo group wrote and asked a couple of questions. Here, for the record, are my responses.

“Are there possibilities where a large population is not ridden with poverty?”

Yes, casual empiricism demonstrates that there are large populations in the world that are not ridden with poverty. Take, for instance, approximately 300 million in North America (US and Canada, primarily.) Or the 500 million in Western Europe. Taken together, the population of US, Western Europe, Japan, the Asian Tigers, and Australia are above a billion people who are not poverty stricken.

Poverty (P) is a function of not just population (p) alone. In mathematical notation, P=P(p) is not the correct formulation of the P, the poverty function. Instead, the poverty function is P=P(p, t, r, i) where p is population, t is technology, r is resources, and i is institutions. The greater the population p, the greater is the poverty, all other things being equal. Hence p enters positively in the function. The greater the technology t, the lower the poverty function. So t enters negatively in the poverty function. Therefore, we can denote the poverty function as P=P(p+, t-, r-, i-).

A poor third world country has high population and relatively low t, r, and i. Compare that to that of an advanced industrialized economy: low p, but high t, r, and i.

The important thing to recognize is that it is not the raw population numbers that matter. It is what can be called the ‘normalized’ population numbers which we can denote as ‘np’. The normalization has to be done with respect to the other parameters t, r, and i. So np=np(p, t, r, i). Again in mathematical notation, P(p, t, r, i) = P(np(p, t, r, i)) = P(np).

The last bit is shorthand for “poverty is a function of normalized population figures.” More compactly, P = P(np+) which means that the higher the normalized population, the higher the poverty.

How does one arrive at the normalized population figure? The first step is to take the raw population figure p and divide it by the resource numbers r. Note that the resource r is a vector. For instance, it would include scalars such as total arable land area, the total amount of fresh water, the stock of physical capital such as roads, power stations, stock of fossil fuels, the stock of renewable energy resources, factories and farms, and so on. Then you do the same for the other parameters, technology and institutions and arrive at the normalized population figure.

The bottom line is that raw population numbers don’t amount to a hill of beans. Indeed, any raw number is essentially meaningless. We need to normalize the raw numbers before they can be meaningful. For instance, India is the largest producer of milk and produces 38,945,021 gallons of milk a year as compared to Denmark with only produces 1,045,983 gallons a year. India therefore produces 30 times more milk than Denmark. But that is meaningless unless one also knows that India’s population is 300 times that of Denmark. The proper normalization in this case is per capita milk production and consumption. That is, you take the raw milk production numbers and divide it by the respective population numbers to get the meaningful statistic that Indians only produce 10 gallons per year per capita while Denmark produces 100 gallons per year per capita.

It is simple arithmetic and those who refuse to do arithmetic are doomed to speak nonsense.

(Disclaimer: All the numbers above are straight out of a hat. They are definitely not accurate. They are for illustrative purposes only. The exact numbers are left as an exercise for the interested reader. For all others who are basically lazy like me, the fake numbers should suffice. You gets what you pays for.)

“Considered that population and poverty are positively correlated, how can it be shown that solving the population problem alone will solve the poverty situation. Are there other causal factors to consider?”

It would be silly to posit that solving the population problem alone will solve the poverty situation. That line of thinking will arise from a failure to distinguish between necessary and sufficient conditions.

Solving the population problem is a necessary condition but not a sufficient condition for poverty alleviation. Necessary conditions are — umm — necessary. If you don’t meet that condition, what you expect to happen won’t happen. But if you do meet the condition, what you expect may still not happen. That is so because while the condition is necessary, it is not sufficient for the event to occur.

So some conditions are both necessary and sufficient, some are necessary but not sufficient, some are sufficient but not necessary, and some are neither necessary nor sufficient.

Taking the horse to the water is a necessary condition for the horse to be watered. It is not sufficient because the horse has to do the drinking. If the horse doesn’t want to drink, fulfilling the necessary condition is clearly not sufficient for the horse to be watered. On the other hand, the horse may want to drink but if it not led to the water (the necessary condition), the horse will not be watered.

Not having shackles on one’s leg is a necessary condition for winning the marathon but it is not sufficient.

I would leave the rest of the discussion of necessary and sufficient conditions for the aforementioned interested reader. For now, here is the bottom line. Solving the population problem is a necessary condition to address the poverty issue but it is far from sufficient. Having a very high normalized population number is like wearing shackles during a marathon. Removing the shackles is a necessary condition but merely removing the shackles will not assure you victory; you will have to run faster than the others to win.

10 thoughts on “High Population Considered Necessary but not Sufficient for Poverty

  1. Venu Gopal Monday August 30, 2004 / 10:56 am


    What is your response to this article from IHT?

    It says the demographic ‘bomb’ is now fizzling to a ‘pop’, except for countries such as India and Pakistan. The surprising statistic was that China’s birth rate is now below France.

    Venu Gopal


  2. Jason Koulouras Monday August 30, 2004 / 2:37 pm

    If we believed that the current human population of the planet as a whole was optimal, we would want the birth rate to roughly equal the natural replacement rate. That is the number if births per female over her reproductive years would be about 2.1 per person in a society with access to good health care. This would ensure the population was static in numbers and that the population pyramid profile did not have bulges.


    Demographics are a difficult yet very interesting area of study.

    There are geographical or political areas of the world where it seems fairly obvious that there are just too many people per arbitrary measure (let’s say people per km squared). Examples come to mind such as India and China and right down to city level such as Manhattan and can even be down at the street intersection or neighbourhood level.

    One of the potential outcomes is that a country has a huge population explosion driven by birth rates over the natural replacement rate and then during the lifetime of those people, health care improves radically (which is a good thing) thus increasing the life expectancy of the population. Concurrently, the birth rate plummets towards or perhaps even below the natural replacement rate (remember this would be over decades) and you end up ultimately with a population “bulge” moving through the pyramid that has significant implications for society in terms of jobs, housing, economics and political leanings.

    Ultimately this bulge gets older and older and becomes from a work perspective “non-productive” (no emotional statements here – just the fact that as the body ages, it gets harder to work) and they need to rely on the younger generations (of which there may be fewer) to assist them.

    There are no simple answers but there are significant implications to any population policy.

    Very interesting post and welcome back!


  3. Atanu Dey Monday August 30, 2004 / 3:10 pm

    Thanks for the link, Venu Gopal. Upon reading the article, I fell as much solace as a starving man would feel upon learning that obesity is a major problem that Westerners suffer from and that on average the world produces enough food to feed everyone on earth adequately.

    My primary concern is the over population of India and what it means for hundreds of millions who have to suffer the consequences. The facts that some countries in the world have shrinking populations and that the global population growth rates are coming down are fairly tangential to my primary worry.


  4. Gaurav Bhatnagar Wednesday September 1, 2004 / 12:44 pm

    This might be a naieve question but how do we know that population is the cause for poverty and not vice versa. The western developed nations are seeing alarmingly negative growth rates. That seems to indicate that prosperity leads to lower populations. So are we poor because we are populous or are we populous because we are poor? I guess the answer is a bit of both and like you mentioned population is a function of several factors.


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