Addressing Malthus With Zombies

On the new Economics Stack Exchange, user Mathematician asked:

Malthusians and Neo-Malthusians believe that, eventually, the population of the earth will be exceed the number of people able to be sustained by the earth's food production. As such, they advocated different forms of population control. However, it appears that an increase in the population beyond that of the food supply would cause an increase in the overall real price for food. Proponents of Malthusianism, evidently, are not waiting for food prices to rise before advocating population control, but I do not see how we should be worried until the real price of food increases. If Malthusianism is correct, how soon before the population crash would prices begin to rise?

In response, I put together an excellent answer that I wanted to preserve here.

This question rests on a few assumptions.

So let's dig into them.

What Malthus Said

First, the Malthusian collapse you are referring to is similar to the Malthusian Trap, from whence it derives, so let's look at that.

From Wikipedia:

In accordance with the theory, cross-country evidence indicates that technological superiority and higher land productivity had significant positive effects on population density but insignificant effects on the standard of living, during the time period 1–1500 AD. In addition, scholars have reported on the lack of a significant trend of wages in various places over the world for very long stretches of time. In Babylonia during the period 1800 to 1600 BC, for example, the daily wage for a common laborer was enough to buy about 15 pounds of wheat. In Classical Athens in about 328 BC, the corresponding wage could buy about 24 pounds of wheat. In England in 1800 AD the wage was about 13 pounds of wheat. In spite of the technological developments across these societies, the daily wage hardly varied. In Britain between 1200 and 1800, only relatively minor fluctuations from the mean (less than a factor of two) in real wages occurred in Britain. They peaked at around 1450 and in 1800 they were actually significantly worse.

So to go back to the source, Malthus didn't predict a population explosion at all (or food price rises for that matter). In fact, his theory was specifically that population growth fluctuated with economic development such that the prices of wheat (in terms of wages) remained relatively stable over two millennia.

This was known as the Malthusian Trap, where technological advancement would always be matched by (not exceeded by) population growth, resulting in the stagnation of living conditions.

Since the time of Thomas Malthus, new evidence has emerged that, while the trap may exist, many societies break out of it, and achieve explosive growth in living conditions. This is generally termed, the "breakout". In In A Trap At The Escape From The Trap?, Andrey Korotayev suggests that this breakout leads to social upheaval, and may have played a role in events like the revolutions in Latin America, or possibly even the formation of the US. Unfortunately if we delve too far down the social macroevolution road we wind up having to have the Guns, Germs, and Steel discussion, and that's straying dangerously off topic, though I also want to throw in a reference to Huntington, as another great and accessible read on the really big picture.

But More People...!

But moving back to your assumptions. Let's assume that population and technological growth became uncoupled by the "breakout". Now all of a sudden standards of living are at all time historical highs. Under Malthus we would expect the population growth rate to also be at historical highs.

But it's not.

In fact much of the developed world is at "peak population", facing major demographic shifts as baby-boomers age out of the workforce faster than they are being replaced. Japan faces a "China's growth rate has slowed dramatically and is now lower than the US's.

In fact, according to the UN, the projected world population over the next several decades looks like this:

Which you may notice is not an explosive growth. For more information on this, I'll defer to the experts at the Population Division of the Department of Economic and Social Affairs, and their technical paper

Cause and also Cause

Lastly, you're assertions rely on the assumption that increased population means food prices go up.

But that's not how numbers work.

Prices are denominated in currency.

More people (without a correlating rise in currency), actually means there's fewer dollars per person. In that scenario, food prices would go down (although probably slower than wages), leading to shortages. Price is a way of rationing scarce resources, but it's not the only way. The other way to ration is queueing, or shortage. This is what we see happen in developing nations. Rice is not more expensive, there just isn't enough rice there.

If everyone only has $6/lb, or he won't sell any.

An Inflationary Theory

In the event that the population increased, and central banks also increased money supply, than standard economic models would predict that the prices of all commodities (not just food) would rise, since the relationship to amount of quantity over the amount money would have changed, or roughly

where 

This would be conformant with standard economics, and not reliant on a Malthusian population collapse.

The only way we would expect prices to rise dramatically without central bank intervention would actually be after the collapse, as people accumulated currency, and would trade more currency for food.

TL;DR

In the event of a zombie or post-nuclear apocalypse, cash will decline in value relative to commodities, so stock up on rations and bullets because dollars won't help.

References

http://en.wikipedia.org/wiki/Aging_of_Japan

: Current research. You'll have to take my word or pull the data from St Louis Fed and BLS yourself.

Fallout: New Vegas. (2010). United States of America: Bethesda Softworks.

Starvation and the Necessity of Taxation (Part 1 of many)

I've developed a simulation to demonstrate the necessity of taxation in simple zero-sum economies.

In subsequent posts, I intend to expand this proof of concept to include economies with growth, and eventually with inflation, trade, and progressive redistribution models.

Effectively this simulation demonstrates that in any economy, taxation and redistribution is necessary to prevent members of society from dropping out of said economy, or more succinctly, dying.

Population

Starting Wealth

Average Trade

Tax Rate

Tax Period

The math behind this proof is fairly complex, so I'll start from the beginning and walk through the basics.

In this simulation, we assume that each person in the economy trades with another member, and that in each pairing one profits at the expense of the other.

Bad economists will argue that all trades are inherently profitable for all parties involved, but they are bad economists. In reality, each participant winds up with goods or services they may value more, but if we accept he existence of money and markets, these goods and services have a value for which they can be traded, and profit is defined as the increase in the market value of an entity's assets.

Following that, the simulation also assumes that everyone starts out with the same starting wealth. Obviously, this does not represent real conditions in an economy, nor does it purport to. In fact these idealized conditions represent a perfect economy, and any deviation from them only amplifies the random-walk effects of the simulation. Future iterations will include the ability to create and edit individuals within simulations, but for right now, as a proof of concept this demonstrates the math.

In the simulation, there are a two other variables, tax rate and tax period. Tax Rate represent the amount of profit (expressed as a percentage) recaptured and redistributed by an idealized government entity. Again, inefficiency in this government entity can be modeled, but only enhances the downward trajectory of the unfortunate individuals that are already "losing". Tax Period is how many trade periods occur between tax events. A tax event is when the government entity assesses profit, claims taxes, and redistributes wealth.

What this leaves us with is a probability that a participant in the model economy will reach insolvency by a period n.

This probability of an individual will reach insolvency for systems without taxation can be expressed roughly as:

where w is the starting wealth and t is the average trade.The probability that one individual in the population will reach insolvency is simply

pq

where q is the total number of individuals in the economy, and the probability that a percentage (x) of them will reach insolvency by time n can be approximated as

px

for all x such that xq > 1.

Taxation and efficient redistribution of course lowers this probability, but modeling its effects are complicated, and the subject of further discussion. For now, play with the colorful lines, and see if you learn something.