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.

A Bit About BitCoins

What is a Bitcoin?
Nothing. They don't exist. Not even in the sense you're thinking they do.

Bitcoin is actually a system of recording transactions, and not a unit of currency. Bitcoins do not have serial numbers, are absolutely indistinguishable from each other, and can be broken down into any smaller unit of value without having to exchange one object for another (like a dollar for four quarters). It's important to keep this in mind.

How do I get a Bitcoin?
Again, you don't.

You can create a wallet, which is an address in the system, that can be credited a payment of a certain amount of bitcoins, but you never actually receive a bitcoin. While functionally, you have the authority to spend all the bitcoins that have been credited to the address, so in simple terms, you "have" those bitcoins.

The issue is that the bitcoins cannot be taken from that address. Bitcoin relies on a complicated encryption system that means a transaction must be voluntary (i.e. you must provide the password [actually a private key] to the account for each transaction). That also means if anyone gets your password, they have your bitcoins. There's no such thing as "cold storage" because every address is part of the network at all times.

That being said it's safer to keep your private keys away from machines connected to the internet unless you're authorizing a transaction.

How much are they worth?
Well, as Buffett said, price is what you pay, value is what you get.

Don't be coy. It doesn't suit you.
You are correct imaginary interlocutor, so in an effort to answer your question the only way I know how, here's math.

Bitcoins have a fixed supply, and a fixed velocity. There can be no more than 21 million of them, and each one can trade hands roughly once an hour. (This is not 100% accurate, but for now we'll use it). What that means is that there can be at most 184 billion bitcoins worth of transactions a year.

That sounds like a lot.
No it doesn't. The United States GDP was roughly $16.4 trillion last year and that's about a quarter of the global GDP. That means that each bitcoin is worth roughly $356 2012 USD, if you assume BTC will replace 100% of global currency. Scale to your liking depending on the anticipated adoption rate.

Why is there an extra number there?
Because USD are inflationary, in that more are issued each year. We do this because economics tells us that is how to run a healthy economy. Generally inflation is used to prevent wealth accumulation which prevents trade and destroys economies. Bitcoins, however, are deflationary, in that there's a fixed supply of them.

This is very, very bad. It is also why no country has used a non-fiat currency in decades. That being said, the relationship between USD and Bitcoins is such that the value of a Bitcoin goes up every year, or more precisely, the value of a dollar goes down.

Are there other ways to get Bitcoins?
Yes, you can mine them. In practical terms, you cannot mine them. What you can do is purchase mining power from a commodity exchange like CEX. Mining power is measured in GH/s or billions of equations solved per second.

That sounds confusing.
Indeed.

What are GH/s worth?
Well, to give you the straight dope on that you need to know what today's risk-free rate of return is. If we assume that to be 3%, than a GH/s is worth roughly 13.9 BTC until next year, then it goes down by about 30% every two weeks as the difficulty increases.

Caveat Lector
This is economics, not trading advice
Now, on to the more important caveat. You cannot buy a BTC for $356 USD. You cannot sell a GH/s for 13 BTC. These things exist in thinly traded, ill-informed, wildly volatile and incredibly speculative markets.

The equations above tell you the value, not the price. I make absolutely no prediction as to what the price of any commodity will be at any given time, because "Markets can remain irrational a lot longer than you and I can remain solvent."

Induced Economic Effects Part 2 - Template Entities and "Buck Rot"

So last week we introduced the concept of money flowing into, through, and out of an economy based on an initial investment and subsequent transactions.

We also promised to update, and failed to deliver.

Of course I'm using the royal "we", in both senses, but that's neither here nor there.

Today, I want to introduce the concept of iterated transactions, because when we talk about how much money remains in an economy after a given period of time based off of an initial investment, what we're really trying to capture is a sequence of iterated transactions.

One of the fundamental truths of economics is that money itself has no value, and only its use gives it utility in the traditional economic/utilitarian sense. This is true whether we're talking about USD, BTC, or CNY. It's the ability to spend money that gives it its value, and consequently, the velocity of money is a core concept in economic analysis.

What is "the velocity of money"? It's very similar to the physical concept of velocity, in that it is the number of hands a unit of currency moves through in a given period of time. So in the case of economics, it is helpful to think of money (or value) as "mass", people (or entities) as "distance", and time as ... well time.

One of the derivations of this, and I won't go into too much detail in this post on it is the "stickiness" of prices in the New Neoclassical Synthesis, which is that prices are not perfectly fluid, because it takes a shock of sufficient "force" (similar to Newtonian F=ma) to move prices, and that they have a proportional rate of change equal to their momentum (big transactions that have been happening frequently for a long time change more slowly than little transactions that have been happening infrequently for a relatively short period of time).

When we talk about induced economic effects, and attempt to quantify the size of the residual impact after a given time, we need to talk about how much of each dollar stays in the economy after each transaction. To do that its useful to discuss template entities. The reason we have template entities, is that in practical terms, it's very difficult to quantify each individual transaction, but in aggregate, we can take averages, and develop a theorem with strong statistical validity as long as there's a solid average.

Last week I used a 7-11 as our example entity, and discussed the purchase of a candy bar. If we assume that every entity has a similar structure in terms of money that stays in the economy vs money that leaves the defined region, we can come up with a formula.

So again, for simple discussion, let's assume in each transaction, roughly 50% stays in the geographic region. That number is of course a placeholder, and there's a substantial body of work to calculate the actual value, primarily by the US Bureau of Economic Analysis through their Regional Input/Output Multiplier System, known colloquially as RIMS II.

What our simplified assumption tells us, is that for every dollar spent in the region under analysis, fifty cents stays in the region. Combining that with a velocity of money, which we'll assume to be at 1.5 per quarter, or 6 per year (which is close enough to the actual value for this simplified analysis) we can see that within a year, each dollar is spent 6 times, each time, half of it leaves the economy, or that our residual is equal to:

or the initial investment times the one minus the amount left after each transaction raised to the number of transactions we expect to have occurred in the time period. In our simplified example, this is effectively a half-life.

Barring outside reinvestment, the money in an economy decays at a predictable rate, hence the term of art I like to use, "buck rot".

In this example world, every year ~98.5% of our initial investment decays out of the economy, which is why reinvestment and exports play a crucial economic role.

Which we'll talk about soon. Before that though, there's a few posts I've been meaning to publish on the emerging Bitcoin phenomenon. 

Induced Economic Effects

A lot of people ask me what I do for a living.

Well, mostly the people paying me, but they ask it a lot, so I figured I'd take a blog post to talk about something relevant to my interests.

These days I spend a lot of time studying and quantifying the economic impacts of investments in different communities based on a concept called "Induced Economic Effects".

What it boils down to, is that for every dollar invested into an economy, a certain number of cents can be expected to stay circulating in that economy.

So, for example, if you were to buy a candy bar from your local 7-11, and for some strange reason, it were to cost exactly $1.00, my job is to figure out where all one hundred pennies wind up, and how quickly they get there.

I didn't say it was a good job.

Econometric Analysis has not led to nearly the debauchery I was promised, as both the booze and the bitches have been mysteriously over-represented in the brochure.

That being said, tracking a dollar is hard work. Tracking millions of them is even harder, but because this is a blog, and you free-loading readers aren't actually paying for this, we'll stick to the example of the dollar at the 7-11.

So let's follow the money.

Assuming you live in a civilized state like New Jersey (and not some communist VAT utopia like the EU), your state has a sales tax. Sales tax can range anywhere from 0 to 25%, but in this example, we'll assume it's going to be 6% because you're not the kind of person to shop in one of those sketchy low sales tax HUD areas.

That means that six pennies have disappeared to the coffers of the state, so we need only follow ninety four more. (Actually, that's a bald faced lie that we'll return to in a bit, but for now pretend to believe it.)

Of our remaining ninety-four cents, let's assume that the retailer marked the product up 100%, as is their custom. This means that forty-seven pennies disappear out of our economy back to the manufacturer. If you're keeping track at home, we've now accounted for nearly half of the first generation of pennies in just two short hops.

And this is where things get hairy. Of the forty-seven remaining pennies, some percentage went to overhead. Traditionally in retail we anticipate approximately 30 percent of Net Revenue to be consumed by overhead. In this simplified example, we'll assume that ~30% of the net revenue from every sale covers the SG&A expenses of the store since 7-11 generally runs a pretty tight ship. that takes fourteen more pennies out of the equation to the bank, the power company, and whatever other expenses the shopkeep has. This leaves thirty-three pennies for labor.

Not bad.

Or, if you're one of my clients, "What the hell are we paying you for, any idiot could have told us that?!"

True, and the difference is, this is where an idiot leaves the discussion. Because in reality, this is where things are just starting to get interesting.

If we assume that the region or economy under analysis is the state, how much money is left in the economy?

The correct answer is: None.

"Wait... what? I know I'm bad at math, but if we start with a dollar, how'd you get to none?" I can hear you asking now, because I, like the FBI, can turn your computer microphone on at will in direct contravention of any perceived rights or liberties you may have.

It's a gift.

What's actually going on is that after the first generation of transactions, a portion of each of these expenses stays in the state. At this point, to make things easier we'll have to create a template entity and assume that all of the recipients of our pennies behave the same way. While we know this is not true, we can make the assumption that on average they'll all even out to something.

What is that? Well stayed tuned, as tomorrow's post will detail template entities and the time-decay of microeconomies, or as I like to call it, "buck rot".

Income Inequality and The Cost of Education

What's the value of a good education?

Hard to say in America, where the quality of education is falling faster than the cultural relevance of my refences, but what we can quantify is what's the value of an education.

Let's look at some numbers.

Below is the average weekly income of a high school graduate versus the average income of a college graduate (bachelor's degree any field).

While this only tells half the story, it's a compelling half already. What we can see from this graph is that the average college graduate earns roughly $23,000 per year more than the average high school graduate, and that that gap is widening by about 1% a year.

Whew, that's problematic if you're that guy without a degree.

But wait, it gets worse.

According to this chart that I totally did not make up (with numbers sourced from 11 years of BLS data), there's a roughly 16 point difference in labor force participation, meaning a college graduate is almost 28% more likely to be employed at that higher wage than a high school graduate is at the lower.

What does this say about the cost of education?

Well, if we assume that 18-year-olds behave in an economically rational manner and that unicorns are a thing, we can calculate what's called a "Net Present Value" of a college degree by taking a discounted future return on the increased earnings and probability of earnings to yield a "value" that a rational consumer should be willing to pay for the privilege of being roughly 30% more likely to be employed at a salary roughly $20,000 higher than they would be without it.

Summing up the tedious math of probability weighted present values of future returns, we can safely say that the "value" of a college education in the United States in 2003 was roughly $188,495. Projecting forward at that growing with that 1% annual gap for the next ten years, someone entering college today would rationally be willing to pay over $200,000, and still come out ahead of their diploma-only counterpart.

Now of course this simplifies the equation quite a bit by ignoring the likelihood of dropping out, which is staggeringly high in the US, but even assuming there's only a 50% chance of graduating, $25,000 per year is where tuition should be based off the economic factors.

Not surprising since the average published college tuition for a four year school ranged from $15,130 to $30,094 for the 2013-2014 school year.

Funny how economics works out like that.

Raw Data (Note Q4 '13 was projected from an average of the previous three quarters since data was unavailable at the time of writing)

BLS (Tables5&6 were used) 

Tuition 

Unemployment and Gender

A quick post to follow up a discussion from Google+.

A big factor in labor dynamics over the last four decades has been a shift in demographics.

One of the problems with gender equality is that in many cases it means a woman can do a job just as well as a man. In fact, statistically speaking, roughly 50% of the time, she can do it better.

What this means is that often when a woman joins the workforce, as thankfully they have done in droves over the last half century, they are often replacing a man.

Labor force participation is a zero-sum game, in so far as it has held steady between 56 and 64% since 1976. An unfortunate side effect of this is that men have seen steadily increasing unemployment since for as long as we have reliable data.

As shown in the graph, unemployment among women declined from 1976 to 1997, and plateaued, not rising until the recession of 2009 (Black Arrow), while men had faced rising unemployment at about a quarter point per year, until 2009.

Same chart, Googlified

That being said, from a strictly economic standpoint, any time a woman replaces a less qualified man, society benefits from increased productivity, so we shouldn't exactly be mourning the progressive improvement of American society.

Especially, as the data indicates, we still have a long way to go.

Data used in this analysis were from the United States Bureau of Labor Statistics, specifically Series:
LNS10000000 - Civilian noninstitutional population
LNS11000000 - Civilian labor force
LNS10000001 - Civilian noninstitutional population, male
LNS11000001 - Civilian labor force, male
LNS10000002 - Civilian noninstitutional population, female
LNS11000002 - Civilian labor force, female

Raw data available here.