How then, do we move backwards? How does a society, with most of the people having no clue of future events, move from being dependent on a vast and intertwined network of goods and services produced by the indigenous people of whereever, to a local resource and renewable energy based society, and do so in the timeframe available (20-30 years using the most liberal extimates, 10-20 with resonable estimates, 5-10 with worst case scenarios), all the while prices on everything increasing, world politics getting more militaristic, governments continuously reducing civil liberties, shortages of goods on the market and weather patterns resembling bad Hollywood movies?
Joined: Feb 12, 2006 Posts: 98 Location: New York State, USA
Posted: Thu Oct 11, 2007 12:26 am Post subject: production versus exports
User westexas at TheOilDrum has been pointing out that oil producing countries are actually consuming more and more of the oil they produce. When production is flat, this increasing consumption means that exports will be declining. There was some discussion of how to model this, so I thought I would take a swing.
My thought is that the main difference between consumers in a producing nation versus consumers in a non-producing nation is that the money spent on oil in a producing nation stays in the nation, or most of it anyway. So an increasing price doesn't hurt consumers in the producing nations as much as it hurts in non-producing nations. I.e. the difference is in the elasticity of the demand curve.
So here are the equations I propose to model all this. I present them as a collection of multiple producers and multiple consumers.
The producers are each governed by something like a logistic equation, but with a term added for price sensitivity. I need the price to change to make evident the different price sensitivities of the various consumers. The price will get set by the balancing of supply and demand in the marketplace.
I want to capture somehow the idea that countries grow or shrink. The amount consumed by a nation is not just a function of the price, but also of how "big" the country is. If a country consumes a lot, then the country can grow quickly. But if the country isn't able to consume enough, it will shrink.
I wrote a little simulator in excel, for a system with just one producer and two consumers. The consumers have different elasticities, i.e. different sensitivities to the price. The lower sensitivity consumer is intended to be that of the producing nation.
One tricky bit that I don't know how to put in equations is - when the price gets high enough, my simple linear demand curve ends up in negative consumption territory, which is obviously nonsense. So my simulator just knocks consumers out of the market place, i.e. assigns 0 consumption, when the price gets that high.
So here is the evolution of the amounts consumed by the two consumers. I set the initial conditions so the producing nation starts out much smaller than the non-consuming nation. But the curves cross eventually
Here is the total consumption on the same graph as the price. The price goes up slowly, but then when the price sensitive consumer is knocked out, only the price insensitive consumer is left, and the price really takes off.
An interesting exercise!
Joined: May 02, 2005 Posts: 3249 Location: One more question...
Posted: Thu Oct 11, 2007 12:57 am Post subject: Re: production versus exports
jimk wrote:
...
The price goes up slowly, but then when the price sensitive consumer is knocked out, only the price insensitive consumer is left, and the price really takes off....
Thanks Jim!
Next in line after the price-sensitive consumer will be the non-productive consumer. _________________ "Don't ever become a pessimist... a pessimist is correct oftener than an optimist, but an optimist has more fun, and neither can stop the march of events."
Robert A. Heinlein
Joined: Feb 12, 2006 Posts: 98 Location: New York State, USA
Posted: Thu Oct 11, 2007 9:40 am Post subject: Re: production versus exports
Sometimes there seems to be a conflict between economics and reality. An economic perspective might seem to imply that if the price goes high enough, we can just keep discovering oil. An interesting feature of my tweaked logistic equation is that it is still governed by a fixed amount of recoverable resource, but economics can shift around when we extract that resource. The more we extract early in the game, the less we'll have to extract later.
So here are five plots, superimposed, of total consumption versus time, for the same system of one producer and two consumers. The only difference across the plots is the price sensitivity of the producer.
Joined: Feb 12, 2006 Posts: 98 Location: New York State, USA
Posted: Fri Oct 12, 2007 8:23 pm Post subject: Re: production versus exports
One thing that makes this simulation hard to understand is that I took a big leap from the usual logistic - I added price sensitivity to the production, and I created two competing consumers with different price sensitivities.
It seems useful to take a step back and consider the single consumer case:
What this shows ought to be obvious... the downside of the slope will be steeper than the upslope. On the downslope we have more people more dependent on petroleum. So this shifts the demand curve. If the production is at all price sensitive, the logistic will surely be distorted to a more rapid decline.
Joined: Feb 12, 2006 Posts: 98 Location: New York State, USA
Posted: Fri Oct 12, 2007 9:12 pm Post subject: Re: production versus exports
A curious feature of some solutions of this model - the price can go negative. This means that production is actually less that the straight logistic equation would predict. Thinking about this, I realized - this really happens! It's like what OPEC does, or the Texas Railroad Commission. The whole point of these cartels is to supress production.
Joined: Feb 12, 2006 Posts: 98 Location: New York State, USA
Posted: Thu Feb 28, 2008 6:14 pm Post subject: Re: production versus exports
I am starting to learn C#. So that gives me a bigger hammer than Excel to let me crunch equations!
The linear supply/demand curves I had above were clearly too simplistic - the possibility of them going negative being the most obvious trouble. So here are some fixed-up equations:
This shifts the meaning of the price - it becomes more realistic, for starters. Now a price of 1 means a producer is following the pure logistic equation. As the price goes higher, the producer will pump more crude - of course, this just depletes the fixed-size reservoir more quickly! And when the price is less than 1, the producer will pump less that the pure logistic would predict. Similarly, consumer demand is price sensitive.
My C# simulator puts out a text file which I feed into Excel to get graphs like:
This is a system with two producers and three consumers. The two producers have all parameters equal except the price sensitivity exponent - one is 1.5 and the other 1.7 - that small difference makes their peaks look quite different!
The three consumers differ in starting size as well as price sensitivity exponent. That way I can get the curves to cross in various ways.
Anyway I think these new power-law supply & demand curves are a lot more realistic or at least less temperamental numerically - the wierd discontinuities have disappeared from the simulations.
Joined: Feb 12, 2006 Posts: 98 Location: New York State, USA
Posted: Fri Apr 18, 2008 8:09 pm Post subject: Re: production versus exports
Since oil prices are in the news these days, I thought I should post the variation in price generated by the simulation that produces the production/consumption graph above:
Posted: Sun May 18, 2008 10:49 pm Post subject: Re: production versus exports
Albente,
The graphs are clear, I'm surprised you don't understand.
My interpretation is that as peak oil hits because everyone is using more of their own dwindling supplies, and exporting less, we can expect more assaults on person and property.
Therefore what our NY friend is saying is that EVERYONE be trained to use sub-machineguns NOW:
Posted: Mon May 19, 2008 12:23 am Post subject: Re: production versus exports
Your reply is correct, Virginian. It was just one of those obnoxious comments that sometimes I can't help to make. Some people drive 'under the influence', others post while under the influence.
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