Monday, January 25, 2010

Simple Population Models

In a Master's course last semester I built a model to compare simple population cohort models using System Dynamics and Agent Based Modeling. Someone also asked in the System Dynamics forum if it was possible to embed models in a blog, so I thought I' try it out here. The model below simulates people moving through an aging chain, where at the age group of fecund, they influence the birth rate. Both models produce similar dynamics, but the representations offer a few unique insights on problem formulations. The System Dynamics model is quite a bit easier to build and calibrate, producing good fits to the UN data. The agent model is more complicated and is prone to stochastic effects (which could be smoothed with more agents), but it also more easily allows for additional individual attributes such as gender and wealth. Use the navigation buttons to explore the different implementations and run the model to 2050 to have more time and glimpse of where we might be headed (the population scale is per million people). Note, you'll need to have Java and increase the amount of applet memory available to at least 400M. See this page for a good explanation on how to do this.

<applet code="world_population_aging_chain/Simulation$Applet.class" archive="," width="902" height="718"> </applet>

Thursday, January 21, 2010

Cash for Clunkers Impact

When this program was rolled out, a friend asked me what the impact on consumption would be. I finally got around to running some of the numbers. Please let me know if you find any mistakes in the math. In summary, the individual benefits are pretty good, but the impact on the country as a whole are easy to dismiss.

According to the summary statistics from the program web site the average mileage of the new vehicles was 24.9 MPG and the trade-in mileage 15.8 MPG. This means there is an average overall increase of 9.2 MPG, or a 58% improvement. Not bad, right? So for an individual that drives the average 12,000 miles per year, the additional 9.2 MPG means they will save 281 gallons per year (note the math is 14,000/24.9 - 14,000/15.8, not 14,000/9.2). Using the average price of regular for 2009 of $2.31 per gallon, this is a yearly savings of $649 or a monthly savings of $54. So in addition to the tax rebate, buyers have a virtual $54 taken off their monthly car payment, making this a real "no-brainer" for those that had the opportunity to take part. This is especially true if you look at the current gas prices and longer term trend.

So what was the impact on the country? In total, there were 677,081 vehicles replaced, creating a savings of 190 million gallons per year! Sounds pretty great, right? Well it's a start, but when you compare it to the total United States consumption of 378 million gallons/day, it turns into a drop in the bucket. In numbers, this is only a 0.1% decrease in consumption per year. This is a far cry from the 58% improvement we started with.

There are some good insights here still. As an individual, when you go to buy another vehicle. Think about the true cost per year. If you get a vehicle that has even a modest MPG improvement, you might be able to afford a larger car payment than you think. Myself for example, if I were to get a Prius, I'd go from about 26 MPG to 48 MPG (highway, which is what I mostly drive). That's a difference of 22 MPG. I also drive around 20,000 miles per year and the 6 month gas price average is $2.56. That means I could save $902 a year or $75 a month. Up next, electric vehicles, but alas my lunch hour is over.

Wednesday, January 13, 2010

System Dynamics Forum Survey Results

I wanted to try out the Google Spreadsheets Forms for doing surveys and some questions about the System Dynamics Forum provided a good excuse. Here are the results.