Additional Math Pages & Resources

Thursday, August 5, 2010

A dollar is not always worth a dollar

Of course, you say, the dollar's value can appreciate, depreciate, etc and so it doesn't always have the same purchasing power.

That's not what I meant. I was just repeating a statement in a fascinating new book called Numbers Rule. 

The statement meant that money is not equally valuable to people. For example:
  • If you have 3 dollars, one more dollar increases your wealth dramatically (is it 25% increased? or 33%?)
  • If you have 300,000 dollars, one additional dollar makes very little difference to your wealth or purchasing options.
The more money you have, the less each of those units should mean to you (assuming you're not a maniac or miser). With lots of mathematicians weighing in on this, the odds have been calculated and we've determined that
  • if you have only one dollar, the next dollar is worth 0.3, which I think means it increases your purchasing options about a third more than just having $1.00
  • if you have a million dollars, the next dollar is worth 0.0000004, meaning it does virtually nothing for your purchasing options
This whole subject is known as the St Petersburg Paradox. It evolved from some probability questions posed by Swiss cousins, Nikolaus and Daniel Bernoulli. Daniel is famous for lots of other things, including the Bernoulli Principle which has to do with the flow of liquids and gases over solid objects. This plays out in the lift of an airplane wing, the flow of air and fuel through a carburetor, calculating speed of a boat or airplane, etc.

OK. Enough history. Taking this subject, and looking back at yesterday's blog on Billionaires donating their fortunes to charity, does this dollar is not always worth a dollar principle mean that they don't feel the pain of giving up their dough?

I'm not sure that it does. Perhaps if you learn to give when you have a little (the working poor), you find it easy to keep on giving when you have a lot. And alternatively, perhaps if you begrudge giving when you have a little, you will rarely want to give a large amount, even if you have a large bank balance. My grandfather was a wealthy man but he definitely didn't like sharing ... or donating.

I'm sure the mathematics of generousity have been well studied and we won't add to this today with our elementary math blog.

And we don't have to get into a lot of math to know that the dollar goes up and down against other currencies. Here's the graph of the dollar against the euro for the past 6 months.

The higher the bars, the more purchasing power the dollar has compared to the euro. Our company's accountant and his family are off on a European Vacation today. He's bemoaning the depreciation of the dollar and its effects on his wallet.

Q1. During what month on the chart would the accountant's dollars had the most value compared to the euro?