Upgrading & Early Termination Fees

Here's an interesting story about a guy trying to negotiate upgrades for his family to the latest iPhone. All comments aside about the scam that constant upgrade "opportunities" offer, the story is an interesting mix of straight math and emotion. So basically, economics. Homo Economicus might have just skipped the upgrade altogether (or took his family back to flip phones).

The story in itself seems like more of a hook than the basis for a problem you'd actually spend the bulk of a class period on, but it opens up larger questions about early termination fees, upgrade costs, etc. Given deal X from company A that gives you free or cheaper phones with a new account, at what point is it "worth it" to leave your existing phone company and suck up the early termination fees?

There are lots of other interesting variables that could factor into the decision:

• How many phone lines you have
• Variations in cost between the actual monthly phone plans of the two companies
• How soon you'd be eligible for an upgrade with your current company
• How soon the other phone lines would be eligible for an upgrade
• What kind of quantifiable measure you put on being cooler than your friends and/or having the latest thing. Would it change your mind about waiting out your time until an upgrade if you knew that all your friends would have the new iPhone before that? How many friends would you care about? Can you quantify how much you care? 

The Painted Cube, Revisited

I'm a big fan of the "Painted Cubes" problem (although to be honest, I don't think I have ever actually used it with kids...). I feel like most math-y people have seen the problem at some point: If you build an n x n x n cube out of unit cubes and paint all the faces, how many of the unit cubes will have one face painted? 2 faces? 3? 0?

This problem from NRICH Maths is a a cool extension. I love the use of the word "some"--it's so interesting how that word both increases access and makes the problem so much harder. I haven't actually done any work on the problem yet, but it just makes me want to play!

Is the Google Offer worth it?

This came from some real-life math I was doing today as I was trying to book at flight from SFO to Chicago. Google Offers had a deal on airfare (on Virgin America): $50 for 50% off your next flight (round-trip or one-way). 50% off--awesome! But how good of a deal is this? Is this Google Offer always worth buying? How can you tell when it's worth it and when it's not? Is there a situation where it could even end up costing you more to use this Google Offer? How can we create a model to tell us when this Google Offer is worth it, and when it's not.

To complicate matters, this offer came out at the same time that I also happened to have a coupon for Virgin America--a coupon that I got for free from an online promotion--for 20% off my next flight. How does this change when it's worth it and when it's not worth it to buy the Google offer? How does it change the model?

Use multiple representations to explain your solutions (t-table, graph, equation, etc.)

Avoid the monthly fees

http://consumerist.com/2010/12/chase.html

Chase will charge you a $12/month fee unless you do some stuff (like use their card or keep a lot of money in your account to fund their bank). "What's the best option?" sounds like an algebra problem in the making! Everything should just be linear, right (assuming you're looking at a constant amount of money coming out of your checking account each month)? Or you could talk about piece-wise functions, especially if you look at keeping a minimum balance.

Such a good question: what does it cost you to keep money in the bank?