From Maura:
We spent a good amount of time going over some of the homework problems. Probably too much time, and now that I’ve thought about it more I’m still not sure they saw the main idea. The challenging problem on this assignment was problem 3.9: show that a 10% improvement in fuel economy expressed in gallons per hundred miles leads to a 10% decrease in fuel consumption. Part of the challenge here is language (fuel economy? fuel consumption?); another challenge is that there are no numbers to work with (other than the percentages); and another challenge is the challenge of reading carefully and using the correct units. We worked it out with an example but I think it’s a difficult enough problem that the main idea that working in gallons per mile (or gallons per hundred miles) is a much better way of asking and answering questions about fuel economy.
We also went through problem 3.20 about wholesale and retail prices. Again, language is an issue here, as is paying attention to what we are asking.
We started chapter 4, Inflation. This material fits very naturally with the “1 +” idea of chapter 3. Again the challenge here is terminology. In this case, the problem is that the dollar changes value over time but we use the same terminology. We talked about an example to get the idea across the money changes value: when my dad was young, he paid 10 cents to see a movie. Were movies cheap back then (end of the Depression)? Not really, but things cost less. Our inflation calculator doesn’t work very well if we go back to 1939, so we looked at an example from the 1980s. A movie cost about $7 in 1995; the inflation calculator tells us that we’d need just over $10 to buy now what we could buy with $7 in 1995. That’s a nice example, as the price for a ticket has gone up with inflation but not by much more.
We also worked through the Red Sox ticket example, which is a very good way to see that prices change for different reasons. If we want to compare prices over time, the honest way to make that comparison is to take inflation into account. Once we do that, we can then talk about how prices have (or have not) increased. Again, the challenge here is that 2003 dollars look the same as 2008 dollars. We have to really push ourselves to think of the 2003 dollars as something different: I told the class to pretend dollars were blue back then, and that they were exchanged for red dollars in 2008. The inflation rate points to the exchange rate.
Then I made a crucial mistake, which is that I started an example on the fly with 5 minutes left. I should have used the salary example in the book, as it’s very straightforward. Instead, I thought I would show them how a salary increase is really not an increase because of inflation. The basic idea is clear. If my salary in 2007 was $40,000 and I received a 2.5% raise, my salary in 2008 would be $41,000. But the inflation rate from 2007 to 2008 was about 3.8%; if my salary had increased with inflation, it should have gone up to $41,520. It’s clear that my raise has not kept up with inflation. The bigger challenge is to figure out the percentage that I’ve lost because of this.
From Ethan:
Exam next Tuesday.
- I am constitutionally unable to write an exam that’s short enough to fit into a class – I find too many interesting (to me) things to ask about.
- Therefore students get to take the questions home after the exam and rework problems they think they can improve their answers to.
- Exam is open everything – book, notes, homeworks, internet. That’s good news (no memorization) and bad news (I can ask harder questions, it’s easy to waste time looking on the net when what’s needed is thinking).
- At least one of the questions will be one from the book that hasn’t been assigned as homework.
- I grade on a curve. I don’t have a fixed number of A’s to award. And I don’t know how good a grade has to be to count as an A until I see how the class does as a whole – that will tell me how hard the exam was.
- Students wanted to keep their homeworks to study from, so I didn’t collect them.
Then on to substance. I worked the last homework problem (UMass research funding increase) and the discount followed by sales tax problem. Good exam practice.
New material today: inflation. Used the BLS on line calculator to see the real relative increase in Red Sox ticket prices from 2003 to 2008 (Fig 3.1 in the book.) First we changed 2003 prices to 2008 dollars, and discovered that the true increase for ordinary seats was about 4%, not the literal 23% implied by the dollar amounts. For the premium seats it was about 1%.When we found the inflation rate (by using $100 in the BLS calculator) it turned out to be about 17%.
I used that example to show that the inflation rate was independent of the amount you started with – that’s what “rate” means in this context. (I didn’t say the units were $ per $, for fear of confusing them.) We did look at converting $1, $100 and $1,000, and saw that the rate was always the same – what looked different was the amount of precision, because the calculator rounds to pennies.
We checked the yearly inflation rates from 2005 through 2010, and saw the small deflation between 2008 and 2009 – presumably because the inflation rate is an average over commodities and housing prices crashed. I promised a discussion of that kind of average after the exam when we start the next chapter.
Finished by calculating the true value of a 10% raise when the inflation was 3.3%. The answer isn’t the difference (6.7%) – you can’t subtract percents in this situation (just as you can’t add them for successive increases or successive discounts). But it’s close.
Then they asked me if my salary over the years had kept pace with inflation. I said it had, and more (since I’d had real raises corresponding to promotions), that my salary was in fact a matter of public record since I was a state employee (but I didn’t tell them what it was), that it was less than what college classmates of mine made who’d become doctors or lawyers, but that I was being paid for doing what I loved to do, and would do anyway even if I had a trust fund and didn’t need to earn a living. I suggested that finding such work for themselves should be the real goal of their education.
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