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There are lots of people who own property, even income properties (that they rent to others) that yield maybe 5 or 6%, while simultaneously borrowing on credit cards charging 25%+ interest. Unfortunately, people are not perfectly rational. Even beyond that, are the people who have RRSPs, GICs, etc. while carrying significant credit card debt.

If they take the mortgage, have them show their assumptions for both nominal and real earnings.

Then have them consider this assumption. What if there are 6 billion people, 4 billion want jobs, and there are only 3 billion jobs. What happens to wages?

Will they be able to make the interest payments?

I tend to agree with Joseph Heath that people have a very heavily 'scaffolded' rationality, in the sense that we need a lot of support from the environment in order to make rational decisions. e.g. Religious condemnation of lending and borrowing provides defense against hyperbolic discounting that leads people to make poor decisions with respect to borrowing.

Or not, as the case may be.

Or Dubai, for that matter, with their 'Islamic' loans.

I would argue that real decisions can be made informally through an analysis of the long-term, this applies for those who drastically value money or who have a plan set out for life. For those who have a moderate outlook on life will make the decision based on their current situation and projecting moderately in the future so they would most likely seek advice. The person who does not care and is acting on impulse will most likely end up making a decision without thinking it through, such as taking a loan with no money down and low interest, these people will also make decisions by taking credit cards at 25% interest, maxing them out, and then worrying about the bills afterward, while screaming that the rich should pay more taxes to bail them out.

Another aspect of this is based on the foundation that most of your students still think that they're in for an easy ride, they currently are not thinking about how much money they're currently borrowing, because many have never had jobs and currently use student loans as if its a small credit, or their parents pay, and they don't think of it because it's not their hard work that went to earn that money which they're benefiting from. It's a lack of ownership and labor that they haven't applied to it, yet.

I'm surprised that they had issues with the question though, it's 11th grade math. I use to love the finance part.

So I can blame you, Nick, for the fact that my 3rd yr students (prerequisite, econ 1000) are unable to draw indifference curves that (a) have a negative slope and (b) don't cross plus (c) don't understand what the heck they are for anyways ;-)

I'm with Justin - the innumeracy out there is truly frightening. Students are so impressed if you can do simple mental arithmetic while standing at the blackboard. How about a post on how to improve math education? Steve?

Justin raises a good point: in Ontario, grade 11 math is required for graduation, and the university stream (at least when I took it ~8 years ago) does cover these PV/FV calculations. I can't quite remember if we covered present value of a perpetuity, but even so, the idea of PV or FV should not be foreign.

I wonder how many people get into economics without realizing how important math, or at least numeracy, is.

Real decisions - rational or otherwise - however, do not "ignore taxes, repairs, inflation, insurance, etc." and shouldn't.

True, but if you can't figure it out when these complications are ignored, you haven't a hope of figuring it out in more complex settings.

Off-topic: "Advisers aim to fix Ontario's welfare 'quagmire'" http://www.thestar.com/news/ontario/article/733388--advisers-aim-to-fix-ontario-s-welfare-quagmire

Unfortunately, it seems none of these advisors is an economist, even though it sounds like the problem is one of incentives.

The heuristics we come equipped with 'out of the box' are not rational, probably because for hundreds of thousands of years the consequences of most mistakes was death. In situations where we are weighing the possibility of loosing what we have we tend to make decisions based on heuristics that overestimate risk (e.g. the equity premium), and in situations where we are weighing trade-offs of consumption today versus consequences later, we tend to understate risk - especially if it means being safe and cozy today and possibly less so in the uncertain future (e.g. mortgages and consumer debt).

It takes a lot of training and continuing practice to overcome our built-in heuristics.

Paraphasing quotes from my MBA finance prof from over 20 years past...

You have to do the numbers. You have to do the math. That said, if you do, it will put you ahead of most others. Most business decisions are two guys going out for a round of golf, and saying "Sound good to you?" and hearing "Yeah, sounds good to me."

I do get the impression that the elementary and high school curriculum may have lots of useful math listed, but it is packed so full that there is little time to teach things using more than one learning style. If they don't get it on the first pass, it's not re-presented.

Yes, the innumeracy is frightening. I really get the impression that although more has been presented than 30 years ago, because of the pace, less is sticking. They don't have the same handle on things we did in the late 70's.

I find it incredible that most people end up buying a house because "it is the thing to do, that anybody should do", even after what happened in the US. I always get the same sentence when I talk about it: "I'm sick of giving away my money to the landlord", without any consideration for money thrown to banks. I never went into a deep discussion about it with anybody because I suspect it could create a lot of tension in a casual setting, I usually just throw around something like "renting can make sense in some cases. It seems to me that the "ownership society" is now a deeply ingrained prejudice for home ownership. And the impression that home values will always rise long term doesn't appear to have been wiped out of everybody's mind.

Ha ha, I always get a laugh when some Americans I know talk about housing prices, they think that prices will keep going up. Nominally, they will if the Fed expands its balance sheet. In Real terms it will keep going down if houses keep going up in numbers, in a specific area.

The problem with the Education system is mostly surrounded with the failure of schools to teach simple arithmetic, reading, and writing. If they got those three perfectly correct, then high school could be turned into the prep for university or an early college entry. Imagine how many students would go to college if they didn't have to wait until after high school and being filled with classes they will never apply to anything that they are interested in. Stimulate their passion. And, save the province some money. Most programs have too many subjects grouped together, instead of having math and then a finance course or such. Back in NB, I had the option of taking natural sciences or math and a combined social science class as electives, that's it, no sociology or philosophy. I was honestly not properly prepared for my first year of University, from the switch of French to English and then not having adequate preparation in social sciences or even basic figures that most individuals should know.

But back to your class Nick, you should ask how many are Political Science students, and how many like math. You'll probably get the same response my friends give me, "I hate math with a passion!"

With respect to the learning exercise, I would be interested in how many students would purcahse the house at the given parameters before the FV formula was taught and then after it was taught. From that point, it may be possible to distinguish whether the students could i) use a heuristic to accurately predict PV/FV (i.e., how many correctly made the right financial decision), ii) whether they made errors which could be corrected through instruction of the formula (how many recognized that they made the wrong decision) or iii) were unintentionally placing some utility/disutility value the on owned house (how many, even after recognizing that their decision was not financially optimal decided to still purchase/not purchase (i.e., an endowment type effect)).

I expect a great many if not majority would ask what the payments were and decide whether they could afford it or not on that basis. Not many would know how to compute the payment. Once they have to consider that was an artificially low teaser rate that would increase even without interest rates rising, or an adjustable rate that they have no idea is currently low or high and how much that might affect their payments, or how their income might fluctuate, most would find it incalculable.

The homeowner preference probably has more to do with a like for larger, more comfortable spaces, and a dislike for landlords, than financial considerations.

As if I don't already get enough 'finance' people applying for jobs when what I really want is an economist. Thanks greatly.

I'm liking the comments on this thread. Not ignoring them. Just don't have much to add to what everyone else is saying.

Trees don't do any math, but yet their arrangement of leaves provides a near-optimal solution to the problem "how to maximize capture of sunlight, while minimizing wind resistance, subject to various constraints". Trying to solve this problem with a computer is quite difficult for top mathematicians. The secret to the tree's success is that it works bottom-up: each leaf grows in the direction of maximum sunlight and leaves which present too much wind-resistance get knocked down. By trial-and-error, the optimal result is reached. It is possible that humans can also use bottom-up trial-and-error approaches to get an optimal result. Sometimes very successful businessmen, whose success is reproducible and thus not a matter of luck, can't articulate their methods for financial analysis but rather rely on something like "gut instinct". And yet they always make the right decision.

Trees practice. Businessmen practice. Most people don't get much practice buying houses.

Isn't Wicksell's point in Chapter 8 of Prices and Interest precisely that the market-rate of interest should not be used in the NPV equation. i.e., the valuation depends on the natural-rate.

Therefore, when someone chooses to buy a house we can post facto declare their what their time-preference must be and move on...

Speaking of assumptions about real and nominal earnings from the REAL WORLD, here is this link.


"For Richard Crane, the "new normal" in the labor market began when he was laid off from a New Jersey battery plant in the summer of 2006.

Mr. Crane had been earning more than $100,000 a year operating heavy machinery at Delco, a former unit of General Motors. He worked there for 23 years, since graduating from high school. But when he lost his job he was thrust into a netherworld of part-time gigs: working the registers at Taco Bell, organizing orders at McDonald's, whatever he could find.

More from WSJ.com:

• Job Cuts Loom as Stimulus Fades

• New Job, Same Firm: Learning the Ropes

• Downturn Hits Haven for Disabled Workers

"I thought it would be temporary," says Mr. Crane, 49 years old. Three years later, he is selling outdoor furniture by day and pumping gas by night, while worrying about his skills atrophying and spending scant time with his teenage son. He makes about a third of his former pay."

And, "After being laid off by the New Jersey battery plant in 2006, Mr. Crane took a job stocking shelves at Costco in the fall of 2006. His pay was $10.76 an hour -- the same money he earned when he was hired by Delco in 1983, just out of high school. "It's sad," says Mr. Crane, who had been earning about $28 per hour at Delco, before overtime.

In late 2007, he took a job at Lowe's while working at a series of fast-food jobs on the side, as well as a stint at Pathmark supermarket. He still works at Lowe's, earning $15.96 an hour selling lawnmowers, outdoor furniture and Christmas ornaments. At night, he pumps gas at a Quick Check for $13.70 an hour.

Typically, he works between 61 and 63 hours per week. It wouldn't be so bad, he says, if the hours were consecutive. But with the gap between jobs, he can only sleep a few hours a night now -- sometimes just an hour. Last week, he managed to clock 87 hours and barely saw his son.

"That's all I do -- every day -- I just keep working," he says. "I've got to. I'm not going to lose everything I have."

His wife, who had been a stay-at-home-mother, also took a job. She earns about $20,000 working at a nursing home.

Last year, they collectively earned of about $42,000. This year, they expect between $48,000 and $50,000.

Mr. Crane has applied for hundreds of jobs, among them sanitation worker, bridge painter, tree cutter and transit worker. There were some factory openings, he says, but they pay less than Lowe's."

And, "Among the underemployed is Marty Rasmussen of Walnut Creek, Calif., who was a banking executive for more than 15 years. He and his wife earned a combined income of more than $250,000 a year. As a hobby, he built cabinets and furniture.

Two years ago, he was laid off by a big bank in San Francisco. While job-hunting, he volunteered to build cabinets for a local Lutheran church, and some fellow parishioners hired him to do work. His onetime hobby became his sole source of income. In the last year, he earned more than $10,000 replacing windows and installing crown molding. He just finished a pair of nightstands commissioned by a friend paying $700. His wife also lost her job this year and is collecting unemployment benefits. "It is hard transitioning from hobbyist, because I'm used to giving my work as gifts," he says."

greenspan, bernanke, & the rest of the fed must be really proud of themselves.

How about retirement assumptions?



""Well, Senator, I was about to address entitlements," Bernanke replied [to Senator Bennett]. "I think you can't tackle the problem in the medium term without doing something about getting entitlements under control and reducing the costs, particularly of health care."

Bernanke reminded Congress that it has the power to repeal Social Security and Medicare.

"It's only mandatory until Congress says it's not mandatory. And we have no option but to address those costs at some point or else we will have an unsustainable situation," said Bernanke."

Maybe someone should tell bernanke it is not mandatory to make interest payments to spoiled rich people (his banking buddies)?!?!?

Nick, You can't infer anything about the efficiency of market prices from these classroom examples. Otherwise I wouldn't believe in the EMH. One reason is the Wisdom of Crowds argument. Another is that uninformed consumers can rely on experts for some (not all) of the information they need. Buying (or renting) a house is an exceedingly complex decision. But when you see how consumers in different countries respond to different incentives, which change over time, you have to be impressed by the power of incentives.

Good choice Nick! Only a small percentage will go on to graduate school. Might as well as teach a few things that could turn out useful regardless of how life travels.

So did you give the students 3 hours of number-crunching exercises?


Some of you should cut the 1st year students some slack. Sheesh! FV = PV X (1+r) is not simple. Figuring out gross and net interest rates alone is not a given until people spend some time with it.

If you really want to deeply depress yourselves, read the financial chat room fora where folks discuss specific stock picks. Many of these people have much at stake, yet many are innumerate, and understand next to nothing about macroeconomics and international finance.

Who knows? Monetary policy is in such a state of disarray, perhaps the ignorance is a blessing in disguise. Successful stock picking is likely an illusion for many so why would calculating fundamental ratios help investors? I tend to think some numeracy skills are valuable but maybe I simply want others to value my skill sets?

Actually, Nick, I would question whether you have got the teaching priorities right.

In my experience, the most common way that people get into big financial trouble is by comparing the current cost of a potential mortgage-enabled house purchase (which is particularly unwise if mortgages tend to be floating rate, as here in the UK) with renting a house - ie it is considered sensible to buy if the mortgage cost is less than the rental cost. You might do your students more good by teaching them the present value formula and then taking them through a spreadsheet exercise with a few examples of interest rate changes. The c/r formula is a seldom encountered special case, but I suspect that it is taught, especially when its derivation is included, because the prevailing economics culture favours elegant mathematics.

I also think that economics in general, and especially in central banks, gives insufficient attention to the microeconomics of interest rates. For example, a tightening in bankruptcy terms should lead to a fall in equilibrium interest rates, but I would doubt that many central bank economic models would even attempt to include this. Another common misunderstanding which may have contributed to the financial crisis is the idea that, if saving does not yield a positive return, it is not worth doing.

Modeling future inflation/deflation is yet more challenging. Inflation transfers wealth from savers to borrowers. Locking in nominal cash flows while letting deflation/inflation "float" is a swap that hardly anyone understands how to value. I sure don't and I'm nominally at least an expert...

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