These are the things people associate with economic bubbles.

Ask most people and they will tell you a bubble is when people pay more for a thing than it is worth in a reasonable market. That's a simple model for demand bubbles, but not the complete picture.

For many quantitative economists, the basic bubble is the speculative, positive price variance bubble. But, there are also negative bubbles, when pricing collapses yet producers continue to believe demand (and prices) will soon increase offset the oversupply. These are deflationary gluts.

Bubbles, positive and negative, occur when the market price for any good or service rapidly departs from the long-term median trend of price stability.

A severe bubble is when a significant number of consumers are willing to go into debt to obtain a good or service with the primary intention of selling the good (or service-related improvement) before retiring the debt. Basically, bubbles are the result of leveraging purchases on products you don't intend to keep through their useful lives.

Wait! Don't retailers and investors do this?

Sort of. A retailer, however, attempts to add value to the purchase price. If I am a grocer, my value-add is that I take time to locate the best fruits and vegetables, assembling them into a single location for your convenience. I might add other services, too, like information labels, expert employees, and keeping the produce in great condition.

Only a foolish grocer would convert his or her entire produce lane to the single most expensive fruit or vegetable available, purchased entirely via credit. Diversity is part of the value-add.

It is credit that marks most bubbles.

An easy example that currently concerns me is the automotive market. People are using low-downpayment, extended-term loans to buy cars and trucks at elevated prices. Many consumers hope to sell or trade in these cars before the debt is retired. In all likelihood, the optimal utility of these vehicles will not be realized by the almost-owners (remember, the lenders own this glut of cars) before they part with the cars and trucks. Paying more than is logical for a good you will never actually own? That seems like a potential bubble.

If you won't retire the debt on a purchase, why did you make the purchase? Will the utility return exceed the cost?

In the housing market, the old-fashioned dream was to pay off the mortgage and own the house. The bubble started when people borrowed to purchase homes they never intended to live in or rent beyond the term of the loan. My wife and I bought a house in this situation, rationalizing the payment as better than renting. That's not always the case, despite tax incentives that make home ownership seem desirable. (You should do the math, to compare rent versus the

*true cost*of homeownership beyond the basic mortgage payment.)

The negative asset bubble is built on false hope, too.

The Irish Potato Famine was a destructive bubble created by false hope that planting more of something that was failing to grow would somehow outrace the blight. Producing more of something, or trying to produce more, is a deflationary bubble that pops with the same destructive force as the inflationary bubble.

Some argue there are no bubbles or gluts, because markets self-correct. If everyone plants potatoes and the potatoes survive, the price of potatoes falls. The falling price leads (smart) farmers to invest in other, more diversified crops. The market stabilizes as supply and demand come into balance. The bubble is just an extreme supply, demand, or price fluctuation, not unlike the small fluctuations of any daily market.

For services, I consider a bubble paying more than the service can return in the misguided hope that somehow the market will recognize the magical human capital a consumer has (not) gained. College degrees in some fields are like this. People pay to invest in their "human capital" but the market isn't recognizing the investment as valuable enough to offset the cost of some college degrees.

The inflationary example of the college bubble is that students are assuming more and more debt for their educations. While in school, many are not earning what they might in the job force. This is particularly true of some liberal arts graduate degrees. The opportunity cost of going to college, plus the debt, means that some people might not experience a positive return for the investment made in their human capital. Lots of debt, but no lifetime earnings gain is a bubble as long as people keep assuming more and more debt, pursuing more and more education.

The deflationary example of this is that most graduate students in English and writing programs know there are few permanent jobs. We know this because there is a glut of adjunct professors of writing and a glut of editors in the private sector. Yet, because these students believe, with absolute certainty, that their futures will be different and that the job market will someday recognize their value, we have a record number of graduate students in MFA programs. The MFA programs keep raising tuition rates, students keep assuming debt, but there is

*no demand*(logical or not) for the newly-minted writing experts.

The education bubble isn't like the Tulip Mania, because the engineering student taking on debt will be (statistically) fine. He or she will find a great job and the returns will be realized. But the writing graduate? Unless the utility value is simple intrinsic pleasure, the result is a deflationary cycle that cannot end well.

Teachers of writing? Lower and lower pay as the supply shows no sign of decreasing. Editor? Again, lower and lower pay. Writers? Heck, websites expect us to generate free content. When will people stop chasing degrees with no return? There's no way to predict the end of a psychological bubble. At some point, though, the potential students won't line up and colleges will need to scale back programs or cut tuition… or both. There will be financial pain and ripples throughout the higher education market. (Yes, it is a market.)

Bubbles, as you can see from above, end badly. Someone loses money… or worse.

### The Math of Bubbles

Time for some statistics. Sorry, but I need to use math-ish stuff to explain bubbles a bit deeper from an economics perspective.We'll use grocery store produce for this discussion of bubbles. Avocados seem to be a nice model to study, since the average price this summer (2015) is approximately $1.00 each.

Economists interested in consumer prices survey a representative sample of stores every month to track changes in the cost of living (the Consumer Price Index). Some of these economists sample major produce lines and the data are used to help famers, wholesalers, retailers, and others anticipate likely pricing trends on everything in the produce aisles.

Statisticians try to survey a small but generalizable population. Let's pretend they survey ten stores from different chains and in different regions to represent the overall market. (There are sampling models that help estimate the smallest reliable sample, which is how we can survey a small group to predict national trends.)

In probability, we should be able to plot the prices of the avocados from various grocers and find something of a bell curve. The average price, known as the mean, should be near the middle of our data. Most prices will be near that middle price. Too high, and people won't want avocados. Too low, and the grocers go out of business (along with others in the supply chain).

In our price chart, half of the grocers will price avocados higher than the mean price and half will price them lower than the average. (There is something known as "skew" that results from outliers — those outrageous prices at organic stores and the low, low prices of corner fruit stands. But, statisticians correct for skew and compare median to mean for other adjustments.)

The standard deviation is a calculated value that tell us how far from the mean value another value is likely to be. A good "instrument" finds that about two-thirds of values fall within one deviation of the mean. In a perfect retail market environment, our survey should find that most avocados are near the average price.

In a "normal distribution" (a good old-fashioned bell curve) we can calculate the standard deviation from the mean and break the distribution of the avocado prices into subsets. Within one deviation from the mean we should have 68.27% of data points. Within two deviations, we find 95.45% of data points. Ideally, 99.73% of all data in a normal bell curve fall within three deviations, plus or minus, from the mean.

Here are the prices our survey of avocados finds:

$0.50, $0.75, $0.90, $0.95, $1.00, $1.05, $1.10, $1.25, $1.50, $1.75

The mean (average) price is $1.08, calculated by summing the prices and dividing by the number of grocers visited by our statisticians. Economists want to know the standard deviation, to determine a range of "normal" pricing. (Take a deep breath!) The standard deviation is found by taking the square root of the average of the squared deviations of the values from their average value.

What this means is, we square how far the prices are from the median and add up all those new values. These are called raw deviations.

For $1.00, the deviation is $0.08 ($1.08 mean minus the $1.00). We square the eight cents, and do this for every value in the survey, including any sample that has no deviation.

Our squared deviations adds up to $1.16. We take the mean of these deviations, dividing $1.16 by the ten grocers for a variance of $0.12. Basically, we now know that prices within 12 cents of the average price are within the variance spread. But, we don't have a standard deviation yet. For that, we take the square root of the variance. Finally, we have our SD (standard deviation) of 36 cents.

For our avocados, the average price (mean) is $1.08 and the standard deviation is $0.36. Prices from $0.72 to $1.43 won't worry an economist or statistician because two-thirds of avocados should be selling in that range if our study sample was representative of grocery stores. But, if prices suddenly spiked above $1.80 or fell below $0.35 something serious has happened to the market. We assume this because prices moved outside two standard deviations from the historic mean price.

It isn't a bubble if people are making guacamole with $1.80 avocados and selling it for $5. A genuine bubble escalates, thanks to investors hoping to resell the item. In a bubble, for

**no logical reason**such as a sudden disease or a drought cutting supplies, enough avocado consumers are willing to pay $1.80 or more that this becomes the market price for avocados. Other consumers are pushed out of the market. The price continues to rise as some hoard these over-priced avocados. Investors buy the avocados at $1.80 hoping to sell them for $2.00 to someone else. Prices continue to spiral upwards thanks to these investors, many of whom

*know the higher price is absurd*but are willing to gamble on prices continuing to climb.

Every investor is looking for the "bigger sucker" to pay more for the avocado just purchased. And the next sucker is looking for the next one, and so on.

Some people will cut food they want to afford avocados to sell on the black market. Maybe people give up other items they want to invest in avocados. A few investors work more hours to earn money for avocados. In the worst instances, investors buy avocados on credit. We now have a bubble by both traditional and statistical perspectives. We're outside two standard deviations… and climbing higher on psychology.

And the bubble will burst. Avocados purchased for resell on the black market will rot. Farmers might change crops or retailers might change inventory mixes as prices plunge… back to normal. For those who borrowed money or worked extra to buy avocados, there were lost opportunities to invest more wisely.

The best lesson from all of this is to buy what you need and invest cautiously. Watch out for bubbles, even though most bubbles are recognized when it is too late.

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