Tuesday, November 20, 2007

How much should I pay for a chance at $20 Million?

Millions of Canadians purchase lottery tickets each week hoping to strike it rich. Why do Canadians buy lottery tickets even though the chances of picking the winning numbers are very very slim? Is this irrational? How much should I pay for a shot at a huge chunk of tax-free cash?

Economists tend to value prizes by multiplying the probability of winning and the prize value. Using this approach, I want to estimate the value a Super 7 ticket for Friday's $20 million draw.

To do this, I looked at the Super 7 website for the odds of winning the big prize. Assuming only one person can win the jackpot (for the moment), the probability of winning the $20 million Super 7 is 1 in 20,963,833. The value of my only shot at retiring early (by matching all 7 numbers) is valued at $0.95 (1/20963830 times $20M). However, there are other cash prizes. You can make a profit by matching 4 numbers (or 3 plus the bonus) or better - the odds of winning any cash prize are 1 in 30.72. Adding this, the value of a ticket rises to about $1.35 (given a host of assumptions about the number of winners and ticket sales). Lastly, 1 in 5.887 (about 17%) are the odds of winning a free ticket (which I value at near zero since it is really hard to sell on the street).

So there you have it: Each $2 play is worth about $1.35 (which I call the ticket's ‘investment value’) for this week's draw. Is it irrational to purchase a ticket? Well, at first glance, the answer is yes. However, we know that people don’t just buy it for the investment value, they buy it for fun! Moreover, taking the investment value and the fun factor together, it is easy to see that as the jackpot rises, both the investment value and day dreaming also rise, which leads to more and more people purchasing tickets.

Maybe buying a ticket is not so irrational after all. It is just that, at some jackpot level, people get more utility from buying a ticket than any other $2 investment or marginal consumption (such as a chocolate bar or an 8oz draft of Keith's at the Midtown Bar and Grill).

You may be asking when will the investment value be worth the $2 cost? Answer: When the jackpot reaches $33 million, assuming only one person can win the big prize.

Any other questions?
This article makes an interesting comparison between buying a loto ticket and investing in the DotCom stocks in the late 1990s. Irrational or buying hope?

Saturday, November 17, 2007

Economic Theory at Work: when demand exceeds supply in downtown TO

One of the most basic principles of economics is that when demand outstrips supply, the price will rise. You might of heard about a recent real life example of this at the corner of Young and Bloor in downtown Toronto a few days ago.

The Story: Units in what will be the country's first 80 storey condo went on sale with a frenzy. Apparently, people camped on the street and realtors paid university students to stand in line for weeks (three rotating 8 hour shifts) to make sure they could buy their condos (two max per person) (CBC story). If waiting in line for weeks was not crazy enough, what followed was pure economics at work.

Once the doors opened, realtors at the front of the line bought their two condos and then promptly began selling them to likely unsuccessful investors at the end of the line (who where obviously desperate for a piece of Toronto's famous corner). In fact, they started a live-fast-paced-auction on the sidewalk. As I understand it, one realtor made $500,000 in 25 minutes (less the $6k paid to the three university students with camping gear).

If I was the builder, as soon as I realized that there were people waiting in line for weeks before sales started, I think I would of started to ask some questions (perhaps to an economist). Clearly, the selling price was too low and they left a lot of cash on the table. I am sure they realized in retrospect that they should of been the one auctioning off the units, one by one. I heard they raised the price before the sales started, but this method would never capture all the consumer surplus . For this builder, a chalk board, a piece of chalk and an eraser could of made hundreds of thousands of dollars by matching peoples' willingness-to-pay to the sale price.

Thursday, November 15, 2007

Halifax will never be the same ...

You may be interested to know:
(1) There are no longer free peanuts at Maxwell's Plum.

(2) The Mediterraneo (Barrington Street) has closed.

(3)"After four years in the works, a new sewage treatment plant in Halifax is finally running ... Though the project has to pass a 30-day test period, regional council celebrated Tuesday night ... The Harbour Solutions project was implemented to stop more than 180 million litres of untreated sewage and storm wastewater from flowing into Halifax Harbour every day." (credits to the CBC).

I have been told that the harbour will smell better in less than a week and that Councilor Linda Mosher is planning to swim in the harbour next summer. And no I will not be joining her. (Note: The Dartmouth treatment plant begins operating next spring and the plant in Herring Cove is expect to be ready later in 2008).


Want more information on the Halifax Habour clean-up? A history lesson, factoids and what "stage 1" really means, you can read The Coast (click here) or something produced by HRM (click here) .

Monday, November 12, 2007

What happends when an economist goes to a bar: Ray Fisman explains

An recent article on Slate.com has sparked a lot of interest. Personally, I love to see other economist getting their hands dirty in the field: collecting data, talking to people, and enjoying the fruits of their labour. And where else better than in a bar to observe economic behaviour? We all love to see the market system at work. Fisman's post is a good read. For the fast and dirty type, a few selections from the posting are below.

The Experiment: "To really understand what people prefer, you need to pair men and women randomly in an experimental dating service and document the decisions they make. And so for a couple of years at a local bar just off the Columbia campus, I ran a speed-dating experiment ... After each "date," participants decide if they'd like to see their partner again. For our study, we also asked them to rate their partners' intelligence, looks, and ambition after each meeting."

The Results: (1) "With the obvious qualification that we're talking here about a four-minute version of love and dating, we found that men did put significantly more weight on their assessment of a partner's beauty, when choosing, than women did." (2) "By contrast, intelligence ratings were more than twice as important in predicting women's choices as men's. It isn't exactly that smarts were a complete turnoff for men: They preferred women whom they rated as smarter—but only up to a point. In a survey we did before the speed dating began, participants rated their own intelligence levels, and it turns out that men avoided women whom they perceived to be smarter than themselves. The same held true for measures of career ambition—a woman could be ambitious, just not more ambitious than the man considering her for a date." (3) "When women were the ones choosing, the more intelligence and ambition the men had, the better. So, yes, the stereotypes appear to be true: We males are a gender of fragile egos in search of a pretty face and are threatened by brains or success that exceeds our own. Women, on the other hand, care more about how men think and perform, and they don't mind being outdone on those scores."

The Twist: "Another clear gender divide, this one less expected, emerged in our findings on racial preferences, reported in a forthcoming article in the Review of Economic Studies. Women of all the races we studied revealed a strong preference for men of their own race: White women were more likely to choose white men; black women preferred black men; East Asian women preferred East Asian men; Hispanic women preferred Hispanic men. But men don't seem to discriminate based on race when it comes to dating. A woman's race had no effect on the men's choices."

In closing:
"Does all of this rational-choice stuff take the romance and mystery out of romance (just as some have accused my fellow economist Joel Waldfogel of taking the Christmas spirit out of Christmas)? I hope not. Our purpose is to understand how life-long relationships are formed. The first step in helping people find love and happiness is to figure out what they're really looking for in the first place."

Scanner Errors: Another reason not to loose your short-term memory

A month ago I declared customer service dead, and now I am starting to see examples at every retailer in Canada in the form of scanner errors! We used to take for granted that the posted price will match the scanner read at the cash - but no more!

This holiday season disgruntled service reps will use scanners to ring you through or I guess you could avoid the 'service part' and use self checkout scanners. For the retailers, scanners are a miracle worker (they never call in sick and they count inventory when they ring through products). But for us customers, it means that when you grab that Christmas gift off the shelf, you need to remember the price until you get to the cash. Yes, scanners can lie. More often then you think. Now, I don't have empirical evidence, but over the last few years, I have found my fair share of scanner errors.

What prompted this rant: Today, I was overcharged at Home Depot. I was rather tired and I made it all the way to the car before I realized. I was pressed for time and I really did not what to go back in the store, re-check the price, stand in line at the customer service desk and explain the story. However, it was the principle (and I was kind of angry).

Although the efficient market theory may keep retailers from trying to tick consumers by posting one price and scanning another, mistakes do happen. And I think there is a link between retailers' search for the most marginal labour market participants to fill part-time holiday jobs and the accuracy of the retail miracle scanner. So, get your memory going and protect yourself with a notepad if needed. At least give it a try, it could be rewarding - Home Depot and most retailers kick you back $10 for spotting the error.

Saturday, November 3, 2007

Beer lovers face higher prices as hops shortage looms

Here are some clips from an CBC.ca article about something that is near and dear to my readers' hearts: how a shift in the supply curve to the left will increase the price (demand held constant). Let the herding begin!

The Story: A worldwide shortage of hops — a key beer-making ingredient — could have a big effect on the taste of specialty brews and force smaller microbreweries to hike the price of their products. Brian Titus, president of Halifax's Garrison Brewing Company, said his brewmaster isn't sure he'll be able to make some of his beers in the new year because he hasn't been able to find some varieties of hops at all. "It's bordering on disastrous actually. If you don't have hops then you don't have beer," said Titus.

The shortage can be blamed on a perfect storm of events — bad weather in hop-growing areas of the United States, Europe and Australia and a depressed U.S. dollar. A worldwide shortage of hops could see some beer prices rise by up to 10 per cent.(CBC) Prices for the remaining supply of hops have doubled in recent weeks. With the low American dollar, European and Asian brewers are snapping up the remaining worldwide supply of hops.

Is there anything we can do? Can we substitute away from hops? (my questions)
The shortage has some breweries rethinking their brews and possibly changing beer recipes to cut down on the use of hops.
"So maybe you find something that smells similar but doesn't have the same taste profile and it doesn't have the same bitterness," said Titus.

Larger breweries are less likely to have to raise prices because they buy in bulk with long-term contracts. Craft brewers don't have the means to hedge against rising prices, like their industrial rivals.