July 14, 2024 

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ARC ELASTICITY: The average elasticity for discrete changes in two variables, A and B. The distinguishing characteristic of arc elasticity is that percentage changes are calculated based on the average of the initial and ending values of each variable, rather than only initial values. Arc elasticity is generally calculated using the midpoint formula. Arc elasticity should be compared with point elasticity. For infinitesimally small changes in variables A and B, arc elasticity is the same as point elasticity.

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I'm sure there's a great philosopher somewhere who once uttered the words, "Life's a contradiction and we're all a bunch of hypocrites." Take me for example. Just this morning I walked by Smilin' Ted's All-Comers Insurance Agency to drop off my annual shoe insurance premium (for protection against blowouts), then made a pit stop at Master Sprocket's convenience store where I plopped down five dollars on five (count 'em, five) Super Luck-O Multi-State Lottery tickets. Within a space of two blocks and twenty minutes I bought $37.56 worth of shoe insurance to avoid risk and then spent another $5 to take on some risk. Am I a walking contradiction, or what?

Life's A Gamble

As we saw in our journey through information with Fact 6, Our Unknown Future, the world is filled to the brim with uncertainty. We're never quite sure what the future will bring to our pedestrian lives. That's were insurance and gambling come in. You can find out a heck of a lot more about insurance elsewhere in this guide (hint: search for under the issue about insurance), but a quick comparison between insurance and gambling is well worth the effort.

Insurance is what you do to protect yourself against the risk of a loss. This includes, of course, the various kinds of car, life, home, and shoe insurance sold by Smilin' Ted. You pay a little bit now to avoid the risk of paying a lot more later.

Gambling is a lot like insurance, but in reverse. With gambling you pay something for the chance of getting even more. We have traditional gambling like the games of chance in Las Vegas casinos, church-run bingo, state lotteries, and assorted legal and illegal betting on sports. Less obvious activities are also forms of gambling, including starting a business, playing the stock market, searching for a job, and getting an education. Many of the less obvious ones are all also forms of investment -- you pay something now in hopes of getting more later -- that is, invesment is also a gamble.

So the question remains: Are gambling and insurance a contradiction? Can you do both?

Are Scaredy Cats Gamblers?

We also noted in Fact 6 that people have different inclinations toward risk. Risk averse scaredy cats prefer certainty over uncertainty and are willing to pay for it. Risk loving gamblers, however, enjoy risky situations over certainty. And risk neutral in betweeners have no preference one way or the other. Insurance would appear tailor-made for risk averse, with gambling the elixir of life for risk lovers. That's more or less, but not totally, the case. Let's throw a bunch of numbers together to see why.

Suppose that you have a 5 percent chance of losing $1,000 from a car accident on a cross-country vacation. The expected loss of this predicament is $50, meaning that if you take 100 cross-country vacations, 5 will lead to $1,000 accidents. The $5,000 car repair bill total, when averaged over 100 trips, is $50 per trip.

If you're risk neutral, then on any given trip you don't care if you pay $50 to Smilin' Ted for insurance or are stuck with the 5 percent chance of a $1,000 loss. Risk averse types, however, are willing to pay more than $50 and risk lovers are willing to pay less. As discussed elsewhere, insurance is typically sold to risk averse because insurance companies need to charge more than $50 for this sort of coverage.

Gambling works much like insurance, but in the opposite direction. Suppose that you have a 5 percent chance of winning, rather than losing, $1,000 on something like a charity raffle. What price would you be willing to pay for such a chance? The expected gain for the raffle is $50, meaning that doing this raffle thing 100 times would lead to 5 wins of $1,000 each. Your $5,000 total winnings would then average out to $50 for the 100 raffles.

Much like insurance, a risk neutral in-betweener sort of person would feel the same about paying $50 for the 5 percent chance of winning $1,000 or keeping the $50 and saying to heck with the raffle. A risk averse person, however, would be willing to pay less than $50 for this chance of winning. A scaredy cat, remember, prefers to have certainty (a sure $50) over uncertainty (the chance of winning $1,000). And a risk lover would be quite eager to pay more than $50, because gamblers enjoy the thrill of a risky situation.

The crux of the matter is that all sorts of people, risk neutral, risk averse, and risk loving, are willing to take a gamble -- if the price is right. As a risk averse person, there's no contradiction if I willingly pay $60 to avoid the chance of a 5 percent chance of losing $1,000 and at the same time pay $40 for a 5 percent chance of winning $1,000. I can pay my shoe insurance premium and buy lottery tickets without fear of contradiction.

The House Always Wins

Although I'm buying, who's selling? Who, in their right mind would be willing to give me a 5 percent chance of winning $1,000 for the low, minuscule price of $40.

Let's ponder this from the bookies', er, sellers' side of gambling. Suppose, your charitable organization intends to raffle off a year's supply of Hot Mamma Fudge Bananarama Ice Cream sundaes, valued at $1,000. If you sell 20 raffle tickets for $50 a pop, then you'll raise the $1,000 needed to buy $1,000 worth of Bananarama Ice Cream sundae coupons from Hot Mamma Fudge. Moreover, each of the 20 raffle tickets has an equal 5 percent shot at this most-valued prize. Those 20 tickets will be snapped up by risk loving types, with perhaps a few purchased by some risk neutral people, but no risk averse will take part. Remember, risk averse are willing to pay less than $50 for a 5 percent chance of $1,000. If you want to entice any risk averse into you charity give away, then you've got to lower the ticket price.

That's easy to do. If you sell 100 tickets, then you can raise the needed $1,000 for the Bananarama Ice Cream sundae coupons by charging a mere $10 per ticket. This should entice the risk averse, right? The problem is that each ticket now carries a lower 1 percent chance of winning. If the potential ticket buyers are risk averse and they recognize these shrinking odds, then they're willing to pay, not just less than $50 for the chance, but now less than $10. If, however, they still think they have a 5 percent chance of winning, then they too will snap up those tickets.

You're probably way ahead of me on seeing some sources of big profit in the gambling arena:

  • Your revenue as a seller depends directly on the number of people who pay for the opportunity to gamble and how much they bet (the price they're willing to pay for the privilege of gambling).

  • More people are more inclined to bet more, if they think their chances of winning are higher. The trick is to make people think that their chance of winning is greater than it actually is. This would even sucker, er, entice the risk averse into gambling.

    Most common forms of gambling -- casinos, state lotteries, bingo, contest give-aways, and sports betting -- are profitable because bettors are seldom aware of their actual chances of winning. (By the way, what are the odds of winning the state lottery?) You can bet your last lottery ticket that casino owners, state lottery commissions, and bingo parlors know the odds of winning. And (here's one of those important "ands") they'll charge enough to cover the prize, plus a little extra for their efforts. Whether you win or not, they'll be certain to make a profit. The house always wins!

Even when bettors know their actual chances of winning, it often means very little. What does it really mean if the chance of winning is one in a million or one in ten million? When the odds are this slim, unfounded optimism usually takes over. "Hey, someone's going to win, why not me?"

It's Just For Fun

Of course, a lot of gamblers don't expect to win anything, but partake in the activity merely for recreation. Is there any real difference between spending five bucks on the Super Luck-O Multi-State Lottery versus the latest Brace Brickhead action adventure movie at the Shady Valley Central Town Sprawling Hills Shopping Mall cinemaplex? Both give you a bit of entertainment. On the one hand, your pulse can race as you vicariously watch Brace Brickhead burst through plateglass windows. On the other, your pulse can race when you discover you have guessed correctly the first two lottery numbers and anxiously await the remaining four. Does it matter that you leave the movie theater physically unscathed or that you rip your lottery ticket to shreds having once more guessed only two of the six correct numbers? Both give you a few moments of excitement.

Gambling, thus, falls into the entertainment category that includes movies, tourism, theater, television, novels, and a score of similar stuff. It gives many who gamble (especially risk lovers) a degree of excitement and satisfaction that they could not achieve otherwise. This is good. This is what our economy does -- satisfy unmet desires.

But there's a shady side to gambling as well. A shady side that doesn't, contrary to what you might be thinking, have anything to do with criminals and other nefarious types. By shady I mean an unproductive waste of resources.

Robbing Peter to Pay Paul

When we exclude the entertainment value of gambling, we're left with nothing more than a transfer of wealth and income. When some win, others lose. The Las Vegas winners hit the big-time jackpots only because other people have lost their nickels and dimes. The multi-gadzillion winners in the Super Luck-O Multi-State Lottery are basking in the misfortune of gadzillions of people who have wagered a few bucks here or there. Many of the mega-fortunes acquired in the stock market by buying low and selling high are at the expense of others buying high and selling low.

The transfer of wealth and income from gambling wouldn't be such a bad thing except that society wastes resources in the process. The casino pit boss could be making something productive, like Hot Mamma Fudge Bananarama Ice Cream Sundaes. Or the company that prints lottery tickets could be manufacturing air filters for the OmniChopper 3000 lawnmower.

There is, of course, one big exception to the wastefulness of gambling. That is when gambling involves investment. In this case, the payoff for the winner, a new factory or innovative product, also generates a big payoff for the economy -- economic growth. We have a creation of income and wealth, rather than a transfer.

Although I can't help you pick the winning horse at the racetrack, here are a few gambling tips:

The Winning Tips on Gambling

  • Try to determine if you're more inclined to be risk averse, risk neutral, or risk loving. If you're risk loving, then feel free to satisfy your desire for risk through the thrill of gambling. However, you might want to decide ifyou enjoy gambling more than other things -- like a house, car, stable family life, and bank account.

  • Before considering any sort of gambling, you need to discern the odds of winning as best you can. Keep in mind that those who sell gambling services, like casinos, and state lottery commissions, will do their best to convince you that the odds of winning are very good. Be wary of their claims.

  • From a public policy view, keep in mind that a lot of the gambling, except for the investment variety, involves a considerable amount of income and wealth transfer. You need to ask whether society can put those gambling resources to a more useful purpose.

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Today, you are likely to spend a great deal of time flipping through mail order catalogs hoping to buy either a flower arrangement for that special day for your mother or a New York Yankees baseball cap. Be on the lookout for letters from the Internal Revenue Service.
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