OT: a numbers riddle

[oosik]

And that is another valid reason that I always use my Visa card...........

 

[strantor]

Take another step further:

It is the month of August; a resort town sits next to the shores of a lake. It is raining, and the little town looks totally deserted. It is tough times, everybody is in debt, and everybody lives on credit.

Suddenly, a rich tourist comes to town. He enters the only hotel, lays a 100 dollar bill on the reception counter, and goes to inspect the rooms upstairs in order to pick one.

The hotel proprietor takes the 100 dollar bill and runs to pay his debt to the butcher. The Butcher takes the 100 dollar bill and runs to pay his debt to the pig raiser. The pig raiser takes the 100 dollar bill and runs to pay his debt to the supplier of his feed and fuel. The supplier of feed and fuel takes the 100 dollar bill and runs to pay his debt to the town痴 prostitute that, in these hard times, gave her 都ervices on credit. The hooker runs to the hotel, and pays off her debt with the 100 dollar bill to the hotel proprietor to pay for the rooms that she rented when she brought her clients there.

The hotel proprietor then lays the 100 dollar bill back on the counter so that the rich tourist will not suspect anything. At that moment, the rich tourist comes down after inspecting the rooms, and takes his 100 dollar bill, after saying he did not like any of the rooms, and leaves town.

No one earned anything. However, the whole town is now without debt, and looks to the future with a lot of optimism.

I like this. But with all these interest-free loans it fails to illustrate the effect of usury. And with no financial institutions in the mix, the currency multiplication of fractional reserve banking is glossed over. How about this:

There's a town consisting of 3 people; Bob, Tom, and Sue. All 3 are poor ($1,000 to their name in all 3 cases) but debt free. A banker moves into town and opens a bank. Sue deposits everything she has ($1,000) in the bank. The banker is allowed to lend out 90% of that, at whatever the prevailing interest rate is.

Bob has taxes coming up and doesn't want to spend his money, but he wants to buy a car from Tom for, coincidentally, $900, so he goes to the bank and gets the loan. The banker issues the loan and maxes out his fractional reserve limit. He'll need someone to deposit more money before he can lend more out.

No problem, here comes Tom to deposit the $900 that Bob just borrowed from the very same bank. So now the banker can loan out 90% of that $900 as well, and he has $1,900 on the books for deposits.

Sue decides she wants to buy Tom's now vacant carport, so she obtains a loan for $800. Tom again deposits the cash and the banker now has $2,700 worth of deposits on the books.

Let's recap:
Tom holds: $1,000 (he never did anything with his initial money)
Bob holds: $1,000 (he still hasn't paid his taxes)
Sue holds: $0
banker holds: $2,700

There's now $4,700 in the economy where before the banker arrived there was only $3,000 in the economy. Did the banker spontaneously generate $1,700? Well, sorta, but technically not, because that $1,700 now floating around the economy is cancelled out by $1,700 worth the promissory notes held at the bank in the names of Bob and Sue. If all loans were paid in full at this very moment, the balance of the economy would return to its original $3,000.

But those loans aren't going to be paid in full today, they're going to be paid over time, accruing interest. Where does the money to pay that interest come from? There's only $3,000 in the economy. Come a few years down the road, after more loans have been funded and payed and interest collected, someone is going to be stuck holding a hot potato. The money to pay the interest does not exist in the economy. Someone is going to be insolvent. Someone is going to be bankrupt. We can point fingers and say they should have managed their money better, but the mathematical fact is that one of those people was destined to be the designated loser the second the banker turned the lights on. It could have been any one of them (except tom).

So my town is now drowning debt looking forward to a future of despair. Kinda like the real world.

Sorry to be a buzzkill. Your story really was nice.

Edit:
One more step further. Let's say Bob is the one who files for bankruptcy. He leaves the banker holding a promissory note for, coincidentally, $1700 and has no money to pay it back. The banker calls up the FDIC who squeezes a unicorn until it farts pixie dust and that $1700 magically appears back in the banker's coffers (because after all, he has to be able to fill withdrawals of people's actual money that they actually deposited), so the banker (via the fed) actually DID spontaneously generate the additional currency, and it didn't spontaneously get deposited into Bob, Tom, or Sue's pockets or bank accounts. But for some reason Tom and Sue feel compelled to remind Bob how dishonorable it was to leave the bank holding his insolvent debt. Because it just isn't right to not repay your debts. Poor banker.

 

[bunyip]

Well, it confirms what I have heard about the letter regarding a dishonoured cheque (check) due to insufficient funds, the question is who has insufficient funds, you or the bank?

 

[Fuddy1952]

I just thought of the main fallacy of the restaurant puzzle. Three x $9=$27...but that includes the tip. Adding tip back in is meaningless.
$25 to restaurant for meal
$2 to waitress
$3 change
So $30 total

 

[Jstpssng]

I like this. But with all these interest-free loans it fails to illustrate the effect of usury. And with no financial institutions in the mix, the currency multiplication of fractional reserve banking is glossed over. How about this:

There's a town consisting of 3 people; Bob, Tom, and Sue. All 3 are poor ($1,000 to their name in all 3 cases) but debt free. A banker moves into town and opens a bank. Sue deposits everything she has ($1,000) in the bank. The banker is allowed to lend out 90% of that, at whatever the prevailing interest rate is.

Bob has taxes coming up and doesn't want to spend his money, but he wants to buy a car from Tom for, coincidentally, $900, so he goes to the bank and gets the loan. The banker issues the loan and maxes out his fractional reserve limit. He'll need someone to deposit more money before he can lend more out.

No problem, here comes Tom to deposit the $900 that Bob just borrowed from the very same bank. So now the banker can loan out 90% of that $900 as well, and he has $1,900 on the books for deposits.

Sue decides she wants to buy Tom's now vacant carport, so she obtains a loan for $800. Tom again deposits the cash and the banker now has $2,700 worth of deposits on the books.

Let's recap:
Tom holds: $1,000 (he never did anything with his initial money)
Bob holds: $1,000 (he still hasn't paid his taxes)
Sue holds: $0
banker holds: $2,700

There's now $4,700 in the economy where before the banker arrived there was only $3,000 in the economy. Did the banker spontaneously generate $1,700? Well, sorta, but technically not, because that $1,700 now floating around the economy is cancelled out by $1,700 worth the promissory notes held at the bank in the names of Bob and Sue. If all loans were paid in full at this very moment, the balance of the economy would return to its original $3,000.

But those loans aren't going to be paid in full today, they're going to be paid over time, accruing interest. Where does the money to pay that interest come from? There's only $3,000 in the economy. Come a few years down the road, after more loans have been funded and payed and interest collected, someone is going to be stuck holding a hot potato. The money to pay the interest does not exist in the economy. Someone is going to be insolvent. Someone is going to be bankrupt. We can point fingers and say they should have managed their money better, but the mathematical fact is that one of those people was destined to be the designated loser the second the banker turned the lights on. It could have been any one of them (except tom).

So my town is now drowning debt looking forward to a future of despair. Kinda like the real world.

Sorry to be a buzzkill. Your story really was nice.

Edit:
One more step further. Let's say Bob is the one who files for bankruptcy. He leaves the banker holding a promissory note for, coincidentally, $1700 and has no money to pay it back. The banker calls up the FDIC who squeezes a unicorn until it farts pixie dust and that $1700 magically appears back in the banker's coffers (because after all, he has to be able to fill withdrawals of people's actual money that they actually deposited), so the banker (via the fed) actually DID spontaneously generate the additional currency, and it didn't spontaneously get deposited into Bob, Tom, or Sue's pockets or bank accounts. But for some reason Tom and Sue feel compelled to remind Bob how dishonorable it was to leave the bank holding his insolvent debt. Because it just isn't right to not repay your debts. Poor banker.

Interesting scenario which could be utilized in a HS economics class. You left out income though; no banker is going to loan money to somebody who has no way of repaying it.

 

[strantor]

The riddle has been up nearly 24hrs so I'll spill the beans. Several people gave correct answers in different ways. I've chosen to examine the one below because it's short & sweet.

I just thought of the main fallacy of the restaurant puzzle. Three x $9=$27...but that includes the tip. Adding tip back in is meaningless.
$25 to restaurant for meal
$2 to waitress
$3 change
So $30 total

Yes, the riddle is a fallacy. Obviously; numbers don't lie, so it must be the words lying. There is more than one way to state the fallacy and more than one way to correct it.

The simplest way I've found to state it correctly, is that the $2 tip should be subtracted, not added, to arrive at dollar amount of the actual bill, not the number of dollars originally laid on the table.

$9 x 3 = $27
$27 - $2 = $25

$27 is the actual amount paid, and two dollars of that went to the waitress, the other $25 went to the restaurant.

It's strange how strong the power of suggestion can be. The riddle just casually drops the word "plus" into the equation, and the ensuing mental gymnastics (at least in my case) never question it. I spent the better part of an hour wrestling to make that word "plus" fit into a formula where it quite obviously (in retrospect) does not.

 

[strantor]

Interesting scenario which could be utilized in a HS economics class. You left out income though; no banker is going to loan money to somebody who has no way of repaying it.

Quite true. But there's an unwritten limit to what people will actually read, and what I wrote was already stretching the bounds of what I've empirically found to be the typical person's attention span.

 

[strantor]

Well, it confirms what I have heard about the letter regarding a dishonoured cheque (check) due to insufficient funds, the question is who has insufficient funds, you or the bank?

I'm going to step outside the box and say that in your typical fiat currency climate, neither you OR the bank have insufficient funds, because:



(Pardon the USA reference. It's the best meme I could find. It applies to any economy based on fiat currency)

 

[Fuddy1952]

Thanks for the puzzle! It really had me thinking as I was washing three cars yesterday (three cars/three guys in a restaurant ).
I was thinking how it didn't make sense, they walk in with $30, spend $27 + the waitress has $2.
Then I realized the $27 included that $2 tip.

 

[Jstpssng]

He said don't give it away so I didn't. All that you had to do was work through the problem though.