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        riddles >> what happened >> The Power of Tourism
        
(Message started by: StallionMang on Jan 21st, 2008, 12:11pm)
Title: The Power of Tourism
Post by StallionMang on Jan 21st, 2008, 12:11pm
Due to the presence of tourism in a particular place, the residents have to pay higher electricity bills than they would otherwise.  Explain.

Note: this is a true "lateral thinking" problem, which means you are unlikely to get it by taking blind stabs.  You definitely want to ask yes/no questions on this one.
Title: Re: The Power of Tourism
Post by Three Hands on Jan 21st, 2008, 1:02pm
Probably completely off-track, but I can't help but think [hide]Viva Las Vegas![/hide]
Title: Re: The Power of Tourism
Post by Iceman on Jan 21st, 2008, 1:28pm
........because tourists are swimming in the sea that has electric eels?  

Or the mayor of the city has invited Electric Banana Band to entertain tourists?

Or tourists are suffering from schizophrenia, so instead of taking electric shocks the old way, now they swim in modern electric swimming pools?

Or 'Houston, we have a problem!'

Or these tourists are aliens from Alpha Centauri, which eat electricity.

Or these tourists are soccer fans from England, drunkards and hooligans, breaking windows and pinball machines. And since there are a lot of pinball machines in this place, mostly to entertain the tourists, of course, someone has to pay for the damage. It is rude to ask tourists to pay for all the pinball machines they've broken. Btw, if tourists do pay for pinball machines, they will never come back, and most of this little town's income comes from tourism.
Title: Re: The Power of Tourism
Post by StallionMang on Jan 21st, 2008, 3:13pm
Three Hands, it's not Vegas, sorry.... :)

Iceman, unfortunately, none of your colorful guesses are correct, although I was entertained by them.  

Keep in mind, guys, this riddle is non-fiction, so the answer is not going to be anything ridiculous.

Title: Re: The Power of Tourism
Post by Iceman on Jan 21st, 2008, 4:03pm
It is Christmas, and tourists are drawn to this place because of thousands of light bulbs all over the city? ???  :-[  ;)
Title: Re: The Power of Tourism
Post by StallionMang on Jan 21st, 2008, 4:23pm
Nope.
Title: Re: The Power of Tourism
Post by thecow135 on Jan 21st, 2008, 5:47pm
they don't normally use electricity?
Title: Re: The Power of Tourism
Post by StallionMang on Jan 21st, 2008, 5:55pm
The residents of the area use electricity; they just pay more for it.
Title: Re: The Power of Tourism
Post by SMQ on Jan 21st, 2008, 6:18pm
Do they use more electricity due to the tourism? Or do they pay more for the electricity they would use anyway?

--SMQ
Title: Re: The Power of Tourism
Post by StallionMang on Jan 21st, 2008, 6:53pm
They pay more for the electricity they would use anyway.
Title: Re: The Power of Tourism
Post by thecow135 on Jan 21st, 2008, 8:00pm
are we guessing the city? or are we just explaining it?... because usually this happens as there are more tourists, the need for electricity goes up and the city is unable to produce it so must buy it from other cities..
Title: Re: The Power of Tourism
Post by shasta on Jan 21st, 2008, 8:59pm
When there's a lot of tourism, there's a lot more people there who want electricity. Thus, the demand for electricity increases. And the price of any product whose demand goes up goes up as well, (except in certain rare cases).
Title: Re: The Power of Tourism
Post by Grimbal on Jan 22nd, 2008, 2:31am
Not necessarily.  If the demand goes up, the prices go up as well.

But then the production increases.  Producing on a larger scale can be cheaper than on a small scale.  So the price can well go down below what it was before.
Title: Re: The Power of Tourism
Post by shasta on Jan 22nd, 2008, 5:42am
"Producing on a larger scale can be cheaper than on a small scale. So the price can well go down below what it was before."

Let's say you've got someone who is willing to buy a widget from you every month for $1000. This widget costs you $200 to make. Then thanks to an innovation, you find a way to make this widget for only $100. This guy is still willing to buy the widget from you for $1000 each month. Why would you lower the price of the widget by $100 instead of pocketing the difference? The answer is you wouldn't, especially considering it's illegal to deliberately fail to fulfill your fiduciary duty to your stockholders to make as much money as possible.

The costs of creating a product almost never have anything to do with it's price. The exceptions are
1. If the cost of manufacture are higher than people are willing to pay for the finished product, the product simply doesn't get made.
2. If you get a couple companies that actually do compete with each other instead of using price fixing to act like different divisions of one bigger company then they sometimes lower prices closer to costs trying to capture the part of the market currently buying their competitors' products. This is very rare nowadays, as it tends to be costly to all companies involved and a risky strategy. The super-companies that have emerged from the last century have far cheaper and more effective means of dealing with any real competition that might come along, which means would-be investors are now avoiding investing in them in the first place.



Title: Re: The Power of Tourism
Post by pex on Jan 22nd, 2008, 5:57am

on 01/22/08 at 05:42:21, shasta wrote:
Let's say you've got someone who is willing to buy a widget from you every month for $1000. This widget costs you $200 to make. Then thanks to an innovation, you find a way to make this widget for only $100. This guy is still willing to buy the widget from you for $1000 each month. Why would you lower the price of the widget by $100 instead of pocketing the difference?

Because more people would be willing to buy it at $900, while your profit per unit is unaffected?
Title: Re: The Power of Tourism
Post by towr on Jan 22nd, 2008, 6:11am

on 01/22/08 at 05:42:21, shasta wrote:
The answer is you wouldn't, especially considering it's illegal to deliberately fail to fulfill your fiduciary duty to your stockholders to make as much money as possible.
Really?
Wouldn't it first of all depend on what the stockholders want, and whether at that time squeezing the last drop of blood from the stone is the best business tactic?
Selling two widgets at a profit of 800 (or even 500) is better than selling one at a profit of 900. You always compete against the option of not-buying.
Title: Re: The Power of Tourism
Post by Grimbal on Jan 22nd, 2008, 6:20am
(reply to shasta)

You are right, competition is necessary to make the prices go down when production scales up.  But even between the mega-corporations it is not rare that they fight for a market and end up lowering their prices.  If a company makes juicy profits in a market others will rush in.  Sooner or later prices will drop.

In the electricity market, it really depends on where you live.  In many places it is a monopoly and it better not be a private company running it.  That is a problem.  But in other places the market is open to the competition.
Title: Re: The Power of Tourism
Post by StallionMang on Jan 22nd, 2008, 6:27am
Well, I'll give you this clue, guys.

In this riddle, the reason why the residents pay more has absolutely nothing to do with increased usage due to tourists.

thecow,

Yes, it is a specific place that you are trying to guess, but you will not get it unless you figure out the explanation.
Title: Re: The Power of Tourism
Post by pex on Jan 22nd, 2008, 7:29am
Maybe this specific place uses [hide]old-fashioned, inefficient, expensive, but tourist-attracting ways of producing electricity[/hide]?
Title: Re: The Power of Tourism
Post by StallionMang on Jan 22nd, 2008, 8:17am

on 01/22/08 at 07:29:27, pex wrote:
Maybe this specific place uses [hide]old-fashioned, inefficient, expensive, but tourist-attracting ways of producing electricity[/hide]?



I like your thinking......I will give it a partial 'yes': the thing that draws the tourists to the area requires that there be less efficiency in power generation.
Title: Re: The Power of Tourism
Post by SMQ on Jan 22nd, 2008, 8:26am
Are they unable to [hide]construct a hydroelectric dam[/hide] because of the popularity of their [hide]river[/hide]?

--SMQ
Title: Re: The Power of Tourism
Post by Iceman on Jan 22nd, 2008, 8:30am
...........I knew this riddle is about ice! :D They are Eskimos who insist to sleep in igloos. Still, there are no igloos in this place, but Eskimos agreed to sleep in refrigerators.  8)
Title: Re: The Power of Tourism
Post by StallionMang on Jan 22nd, 2008, 9:11am

on 01/22/08 at 08:26:18, SMQ wrote:
Are they unable to [hide]construct a hydroelectric dam[/hide] because of the popularity of their [hide]river[/hide]?

--SMQ


SMQ, you're very very close....very close, but not quite.
Title: Re: The Power of Tourism
Post by Grimbal on Jan 22nd, 2008, 9:53am
[hide]A dam cannot be built because it would put under water a tourist's attraction.  If they build the dam, they loose the tourist's revenue.[/hide]
Title: Re: The Power of Tourism
Post by Ghost Sniper on Jan 22nd, 2008, 10:11am
Or...

[hide]The river itself feeds another dam downstream, a much bigger, federal-funded dam. If they build a local dam to fuel to local electricity, the dam downstream would not have water to run with, and therefore, interfere with government activity.[/hide]
Title: Re: The Power of Tourism
Post by StallionMang on Jan 22nd, 2008, 10:34am

on 01/22/08 at 09:53:46, Grimbal wrote:
[hide]A dam cannot be built because it would put under water a tourist's attraction.  If they build the dam, they loose the tourist's revenue.[/hide]


Good thought, but no.
Title: Re: The Power of Tourism
Post by StallionMang on Jan 22nd, 2008, 10:36am

on 01/22/08 at 10:11:11, Ghost Sniper wrote:
Or...

[hide]The river itself feeds another dam downstream, a much bigger, federal-funded dam. If they build a local dam to fuel to local electricity, the dam downstream would not have water to run with, and therefore, interfere with government activity.[/hide]


Good try, but government regulations are not part of the answer; only tourism is causing this situation.
Title: Re: The Power of Tourism
Post by denis on Jan 22nd, 2008, 11:30am
[hide]They are on a small tropical island where there  are no rivers, hence no hydroelectric dams. The power generation stations use gas generators (or some similar commodity) and when tourist season arrives, the gas (or related commodity) price goes up as all other prices go up in high tourist season[/hide]
Title: Re: The Power of Tourism
Post by StallionMang on Jan 22nd, 2008, 3:48pm

on 01/22/08 at 11:30:14, denis wrote:
[hide]They are on a small tropical island where there  are no rivers, hence no hydroelectric dams. The power generation stations use gas generators (or some similar commodity) and when tourist season arrives, the gas (or related commodity) price goes up as all other prices go up in high tourist season[/hide]


denis,

Sorry, no.
Title: Re: The Power of Tourism
Post by Three Hands on Jan 22nd, 2008, 5:04pm
Turning it a bit on its head, [hide]Is it due to the dam/power generator being the tourist attraction, and so upgrading the method of generating power, while increasing the efficiency of the generation of power - in turn reducing the cost of electricity - would remove the main tourist attraction from the area[/hide]?
Title: Re: The Power of Tourism
Post by ima1trkpny on Jan 22nd, 2008, 6:30pm

on 01/22/08 at 17:04:13, Three Hands wrote:
Turning it a bit on its head, [hide]Is it due to the dam/power generator being the tourist attraction, and so upgrading the method of generating power, while increasing the efficiency of the generation of power - in turn reducing the cost of electricity - would remove the main tourist attraction from the area[/hide]?

Thinking along this line... maybe the [hide]Hoover Dam[/hide]?
Title: Re: The Power of Tourism
Post by StallionMang on Jan 22nd, 2008, 10:37pm

on 01/22/08 at 17:04:13, Three Hands wrote:
Turning it a bit on its head, [hide]Is it due to the dam/power generator being the tourist attraction, and so upgrading the method of generating power, while increasing the efficiency of the generation of power - in turn reducing the cost of electricity - would remove the main tourist attraction from the area[/hide]?


Three Hands, another good idea, but no.

A clue, for those of you on the verge of giving up: [hide]the closest guesses so far have been the ones suggesting that the construction of a hydroelectric dam would hurt tourism......well, this place does have a hydroelectric dam, but they choose not to use it to its fullest potential.[/hide]
Title: Re: The Power of Tourism
Post by temporary on Jan 22nd, 2008, 10:59pm
[hide]The tourists need electricity, but they have no intention of going back home right away to get electricity cheaper, therefore residents know they can make more money and get away with it by making them pay more for it.[/hide]
Title: Re: The Power of Tourism
Post by StallionMang on Jan 22nd, 2008, 11:02pm

on 01/22/08 at 22:59:54, temporary wrote:
[hide]The tourists need electricity, but they have no intention of going back home right away to get electricity cheaper, therefore residents know they can make more money and get away with it by making them pay more for it.[/hide]


Uh, no.  The riddle indicates that it is the residents who pay more.  Also, we have established in this thread that the electricity used by the tourists is not a factor here.
Title: Re: The Power of Tourism
Post by Grimbal on Jan 23rd, 2008, 4:58am
These people produce electricity using child labor, they pedal on static bicycles that activate dynamos.

But when tourists are present, they are forced to use adults with a decent pay, holidays, health care, etc.
Title: Re: The Power of Tourism
Post by shasta on Jan 23rd, 2008, 9:35am

on 01/22/08 at 05:57:04, pex wrote:
Because more people would be willing to buy it at $900, while your profit per unit is unaffected?


If enough more people were willing to buy it at $900 to give you more profit than selling it for $1000 that's what you would have been selling it for in the first place. Your costs of production are not related to the ideal price point to sell the product at. That's purely a factor of demand. This is why Sony PS2s are  still priced over $100, in spite of being massively mass-produced. Because that's the price that brings them the most revenue, and lowering the price doesn't increase sales enough to compensate for the money which would be lost per unit.
Title: Re: The Power of Tourism
Post by towr on Jan 23rd, 2008, 9:52am

on 01/23/08 at 09:35:47, shasta wrote:
Your costs of production are not related to the ideal price point to sell the product at.
I beg to differ.
Suppose the production cost was originally 900; and you can sell it to 1 person at 1000, or 3 people at 900. In the first case you make an overall profit of 100, in the other case you have no profit. So the first pricing strategy wins.
Now if the production costs drop to 800, then in the first case you make 200, but in the second case you make 300. So suddenly the second pricing strategy is more favorable.
The ideal price point depends both on the sales (a function of price) and profit per sale (a function of price and cost).
Title: Re: The Power of Tourism
Post by Grimbal on Jan 23rd, 2008, 10:02am

on 01/23/08 at 09:35:47, shasta wrote:
If enough more people were willing to buy it at $900 to give you more profit than selling it for $1000 that's what you would have been selling it for in the first place.


Not true.

Let's have
p : the sales price
c : the production cost

Let's say the demand at price p is:
d = 1800-P

The benefit at price p is b = (1800-p)*(p-c)
The benefit is maximum when b' = 0
b' = (1800-p) - (p-c) = 1800+c - 2p
b' is zero for p = 900 + c/2.

With c = $200, the optimal price is $1000
but with c = $100, the optimal price is $950

[edit] Oh, hi towr! I didn't see you step in... [/edit]
Title: Re: The Power of Tourism
Post by denis on Jan 23rd, 2008, 10:10am
All these discussions based on profit may not necessarily apply.

Electricity production and utilities in general are not priced using a profit generation model. Often they even run large deficits (in my case Ontario Hydro has about a billion dollar debt).
Title: Re: The Power of Tourism
Post by denis on Jan 23rd, 2008, 10:17am
How about periodically shutting down the hydroelectric dam to allow tourists to hike in the panoramic canyons while the water is shut off. In these instances, the alternate and more expensive power generation is used.
Title: Re: The Power of Tourism
Post by StallionMang on Jan 23rd, 2008, 11:56am

on 01/23/08 at 10:17:53, denis wrote:
How about periodically shutting down the hydroelectric dam to allow tourists to hike in the panoramic canyons while the water is shut off. In these instances, the alternate and more expensive power generation is used.



Denis, you are extremely close to the answer.  The solution does not involve "shutting down" the dam, necessarily.  And it is not canyons that the tourists come here for.  But you're very close.
Title: Re: The Power of Tourism
Post by shasta on Jan 23rd, 2008, 12:19pm

on 01/23/08 at 09:52:00, towr wrote:
I beg to differ.
Suppose the production cost was originally 900; and you can sell it to 1 person at 1000, or 3 people at 900. In the first case you make an overall profit of 100, in the other case you have no profit. So the first pricing strategy wins.
Now if the production costs drop to 800, then in the first case you make 200, but in the second case you make 300. So suddenly the second pricing strategy is more favorable.


Quoting what I posted initially about this

"The costs of creating a product almost never have anything to do with it's price. The exceptions are  
1. If the costs of manufacture are higher than people are willing to pay for the finished product, the product simply doesn't get made."

I guess what I should have said was "if the costs exceeded the ideal price point if there were no costs of manufacture", which is the point I was trying to make. In the example you provided the costs did exceed the equilibrium point on a graph which assumes costs are $0 in the first case and not in the second.
Thus in the first part of your example the additional two products weren't made because the demand for those units was lower than the cost of producing them, which was the point you'd made and the exception I'd tried to spell out initially.



on 01/23/08 at 09:52:00, towr wrote:
The ideal price point depends both on the sales (a function of price) and profit per sale (a function of price and cost).


I see your point. If the supply demand curve for a product is an actual straight curve which doesn't have a big dropoff or a point where it becomes especially steep, a drop in cost would create a corresponding drop in the ideal price point, (though that drop would not necessarily equal the drop in the costs of manufacture). However, I think there is for most all products a steep drop in the demand curve, such that most people who aren't willing to pay $x for that product aren't willing to pay 1/2 or even 1/4th $x because they just don't want the product that much, (or at all). I also think the cost of manufacture for most items is past the steep part of the curve, though electricity might be an exception.
Title: Re: The Power of Tourism
Post by denis on Jan 23rd, 2008, 12:24pm
OK how about keeping the hydroelectric dam's water flow at very low output for recreational purposes (water slide at theme park, or calm river for kayaking, canoeing etc), while using the alternate power generation source to compensate.
Title: Re: The Power of Tourism
Post by shasta on Jan 23rd, 2008, 12:34pm

on 01/23/08 at 10:02:27, Grimbal wrote:
Not true.

Let's have
p : the sales price
c : the production cost

Let's say the demand at price p is:
d = 1800-P


I have a hard time envisioning a product in which demand actually works this way. Typically I would think that if there are 1800 potential consumers who are willing to buy a product at all at any price, odds are the majority of them are willing to pay X or more, with some number willing to pay much less, with some number willing to spend a buck or two on it.  This creates a steep drop in the curve after the ideal price point. As long as your costs are less than the drop off point, any additional costs which are cut do not lower the ideal price point.

Here's a picture of how I envision the usual graph.

Price

$1000 |
$900   |
$800   |\
$700   |.\___
$600   |........\___
$500   |...............\_____
$400   |..........................\____
$300   |...................................\
$200   |....................................|
$100   |....................................|
$50     |....................................\
$10     |.....................................\__
----------------------------------------------------------------
# sold     5  10   15   20  25    30   35

For a product with this demand, it makes no sense to ever lower the price below $400, regardless of  the cost of production.
Title: Re: The Power of Tourism
Post by Three Hands on Jan 23rd, 2008, 1:23pm

on 01/23/08 at 12:24:26, denis wrote:
OK how about keeping the hydroelectric dam's water flow at very low output for recreational purposes (water slide at theme park, or calm river for kayaking, canoeing etc), while using the alternate power generation source to compensate.


Or even maintaining a nice large reservoir for similar waterborne pursuits...
Title: Re: The Power of Tourism
Post by Grimbal on Jan 23rd, 2008, 2:41pm

on 01/23/08 at 12:34:01, shasta wrote:
I have a hard time envisioning a product in which demand actually works this way.

You are right.  It will never be completely linear.  But  a real curve would still be roughly linear with a negative slope around the point of optimal price, so the reasoning still applies.
Title: Re: The Power of Tourism
Post by StallionMang on Jan 24th, 2008, 8:51am
Denis,

You got the concept down.  The majority of the water is not diverted to the hydroelectric dam, but instead is allowed to flow past.

Now you just need to figure out why and what specific place this is.

It is an extremely popular North American tourist spot.
Title: Re: The Power of Tourism
Post by denis on Jan 24th, 2008, 9:16am

on 01/24/08 at 08:51:36, StallionMang wrote:
.

Now you just need to figure out why and what specific place this is.



Does it have to do with white water rafting?
Title: Re: The Power of Tourism
Post by StallionMang on Jan 24th, 2008, 1:41pm
Nope.
Title: Re: The Power of Tourism
Post by Eigenray on Jan 24th, 2008, 3:36pm
Maybe I have an unfair advantage, having been there a couple times.

At night, they can produce more energy, but there is also less demand... so they pump water up into a reservoir, recovering the energy during the day.
Title: Re: The Power of Tourism
Post by JiNbOtAk on Jan 24th, 2008, 7:46pm

on 01/24/08 at 15:36:43, Eigenray wrote:
Maybe I have an unfair advantage, having been there a couple times.


Where ?  ???
Title: Re: The Power of Tourism
Post by StallionMang on Jan 24th, 2008, 7:59pm
I think Eigenray has it.

Go ahead and bring this one home, duder.   :)
Title: Re: The Power of Tourism
Post by Eigenray on Jan 25th, 2008, 7:03am
They already produce twice as much power as the Hoover dam (enough to power 3.6 flux capacitors continuously!).  They could produce more, but then it wouldn't be as attractive to honeymooners, tightrope walkers, people in barrels, etc.
Title: Re: The Power of Tourism
Post by StallionMang on Jan 25th, 2008, 10:51am
Ha ha!

Congrats, Eigenray.  NIAGARA FALLS is the correct answer.  

From Wikipedia:

During the summer months, 100,000 cubic feet per second (2,832 m³/s) of water actually traverses the Falls, some 90% of which goes over the Horseshoe Falls, while the balance is diverted to hydroelectric facilities. This is accomplished by employing a weir with movable gates upstream from the Horseshoe Falls. The Falls flow is further halved at night, and during the low tourist season in the winter, remains a flat 50,000 cubic feet per second (1,416 m³/s).
Title: Re: The Power of Tourism
Post by Whiskey Tango Foxtrot on Jan 26th, 2008, 10:14am
That is a very cool riddle.
Title: Re: The Power of Tourism
Post by shasta on Jan 26th, 2008, 2:02pm

on 01/26/08 at 10:14:50, Whiskey Tango Foxtrot wrote:
That is a very cool riddle.


I agree.
Title: Re: The Power of Tourism
Post by shasta on Jan 26th, 2008, 3:18pm

on 01/23/08 at 14:41:38, Grimbal wrote:
You are right.  It will never be completely linear.  But  a real curve would still be roughly linear with a negative slope around the point of optimal price, so the reasoning still applies.


Correct me if I'm wrong, but did you really interpret my argument to be that the curve won't be completely linear? Because if you didn't, then pretending to concede that point to me while still simply denying the point I really made, (that the demand curve looks more like a step function), is a very dishonest and patronizing tactic.

I could similarly reply with "You are right, it will never be a perfect step function. But it will have a roughly infinite negative slope at the point of optimal price so my view is still the correct one."

However in the interest of truth let me just point out the following.

The relationship between a drop in cost and a drop in optimum price is calculated as follows.

dP = drop in optimal price
dC = drop in per unit production cost
S = slope of the demand curve

dP = -dC/(2S)

Thus in order for a drop in cost to result in a corresponding drop in optimal price, the drop must be greater than twice the absolute value of the slope of the demand curve. The demand curve you suggested earlier of -1, (the curve when d=1800-p), by the way happens to be the maximum possible slope which can ever immediately follow the optimal price point; and it also happens to be the one that creates the largest possible drop in optimal price versus the drop in production costs, being a 1:2 ratio. As the slope decreases, so too does the ratio. Until the slope is greater than the drop in per unit production costs divided by two, at which point the optimal price no longer moves. Of course, since production costs can't go below $0, that means any products whose total production cost is less than -2S cannot change the optimal price even if they do manage to get production costs down all the way to $0. This is true even if the slope is linear.

So whether or not a product's optimal price will drop in response to a drop in production costs is dependant on 2 things, the slope and how large the per unit drop in production costs is. All around me I see products whose demand curves I believe are quite vertical. People seem to have prices that make them happy, such as $19.99. I imagine there are very few people who are willing to pay $17.99 for a product but unwilling to pay $19.99 for that same product, people just don't shop like that. With higher priced items the disparity becomes even greater, very few people would pass on their dream house because the price was $500 more than they'd set as their limit before they went out looking. So the slopes are pretty steep on all these products. Additionally, all around me I see products whose productions costs are very low relative to the prices. This means the maximum total that per unit costs could potentially drop for all those products is very small. Products with very small possible drops in per unit costs combined with very steep demand curves, (very steep relative to your -1 slope anyway), do not decrease in price at all in response to a decrease in production costs. And I believe most products fit this mold. In fact, I'm having trouble thinking of any that don't.
Title: Re: The Power of Tourism
Post by StallionMang on Jan 27th, 2008, 2:44am

on 01/26/08 at 10:14:50, Whiskey Tango Foxtrot wrote:
That is a very cool riddle.


Thanks, WTF.  

The story behind that riddle:  Back when I was an undergrad at Boston College, some zany professor of mine mentioned that fact about Niagara Falls during a lecture, and in a moment of divine inspiration, I crafted a lateral thinking puzzle out of it.  I posted it on the www.lateralpuzzles.com forum, moderated by Paul Sloane (the macdaddy of lateral thinking).  I felt quite honored when he shot me an e-mail shortly thereafter, asking if he could include it in his next puzzle book.  The dude even took my address and sent me an autographed copy.  Class act.

Interesting footnote to that story:  I have never been able to craft a decent riddle since.  :(
Title: Re: The Power of Tourism
Post by towr on Jan 27th, 2008, 7:52am

on 01/26/08 at 15:18:08, shasta wrote:
So whether or not a product's optimal price will drop in response to a drop in production costs is dependant on 2 things, the slope and how large the per unit drop in production costs is. All around me I see products whose demand curves I believe are quite vertical. People seem to have prices that make them happy, such as $19.99. I imagine there are very few people who are willing to pay $17.99 for a product but unwilling to pay $19.99 for that same product, people just don't shop like that. With higher priced items the disparity becomes even greater, very few people would pass on their dream house because the price was $500 more than they'd set as their limit before they went out looking. So the slopes are pretty steep on all these products. Additionally, all around me I see products whose productions costs are very low relative to the prices. This means the maximum total that per unit costs could potentially drop for all those products is very small. Products with very small possible drops in per unit costs combined with very steep demand curves, (very steep relative to your -1 slope anyway), do not decrease in price at all in response to a decrease in production costs. And I believe most products fit this mold. In fact, I'm having trouble thinking of any that don't.
Actually, there are quite a few; televisions, computers, cars, digital camera's, DVD recorders, etc. They used to be excessively expensive when they were new on the market, and prices went down rapidly as interest*) increased and costs went down.
People that wouldn't buy a $3000 computer (1981 IBM PC) probably wouldn't buy a $2500 either, but a $1000, even $500, one? That brings you in another step on the curve.
High end electronics typically have such a curve as they come on the markets. They are sold at high prices when the market is new, and then get cheaper, even before the competition gets going; because you need to grab a good market share before they do.
It is hard to say what would happen if there wasn't a threat of competition (because there always is), but even so if the costs of production is low enough, selling a million computers at $1000 is better than selling a thousand at $3000. And that kind of difference in sales is what a difference in price can do around a tipping point. The steps in the curve don't have the same length; I would suspect they increase in length exponentially, up to a point. The heights of the steps would tend opposite, getting smaller, because the relative differences are what affects people (you might need to go down $500 from $3000 to get on the next step, while to get down from $1000 a drop of $200 is generous).

*)I'd have said demand, but that might suggest people would buy it at that price; what drives a producer to reduce prices is of course when there is interest "but not at that price".
For example, I've been interested in getting a DVD/HDD-recorder for years, but only recently have they been available at a price I'd buy them at. An entire market of DVD/HDD-recorder buyers that won't buy at a price over 200 euros lay open, waiting for the first producer to meet that price.
Title: Re: The Power of Tourism
Post by Grimbal on Jan 27th, 2008, 10:35am

on 01/26/08 at 15:18:08, shasta wrote:
Correct me if I'm wrong, but did you really interpret my argument to be that the curve won't be completely linear? Because if you didn't, then pretending to concede that point to me while still simply denying the point I really made, (that the demand curve looks more like a step function), is a very dishonest and patronizing tactic.

Yes, I thought your point was that a straight line was an oversimplification of a typical demand curve and that therefore my argument was invalid.

My point was that when the production cost drops, the optimal sales price will might also drop.  Your calculations shows under which conditions, so I guess we agree on that.  I was under the impression that you said that the optimal sales price was independent of the production costs.  If it is not what you meant, I am sorry, it is a misunderstanding.
Title: Re: The Power of Tourism
Post by Eigenray on Jan 27th, 2008, 9:57pm

on 01/26/08 at 15:18:08, shasta wrote:
Thus in order for a drop in cost to result in a corresponding drop in optimal price, the drop must be greater than twice the absolute value of the slope of the demand curve.

I don't see where this comes from.  If demand = d(p), then the optimal price p maximizes d(p)(p-c), so is given implicitly by
d'(p)(p-c) + d(p) = 0.
Differentiating wrt c, we get
d''(p)p'(p-c) + d'(p)(p'-1) + d'(p)p' = 0,
so
p' = dp/dc = d'(p)/[2d'(p) + d''(p)(p-c)]
In particular, if d is linear (d''=0), we have p' = 1/2 is constant, as long as 0<c<p.  [If d(p) = a-bp, then popt = c/2 + a/(2b).]  A drop in cost will result in a drop in optimal price when p' > 0, which will hold as long as c<p, d'(p)<0, and d''(p) < -2d'(p)/(p-c).  If d'(p)=0, then we could certainly have p'=0, but if d' is at all decreasing at p (and d'' < -2d'/(p-c)), then p' > 0.

[What happens if d''(p)(p-c) http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/ge.gif -2d'(p) > 0?  Is this even possible?  I don't see how p' could ever be negative: if profit(p1)=profit(p2) with p1<p2, and d(p1) > d(p2), then reducing the production cost will make profit(p1) > profit(p2).]
Title: Re: The Power of Tourism
Post by onlyme722 on Mar 5th, 2008, 4:32pm

on 01/23/08 at 12:34:01, shasta wrote:
I have a hard time envisioning a product in which demand actually works this way. Typically I would think that if there are 1800 potential consumers who are willing to buy a product at all at any price, odds are the majority of them are willing to pay X or more, with some number willing to pay much less, with some number willing to spend a buck or two on it.  This creates a steep drop in the curve after the ideal price point. As long as your costs are less than the drop off point, any additional costs which are cut do not lower the ideal price point.

Here's a picture of how I envision the usual graph.

Price

$1000 |
$900   |
$800   |\
$700   |.\___
$600   |........\___
$500   |...............\_____
$400   |..........................\____
$300   |...................................\
$200   |....................................|
$100   |....................................|
$50     |....................................\
$10     |.....................................\__
----------------------------------------------------------------
# sold     5  10   15   20  25    30   35

For a product with this demand, it makes no sense to ever lower the price below $400, regardless of  the cost of production.



I've actually studied economics in college, and I can tell you that graphs depicting potential profit don't usually look like that.  They are usually BELL CURVES...like the one a teacher might have drawn to depict how many students stand a chance of getting a C.  In economics even the money you haven't made is still considered in your overall profit, I wish I wasn't forgetting the exact name for this, but it basically means "potential profit".  So if you COULD have made X more money by lowering the price, then that money you didn't make is considered a Loss (so you could have spent 5,000 dollars to produce, you mady 25,000 dollars, but if there are 10,000 dollars out there that you don't have because you didn't bring in enough customers, or sell enough product, then your overal profit is actually only 15,000 dollars).  Therefore, economists always study the best medium price that will bring in the most customers.  It's not as simple as "sell it for as much as people are willing to pay", because while yes they want to do this, they also have to consider how much money they would make at lower prices or they're not being very profitable.


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