(3.5) The RAW of Supply and Demand

[Phelix-Mu]

Consider, dear Playgrounders:

#1: The game says that things not covered in the rules happen as in real life.

#2: The game has prices for things.

#3: In real life, prices change as time passes, subject to market forces (chiefly, the law of supply and demand).

So, my question is:

Does the RAW say that prices given are static? Does it indicate otherwise?

Because, in absence of RAW comment, the laws of economics should affect the game. (See first premise.)

DISCUSS!:smallsmile:

[Flickerdart]

Faulty reasoning. The book provides prices. There is no mechanism to change those prices. Therefore, the prices do not change. If the game had no prices listed, then they could change per the laws of economics, if the laws of economics were the laws of physics (which IIRC is what the "real world" rule actually refers to)..

[Phelix-Mu]

Faulty reasoning. The book provides prices. There is no mechanism to change those prices. Therefore, the prices do not change. If the game had no prices listed, then they could change per the laws of economics, if the laws of economics were the laws of physics (which IIRC is what the "real world" rule actually refers to)..

I may be mistaken, but I also believe that availability is already in question based on settlement size. So prices are already conditional based on supply.

And I should dig up that quote about the in real life thing. It is most often used in physics discussions, but I don't recall it specifically mentioning that area.

As to the general point that prices can't change because no mechanism is provided, the real-life rule suggests that real-life provides the mechanism.

But, as you say, the real-life rule might not cover this.

It all hinges on the rule and any note of prices fluctuating or remaining static. In absence of comment, and if the rule applies, I don't think your reasoning holds. With all due respect, Flickerdart.

[eggynack]

The game does comment though. In particular, let's assume that for a given product, there were some price determined by supply and demand that's different from the price in the book. The real world says, "The item has this price," the game says, "No, the item has this other price, listed right here," and the latter overrides the former. The issue is that you're thinking of this in terms of price changing, instead of in terms of a pair of instantiated prices. As long as the game is telling you that an item is a given price, economics has no authority to change that price unless explicitly given by the game.

[Phelix-Mu]

The game does comment though. In particular, let's assume that for a given product, there were some price determined by supply and demand that's different from the price in the book. The real world says, "The item has this price," the game says, "No, the item has this other price, listed right here," and the latter overrides the former. The issue is that you're thinking of this in terms of price changing, instead of in terms of a pair of instantiated prices. As long as the game is telling you that an item is a given price, economics has no authority to change that price unless explicitly given by the game.

I guess I am getting nitpicky, but the real world doesn't say "the price is x." The real world says "prices change," and gives a mechanism (albeit a vague and pretty complex one) by which they do so. Does the book say prices can't change? No. (Or does it? Citation needed, hence this thread.)

In fact, as I mentioned, prices aren't solid. There are already instances where prices are relative. In a small thorp, that +1 longsword isn't actually worth 2000+gp, because there is no one there to buy it. The interpretation, as far as I can recall, is either that the item has value = priceless or value = worthless, but I don't think the game says, and the practical effect is the same.

In fact, now that I think about it, settlement gp caps already suggest that limited supply and demand exists: the demand for currency. A settlement conceivably could purchase that sword if it cashed in other assets, but they don't. Ostensibly, their money is valuable, and they don't want to spend it all in one place. Because the cash is limited, it's effective value is more than its face value suggests, which is pretty much textbook economics right there.

But I'm probably wrong somewhere. I honestly don't believe that everyone else overlooked something all these years. I just want to know how far I'd have to houserule to institute supply and demand, and how far RAW backs me up.

[Segev]

When you move into quantities of goods such that relative supply changes in proportion to demand, you have moved beyond the expected parameters of D&D as a general rule. D&D's focus is on adventuring, beating up monsters, solving puzzles, overcoming traps, and finding loot to haul back and sell (or use). Legendary treasures, epic quests, etc.

It is designed with the thought in mind that, as fabulously wealthy as the PCs get, they never are so rich that they're shifting economies. By the time they're wealthy enough to flood a small village, they're expected to be based in a huge fantasy city.

The RAW are that prices are static. This is because it simulates a setting wherein the supply just cannot change that much relative to the demand. When you change this assumption - whether as DM or as a player (by playing the game in a way that shifts the supply by that much) - you are outside the boundaries for which the rules were written. The DM is going to have to make something up.

While good for laughs, it is generally a mistake to assume that the RAW should hold when the assumptions for which they were written are violated. Thus, yes, "500 gp of ruby dust" is a set amount, and you can get it at a discount for 450 gp and still have the right amount. But everybody in the setting who knows ruby dust values knows how much is 500 gp, and it hasn't changed in long enough that nobody considers that it might. That's the setting the rules assume.

[Calimehter]

The 3.0 Arms and Equipment Guide has rules for setting up price variations by locale and region, and briefly discusses how trade routes will flow based off of this price variation. IIRC the rules are a bit abstract and GM still has to do a lot of the legwork, but if you are looking for RAW backup to justify in-game price changes, it fits the bill.

[eggynack]

I guess I am getting nitpicky, but the real world doesn't say "the price is x." The real world says "prices change," and gives a mechanism (albeit a vague and pretty complex one) by which they do so. Does the book say prices can't change? No. (Or does it? Citation needed, hence this thread.)
The game may not say that prices can't change, but it does say that the price is this specific number, and any change would contradict that given number. So, you can change from the prices in the book, but they would necessarily have to be to the same number.


In fact, as I mentioned, prices aren't solid. There are already instances where prices are relative. In a small thorp, that +1 longsword isn't actually worth 2000+gp, because there is no one there to buy it. The interpretation, as far as I can recall, is either that the item has value = priceless or value = worthless, but I don't think the game says, and the practical effect is the same.
Price determines what an item is sold for. Whether there is anyone to buy it is another matter. If you'd be willing to sell the sword for a lower price than the one in the book, and someone else would be willing to buy at that new price, then you're working with a price floor rather than a non-solid price.


In fact, now that I think about it, settlement gp caps already suggest that limited supply and demand exists: the demand for currency. A settlement conceivably could purchase that sword if it cashed in other assets, but they don't. Ostensibly, their money is valuable, and they don't want to spend it all in one place. Because the cash is limited, it's effective value is more than its face value suggests, which is pretty much textbook economics right there.
Supply and demand definitely exist. Supply and demand always exist. The issue is that the equilibrium price dictated by supply and demand can't actually become the new price. Market forces are there, but they're going up against an immovable object.

But I'm probably wrong somewhere. I honestly don't believe that everyone else overlooked something all these years. I just want to know how far I'd have to houserule to institute supply and demand, and how far RAW backs me up.
I'd suspect that you'd have to go a reasonable distance to institute it on a big scale, because economics is bigger than this one thing. Small scale would be easier, like in that thorp case above.

[Phelix-Mu]

When you move into quantities of goods such that relative supply changes in proportion to demand, you have moved beyond the expected parameters of D&D as a general rule. D&D's focus is on adventuring, beating up monsters, solving puzzles, overcoming traps, and finding loot to haul back and sell (or use). Legendary treasures, epic quests, etc.

It is designed with the thought in mind that, as fabulously wealthy as the PCs get, they never are so rich that they're shifting economies. By the time they're wealthy enough to flood a small village, they're expected to be based in a huge fantasy city.

The RAW are that prices are static. This is because it simulates a setting wherein the supply just cannot change that much relative to the demand. When you change this assumption - whether as DM or as a player (by playing the game in a way that shifts the supply by that much) - you are outside the boundaries for which the rules were written. The DM is going to have to make something up.

While good for laughs, it is generally a mistake to assume that the RAW should hold when the assumptions for which they were written are violated. Thus, yes, "500 gp of ruby dust" is a set amount, and you can get it at a discount for 450 gp and still have the right amount. But everybody in the setting who knows ruby dust values knows how much is 500 gp, and it hasn't changed in long enough that nobody considers that it might. That's the setting the rules assume.

I like your argument, I like your basis, but I need a citation on prices never changing. I will start digging shortly, starting with the PHB, and I assume it's there. I just don't think we can assume anything RAW-wise without citation, as the actual intent v actual RAW (v actual outcome) of the writers/designers of the game has demonstrably been horrifically at odds times innumerable in the past.

[nothingforyou]

Economic laws will work in D&D, at least the math will. The question is, do you really want to simulate them?

While we're at it, why don't we work on the following things:

1) An effective arcane field theory for D&D.
2) An equilibrium theory for heterogeneous alchemical mixtures.
3) A narrow variant of the Solow-Swan model for resetting wish traps and their value as capital investments, since they're going to completely wreck any semblance of a steady-state market.

[Phelix-Mu]

Economic laws will work in D&D, at least the math will. The question is, do you really want to simulate them?

I would like to anticipate WBL-mancy in high-op games, because it is so easy to do that it would be idiotic not to anticipate it as a DM. My method of anticipation would probably involve a highly bastardized form of economics designed to compensate for existing supply and existing cost, allowing those basic variables to fluctuate reasonably.

Essentially, I don't want to make earning tons of money impossible. It just can't be super, super easy.

In a sense, I am just trying to bring the simulationist side of the game up to speed with the narrative side, which says that there are some bizarre forces at work preventing infinite wealth from changing everyone's life on the Prime. Just like in real life, wall of salt can't provide arbitrarily high wealth, because eventually there is so much salt around that no one needs to buy it anymore (or certainly won't pay its weight in silver for it). Same with iron, same with stone. (Same with spells.)

I don't know that the game needs answers to these questions, I just want to know how far the answers given in the RAW can stretch, given that op-levels render WBL restrictions into an extreme metagame exercise for DMs: pcs get rich is fine. But I want there to be a metric to how rich, how fast, so I can determine more accurately scope of impact of that wealth.

[nothingforyou]

What you're trying to determine is an economic theory of value specialized to D&D. You could look at Debreu's analysis of equilibrium markets for ideas, but when you tack on the weirdness of D&D's mechanics, the math, while technically doable, may as well be your PhD thesis.

The metric you're looking for is way too insane. Even cutting down on its accuracy and bastardizing it for usability would require a high level of undergraduate mathematics.

I recommend you play it fast and loose, with your intuition. Alternatively, see if you can find econ rules in other tabletop games. Maybe you can get an idea of how D&D econ should behave without having to number crunch.

EDIT

Actually, I have another idea. Mount&Blade has a pretty robust economic system of supply/demand for medieval time periods. It won't cover everything that's possible in D&D, but it is 5000x more usable than any theory that covers WBL-mancy in D&D.

Never mind, with the above idea you could literally just use intro college econ, which still won't give you a good idea of how the market looks like in D&D.

[Phelix-Mu]

What you're trying to determine is an economic theory of value specialized to D&D. You could look at Debreu's analysis of equilibrium markets for ideas, but when you tack on the weirdness of D&D's mechanics, the math, while technically doable, may as well be your PhD thesis.

The metric you're looking for is way too insane. Even cutting down on its accuracy and bastardizing it for usability would require a high level of undergraduate mathematics.

I recommend you play it fast and loose, with your intuition. Alternatively, see if you can find econ rules in other tabletop games. Maybe you can get an idea of how D&D econ should behave without having to number crunch.

EDIT

Actually, I have another idea. Mount&Blade has a pretty robust economic system of supply/demand for medieval time periods. It won't cover everything that's possible in D&D, but it is 5000x more usable than any theory that covers WBL-mancy in D&D.

Never mind, with the above idea you could literally just use intro college econ, which still won't give you a good idea of how the market looks like in D&D.

I'm looking at something more like:

#1: Establish a liquid assets amount in a community and the surrounding lands (since some of the people buying will be looking to resell in surrounding communities). Not hard, basing it off of the gp caps for communities in the DMG.

#2: Examine material/item/commodity to be sold. Quality, rarity, ease of acquisition, and default listed price are all considerations here, and it will largely be an artistic process, not a scientific one.

#3: Determine % of liquid assets that buyers in the community will pony up for #2.

#4: Factor in variables like bartering skills, magic to make selling more effective (or less effective), local bribes and taxes due, etc.

#5: Determine a ballpark rate at which the selling of the commodity in bulk depreciates. I'm thinking it's like -20% of determined price for each 10% past the 50% mark of what the community will buy of that commodity. Until, at the end of the % of liquid assets, that commodity is effectively free in that community (or practically so).

So if the community has X gp to spend, I decide they have .2X to spend on salt. After accounting for factors, I decide that, since the salt was acquired in bulk through a fairly well-known spell, and since there is a tax on salt, the overall amount they will spend deteriorates to .15X. The pc uses Diplomacy to barter that up a bit, back to the .2X mark. After the party has sold .1X worth of salt, the price goes down in steps. To actually get to .2X, the pc has to sell a lot more salt than .2X worth of salt by the PHB listing (which is my goal).

Pretty sure I mucked something up, probably by using circular logic and percentages that mean the community will never actually end up spending %X on the salt, since it becomes cheaper and cheaper as %X is reached. But steps and rounding can maybe salvage it. I've been out of school for years, so cut me some slack, lol.

So, the math can be a bit complicated, but as DM I am free to round aggressively or not aggressively in either direction as befits the current state of WBL, expected future state of WBL, and immediate investment opportunities for a sudden pc slush fund.

[nothingforyou]

This commodity exchange is already annoying to do, but if you must, here's how to do it using some micreconomics.

Design a utility function U(x,y) with y being outlays on all goods and x being quantity of the good being analyzed. I recommend U(x,y)=(y)/(x-k), domain restricted to x>k, with k being a number which, the larger it gets, the more salt the community is willing to buy before they get overloaded with it. Let p be the variable price of good x. Then find p in terms of (x,y) where (∂U/∂x)/(∂U/∂y)=(-p), which is where an optimal rational decision maker would buy good x. Your new function p(x,y) will tell you what price they will pay for possessing x salt if their total other assets equals y.

For the recommended utility function, here's what we get:

(∂U/∂x)/(∂U/∂y)=((-y)/(x-k)^2)/(1/(x-k))=(-y)/(x-k)=-p

Then p=y/(x-k). Let's measure x in kilograms. That means, after the k+1 kilogram of salt, the village values each kilogram of salt less than each additional gold coin. y is their total other assets, where y+xp=N with N being net worth. Obviously they'd be willing to pay more for salt if their net worth was higher.

[Phelix-Mu]

That seems a sound approach, but, for my purposes, I'd like to be able to point to my math and have a vague expectation of comprehension among the more mathematically competent of my players. I like your maths, but none of my players would even vaguely understand them (sadly). Transparency is generally a virtue in these kind of games, to a degree, and I wouldn't want more wool than necessary for the purposes of obfuscation.

[nothingforyou]

The math I demonstrated here utilizes the minimum information needed, that is:

1) How much salt costs.
2) How much villagers make.
3) How much do villagers value each unit of salt.

You can obtain supply and demand curves from the above. Your demand curve is

p=(N-xp)/(x-k), with p being price, N being total income, x being salt, and k being some constant.

[Phelix-Mu]

The math I demonstrated here utilizes the minimum information needed, that is:

1) How much salt costs.
2) How much villagers make.
3) How much do villagers value each unit of salt.

You can obtain supply and demand curves from the above. Your demand curve is

p=(N-xp)/(x-k), with p being price, N being total income, x being salt, and k being some constant.

Like I said, seems sound:

#1: That's pretty much what varies here, or at least what we are seeking.

#2: This is generally used for community size, and since I am looking at a snapshot in time (the time the deal is being made), current income levels aren't as relevant as cash-on-hand. But maybe I am wrong. I am generalizing from character v merchant to character v community as a simplification; it should be scalable down to a merchant level without a huge issue in validity.

#3: There is a ceiling on this third value, as I don't want exceptionally rare stuff being sold for more than listed prices without specific exception due to role play. The rogue can Bluff someone in the thorpe to buying magic beans for all their wealth, but I don't want that being an option by default. So list prices are effective maximums. This is why I just said the first 50% is all at listed price, taking the first half of the curve and averaging it out for the sake of simplicity.

Not sure how this effects your maths, but I can pretty much see a graph in my head that seems to suit my purposes. Hoping it matches up vaguely with what your work produces (I think it does, but, lol, really, really rusty).

Anyway, thanks for the help.

[nothingforyou]

1) The price is determined by the equation, so nothing is affected.
2) N should not be total income, that's a mistake on my part. N is net worth. Think of it as budget or money in pocket.
3) It should be easy to just cap the price whenever the calculated price exceeds ceiling.

Here's the formal equation I think you should run with:

p=N/(2Ax-k)

Where p is the price per unit of salt, N is the budget, and x is the quantity of salt being bought. The smaller the variable A is, the less sharply the quantity of salt being bought affects the price that is willing to be paid. The larger the value of k is, the more salt is willing to be bought before the community gets tired of salt.

[Phelix-Mu]

1) The price is determined by the equation, so nothing is affected.
2) N should not be total income, that's a mistake on my part. N is net worth. Think of it as budget or money in pocket.
3) It should be easy to just cap the price whenever the calculated price exceeds ceiling.

Here's the formal equation I think you should run with:

p=N/(2Ax-k)

Where p is the price per unit of salt, N is the budget, and x is the quantity of salt being bought. The smaller the variable A is, the less sharply the quantity of salt being bought affects the price that is willing to be paid. The larger the value of k is, the more salt is willing to be bought before the community gets tired of salt.

Now that is something at least the smarter players will get, so they know that I'm not just blowing math-smoke at them when I claim the math works.

[Kornaki]

So if the community has X gp to spend, I decide they have .2X to spend on salt. After accounting for factors, I decide that, since the salt was acquired in bulk through a fairly well-known spell, and since there is a tax on salt, the overall amount they will spend deteriorates to .15X. The pc uses Diplomacy to barter that up a bit, back to the .2X mark. After the party has sold .1X worth of salt, the price goes down in steps. To actually get to .2X, the pc has to sell a lot more salt than .2X worth of salt by the PHB listing (which is my goal).

Pretty sure I mucked something up, probably by using circular logic and percentages that mean the community will never actually end up spending %X on the salt, since it becomes cheaper and cheaper as %X is reached. But steps and rounding can maybe salvage it. I've been out of school for years, so cut me some slack, lol.

So, the math can be a bit complicated, but as DM I am free to round aggressively or not aggressively in either direction as befits the current state of WBL, expected future state of WBL, and immediate investment opportunities for a sudden pc slush fund.

If your goal is to actually come up with a dynamic price for salt, this sounds reasonable. If your goal is to make it so that as the PCs keep pumping out more salt, they get less and less money for it, there's an easier way to do it. Instead of the community being willing to buy .2X worth of salt, they buy .1X worth of salt. After they buy that much, they're done. Kapeesh. The PCs move on to the next community, which is only willing to buy .05X worth of salt, because the community just over sold them a bunch already.

[Phelix-Mu]

If your goal is to actually come up with a dynamic price for salt, this sounds reasonable. If your goal is to make it so that as the PCs keep pumping out more salt, they get less and less money for it, there's an easier way to do it. Instead of the community being willing to buy .2X worth of salt, they buy .1X worth of salt. After they buy that much, they're done. Kapeesh. The PCs move on to the next community, which is only willing to buy .05X worth of salt, because the community just over sold them a bunch already.

Also plausible.

I really am mainly interested in all of this because I KNOW that one of my players has a head for this kind of minutiae. He once had a changeling Spymaster kickstart his own drug cartel, starting on a streetcorner, recruiting wizards to cast extract drug, and pushing out the existing crime lords. Eventually he teamed up with some vampires to subjugate several cities. At least until he realized that the vampires were eating his drug-addled clientele. Very Breaking Bad, though I don't think that player was even aware of that show. Just an extremely avaricious changeling out to make money.

I used some pretty sophisticated stuff to determine addiction and attrition rates among his clientele, as well as the rate at which his earnings accrued. The player ate it up. All in all, I was likely much too generous; while drug addiction stands to be hugely profitable, it can really only thrive in the long term in wealthy societies, where there are standing assets to liquidate for drugs. Most D&D city-dwellers would be tapped out pretty quickly, and thus the money-tree wouldn't grow quite so tall without moving on to greener pastures.

[Aharon]

This commodity exchange is already annoying to do, but if you must, here's how to do it using some micreconomics.

Design a utility function U(x,y) with y being outlays on all goods and x being quantity of the good being analyzed. I recommend U(x,y)=(y)/(x-k), domain restricted to x>k, with k being a number which, the larger it gets, the more salt the community is willing to buy before they get overloaded with it. Let p be the variable price of good x. Then find p in terms of (x,y) where (∂U/∂x)/(∂U/∂y)=(-p), which is where an optimal rational decision maker would buy good x. Your new function p(x,y) will tell you what price they will pay for possessing x salt if their total other assets equals y.

For the recommended utility function, here's what we get:

(∂U/∂x)/(∂U/∂y)=((-y)/(x-k)^2)/(1/(x-k))=(-y)/(x-k)=-p

Then p=y/(x-k). Let's measure x in kilograms. That means, after the k+1 kilogram of salt, the village values each kilogram of salt less than each additional gold coin. y is their total other assets, where y+xp=N with N being net worth. Obviously they'd be willing to pay more for salt if their net worth was higher.

Now with pretty graphs, please :smalltongue:

(Just kidding. Thanks for this post, it's nice getting refreshers of stuff from time to time - but I didn't expect it here at all...)

[Phelix-Mu]

Now with pretty graphs, please :smalltongue:

(Just kidding. Thanks for this post, it's nice getting refreshers of stuff from time to time - but I didn't expect it here at all...)

The Playground is your local resource for unusual information in unexpected places.

Parenting practices and magical childrearing? Check.

Advanced statistics? Check.

Planar lore that will make your mind boggle? Check.

The "What If?" of the week? Check.

Oh, and an unlimited amount of monk and kender hatred.:smalltongue: