# Trickle down Alchemy Economics

### Skills, Feats, Equipment & Spells

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So I have been thinking a lot about alchemy. So I wanted to look at the math behind it and pondering. First some ideas then we'll get into the math.

• First my math takes into account the base crafting rules and I'm using the basics of what I assume is economic theory material + labor + markup = Total cost of item. Now the current crafting rules in the playtest assume no value in labor costs which I felt needed to be added.

• Second I just wanted to start this conversation looking at the multi-levels items because they all follow the same pattern.
levels| Dice #| Cost in SP
1 | 1 | 30
4 | 2 | 12
8 | 3 | 60
12 | 4 | 250
16 | 5 | 1,200
20 | 6 | 9,000

• Third I assumed that cost for labor is the same as a skilled hireling of 5 sp for a days worth of work.

Changes
Okay so first this I proposed to trade was the amount of time each thing cost. It seems that it was weird that everything only took 4 days no matter how complex. So I changed it to level of item = days of crafting.

I just went with a basic 20% markup and material cost of 1/2 the final cost.

Maths
Level Mark-up Material Cost Cost of labor per. day
1 6sp 15sp 9sp
4 9sp 60sp 12.75sp
8 120sp 300sp 22.5sp
12 500sp 1,250sp 62.5sp
16 2,400sp 6,000sp 237.5sp
20 18,000sp 45,000sp 1,350sp

As far as I can tell there is not pattern or equation behind the cost of material and how much a specific level alchemist would charge for his work.

Thoughts
So we are presented with two different creation/item methods, magic and alchemy.

Now the only real cost for magic seems to be time. By this I mean if you have 4 first lvl spell slots and you use one then it basically cost you 1/4 a day or 6 hours. So the cost of casting these are the amount you can use in a day.

So with magic items costing time then I would suggest that alchemy cost should come from material. Plus there should be some value in the days it takes to craft. Because as it stands I don't see any value in "wasting" a feat for it unless you play as an alchemist. But by decreasing the cost of creating an item through labor time then their is a reason to use it.

Also why is the difference from 16th level to 20th so much larger than any other step? Even following a exponential curve it doesn't work.

If someone knows the math equation to calculate value of items I'd love to look into it and mess around with it.

Sadly, the [table] function of BBCode was not implemented in this forum, so tabular data is hard to read.

In logalog's first table, headed "levels| Dice #| Cost in SP", at first I did not understand what "Dice #" meant. As far as I can tell, only one d20 roll, a Crafting check, is involved in alchemical crafting. However, I checked the New Alchemical Items in Rules Update 1.6 and I see that Acid Flask, Alchemist's Fire, Bottled Lightning, Liquid Ice, and Thunderstone were rewritten to use increasing dice that followed that progression.

We can fill in the price gaps in that table by looking at the Treasure Tables on pages 349-353. I performed a similar examination before in comment #10 of Turkeycubes' thread Magic and Economics: Please pick either supply or demand. There I examined the prices of permanent magic items in order to reveal the hidden Wealth by Level table for Pathfinder 2nd Edition.

Maximum Price among alchemical items: Elixir, Oil, Poison, Potion
1st level: 3 gp (4 gp)
2nd level: 5 gp (6 gp)
3rd level: 8 gp (9 gp)
4th level: 12 gp (13 gp)
5th level: 20 gp (19 gp)
6th level: 30 gp (28 gp)
7th level: 45 gp (41 gp)
8th level: 60 gp (60 gp)
9th level: 90 gp (89 gp)
10th level: 125 gp (130 gp)
11th level: 175 gp (191 gp)
12th level: 250 gp (280 gp)
13th level: 400 gp (411 gp)
14th level: 600 gp (603 gp)
15th level: 800 gp (885 gp)
16th level: 1,200 gp (1,300 gp)
17th level: 2,000 gp (1,908 gp)
18th level: 3,000 gp (2,800 gp)
19th level: 5,000 gp (4,110 gp)
20th level: 9,000 gp (6,032 gp)

The first gold-piece value is the price from the Treasure Tables. The second gold-piece value, which is in parentheses, is the curve (2.8×1.4678^n) gp, p, where 1.4678 stands for the sixth root of 10. That is the mathematical curve that best fits the data.

logalog wrote:
Also why is the difference from 16th level to 20th so much larger than any other step? Even following a exponential curve it doesn't work.

The exponential curve mostly works, but the Paizo developers added some heavy inflation at 19th and 20th levels. The constant on my exponential curve drops from 2.8 to 2.7 if I leave those two entries off. 1st 4 gp, 2nd 6 gp, 3rd 9 gp, 4th 13 gp, 5th 18 gp, 6th 27 gp, 7th 40 gp, 8th 58 gp, 9th 85 gp, 10th 125 gp, 11th 184 gp, 12th 270 gp, 13th 396 gp, 14th 582 gp, 15th 854 gp, 16th 1253 gp, 17th 1839 gp, 18th 2700 gp, 19th 3963 gp, 20th 5817 gp, so with proper rounding 19th level alchemical items would cost 4,000 gp and 20th level alchemical items would cost 6,000 gp.

I had found a similar curve for Wealth by Level, (58×1.4678^n) gp. Since 2.8/58 = 0.048, each alchemical item of the same level as the character costs 4.8% of the character's wealth. Consumables are expensive.

logalog wrote:
Now the only real cost for magic seems to be time. ...

A character could create alchemical items at half price by using lots of time. We need to use TABLE 4–3: Crafting Progress per Day on page 148. I despise that table and its sister table, TABLE 4–4: Skill Income, because on its explicit and unexplained emphasis on level at the expense of proficieny. <begin rant> I mean look at 3rd level, where a character can increase Crafting proficiency from trained to expert. Zero increase in income, except for the character failing rolls less often. That is not what "expert" means! The same thing happens with 7th level with master proficiency and 15th level with legendary proficiency. The table is an insult to the proficiency ranks. Plus, 1st-level characters are all impoverished by those tables, which means aside from peasants in hovels and beggars on the street, townsfolk are 2nd level or higher.<end rant>

A 4th-level expert crafter making four 4th-level 12 gp alchemical items (to take advantage of the batch rules on page 148) spends 240 sp for materials and 4 days of time and then rolls a success, which means that he makes 6 sp of progress each day on the remaining 240 sp of item cost. That means 40 more days. Then he has spent 44 days and 240 sp to create 480 sp of alchemical items. Since a skilled hireling costs 5 sp a day, an expert hireling would cost around 10 sp a day, so hiring an expert crafter to make alchemical items would cost 440 sp in order to save 240 sp. A 4th-level trained crafter would make only 5 sp of progress a day, which breaks even except for the first 4 days, but I suspect that the skilled hireling that a PC can hire is probably less then 4th level and could not make 4th-level alchemical items.

I have been thinking about the crafting rules as written in the Playtest Rulebook and its updates and trying to analyze its patterns.

The numbers in TABLE 4-3: Crafting Progress per Day govern how quickly a character can craft. The Trained column has 21 entries from 1st level to 21st level: 1, 2, 4, 5, 9, 12, 16, 20, 25, 30, 35, 40, 50, 75, 100, 125, 150, 200, 300, 375, 450. Let me figure out the pattern.

First, I look at the ratios between adjacent entries. 2/1 = 2, 4/2 = 2, 5/4 = 1.25, etc. The full list of 19 rations is: 2, 2, 1.25, 1.8, 1.33, 1.33, 1.25, 1.25, 1.2, 1.17, 1.14, 1.25, 1.5, 1.33, 1.25, 1.2, 1.33, 1.5, 1.25, 1.2.

If crafting progress sequence were linear, quadratic, or geometric, the ratio sequence would be decreasing or constant. We should expect some noise from rounding; for example, the Experience Point Awards based on CR goes 400, 600, 800, 1200, 1600, 2400, etc., which alternatves the two rations 1.5 and 1.33. But the ratios of the crafting progress numbers range from 1.14 to 2. That is not rounding, that is disdain for consistency.

Nevertheless, I can clean up the data a bit (I used to do statistics for data science) and find the curve under the noise. Going from 1 to 450 in 20 steps in an exponential curve would give a consistent ratio of 1.357. However, the first two ratios are unusually large, so let's remove them from the data. Then we go from 4 to 450 in 18 steps. That is a consistent ratio of 1.300.

To figure out a good constant for this exponential curve, we look at the values of the constant that each individual entry suggests. 4/1.3^3 = 1.82, 5/1.3^4 = 1.75, 9/1.3^5 = 2.42, 12/1.3^6 = 2.49, etc. The average is 2.02, so let's use 2 as the constant.
Level: Original (Curve)
1st level: 1 (2.6)
2nd level: 2 (3.4)
3rd level: 4 (4.4)
4th level: 5 (5.7)
5th level: 9 (7.4)
6th level: 12 (9.6)
7th level: 16 (12.5)
8th level: 20 (16)
9th level: 25 (21)
10th level: 30 (27)
11th level: 35 (36)
12th level: 40 (47)
13th level: 50 (61)
14th level: 75 (79)
15th level: 100 (102)
16th level: 125 (133)
17th level: 150 (173)
18th level: 200 (225)
19th level: 300 (292)
20th level: 375 (380)
21st level: 450 (494)

But the big question is if prices go up 46.78% per level, then why does productivity go up 30% per level? The crafter will get slower and slower at crafting level-appropriate items. Did the developers assume that the crafter will jump up to a higher proficiency rank before that makes a difference? That isn't enough because the highest consistent rate of increase among the other columns is only 38%.

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Logalog has not yet responded to my math, so let me wrap up my comments with one more comment. In my last Pathfinder campaign, the Iron Gods adventure path, my players played characters highly interested in crafting. The Pathfinder 1st Edition crafting rules were not up to the task. I switched to Making Craft Work by Spes Magna Games, also available at www.d20pfsrd.com under Alternative Craft Rules [3PP].

I suspect I will be using houserules for Pathfinder 2nd Edition crafting, too, due to my dislike of Table 4-3.

Making Craft Work has an introduction that gives 3 examples of where the Pathfinder 1st Edition crafting rules are unrealistic.

Spes Magna Games wrote:

#1 Erlic wants to Craft a one-pound silver ball. His brother Rynook wants to Craft a one-pound gold ball. A one-pound ball of silver is worth onetenth as much as a pound of gold. Even though Erlic and Rynook work on pretty much the same project — melting metal and pouring it into a mold — Rynook must spend much longer on his one-pound ball simply because it’s made of gold.

#2 Erlic next wants to Craft some full plate. Full plate costs 15,000 silver pieces and faces an armorsmithing DC of 19. Erlic has Craft (armorsmithing) +8. Let’s be unrealistic and say that he rolls a 20 for each and every Craft check. 28 times 19 equals 532, which means it’ll take Erlic 28 weeks to finish his full plate. So much for having time to adventure.

#3 Erlic and Rynook want to see who can craft an item first. Erlic decides to make a high-quality box (value 20 silver pieces, Craft DC 15).

Rynook wants to make a crowbar (value 20 silver pieces, Craft DC 10).

The brothers have only a +1 bonus for their checks as they are both untrained when making these particular items. Again, let’s assume they both roll nothing but 20s. Here are the contest’s results:

* Erlic: 21 times 15 equals 315, which is 15.75 times higher than the box’s cost.

* Rynook: 21 times 10 equals 210, which is 10.5 times higher than the crowbar’s cost.

The Winner: Erlic, despite the fact he is making the more complicated item.

The 1st example still applies to Pathfinder 2nd Edition. The 2nd example is partly mitigated by higher-level crafters working faster. The 3rd example no longer applies: 2nd Edition fixed that.

We could create a 4th example for 2nd Edition where Erlic wants to make a paperclip from a piece of wire and requires 4 days to do so.

Going back to the OP, and taking the most general aspect of it.

Technically, the new crafting rules basically work from the premise that materials is generally half of the price of the item, and Labor costs is the other half. They don't really leave a space for markup (other than in theory, markup could be viewed as the 'labor' of the middleman potentially involved in the transfer of the item from crafter to customer)

P.S. Mathmuse, I am glad to see your analysis of the numbers, I don't have time to really digest it, but look forward to making the time. I was wondering how the table was designed to progress, as I wasn't seeing exactly what method they were using. Quickly looking at your report, that's because there wasn't a clear method. :) Makes me feel better.

Honestly, as far as the OP suggested, of 1/2 for material, and 20% markup, leaves 30% for labor. Honestly, looking at that it is not a little unlike some thoughts I'd had. I contemplated having if a crafter paid 1/2 in materials, and worked the rest, I was entertaining the idea of letting them complete it at the 90% or 95% mark, basically giving them a small discount to items they created themselves. (at present, technically, crafters really don't get any discount to creating items they make themselves, they can just create exactly what they want, rather than buying what is available) This sort of completion discount, would thus require them to use their time to get the discount. It would also be far less than the prior discount in 1st edition which turned magic, trap, or gunsmith crafting into a rapid capital multiplier if you fudged on the general rule of selling things at half price.

Giving only a marginal discount, and requiring them to commit enough time to basically earn most of the remaining cost of the item, I think that would act a decent limiter on the impact of the discount. You could then treat that as your markup component.

I would however you make the markup range more like 10% or 5%, leaving labor as 40%-45%. At 20% being markup, that is close to the remaining amount allocated for labor cost, so there seems less of a time limiter to the 'capital conversion' potential of the crafting, opening up more of the risk of the 1st edition issue.

I think the answer to why is 'productivity' slower than cost of items, is that while a bike is level 1, a car level 4, a jet level 10, and space shuttle level 18. They aren't expecting a level 18 engineer to be able to make a space shuttle in the time it takes an early engineer to make a bike. Granted, that may be a little extreme, as there is sort of a scope/size of items, that higher level items may often have increased scope size, which could help insure that component, without eliminating the potential of a level 18 bike, that is powered via broadcast power, rather than onboard battery and can go rather fast as long as it is within a mile of a broadcast station. And having that 18th level engineer be able to put it together about as quickly as a 1st level engineer puts together a basic bike. But I think that general assumption of higher level means higher scope too, is part of that design. [because they can make a lower level item faster, so if faster is the important part, make a lower level item?]

In Response
So after thinking and looking at the data we are working with I realized that the main problem is that while price is on an exponential curve the power of the item is on a linear growth. Which would explain why players reach a limit on the level of item they use.

Back to the Principles
Okay so I wanted to start out with trying to define the difference between alchemy and magic. Because we know that they are different because alchemical items work when magic items do not (non-magic field). So I put forth a few basic principles to look and think about.

• If we relate things to real world-ish an item has two general qualities energy(electric charge) and mass (basic compounds/elements).
• So that would seem to relate to magic relating to energy and alchemy relating to mass. Which seems to follow lore. With magic being the controlling of "arcane" energies. As well as alchemy being the founder of modern day chemistry.
• Now relating this to our crafts I venture that potions and scrolls are about a basic material that can hold different magical energy. Which would mean we could relate it to a battery.
• Looking into books about the concepts of alchemy it was about refining or purifying essence of an item as well as combining two things to add or remove essence.
• So if we accept these two concepts for this world or just in general then the limiting factors are: a persons individual ability to contain arcane energy(why we have spell slots would be that an individual can only hold so much energy which refills while sleeping), alchemy's limit would be the purity of material or refinement time.

Sorry working on a long post I'll break it up post then and start working on the next one.

• Concerns
So having identified the fact that elixir and potion use different things to activate and empower them so lets look at similar elixir and potions. Healing potions and life elixir. This comparison shows how much more power magic has over alchemy.

Healing Potion--Life Elixir
Cost______________Healing amount
3g--3g____________1d8--1d6
8g--12g___________2d8+4--2d6
20g--?g___________3d8+8--??
60g--60g__________5d8+12--3d6
250g--250g________7d8+20--4d6
1,200g--1,200g____9d8+30--5d6

So it seems that the only reason you would want to be an alchemist is maybe a little generality or flavor but a wizard focusing on potions and scrolls would be a lot more powerful. I believe I have a few ideas of alternatives that would improve the alchemist which I'll post in a bit when I have more time to explain it fully.

I agree, that the second edition way is clearly an improvement on #3.

I think that #2 also improves in second edition. You basically can make progress on an item based on your level, with additional boosts when you have increased ranks in crafting.

#1, I'll agree would seem like it fails in this 2nd edition method as far as timeframe goes; at least 'sort-of'.

In one sense, casting silver in a ball is a trade good, and it is staying as silver which is a trade good, and so is really still just a trade good, and most notably, of the same value. The gold ball... exact same thing, it is a trade good, staying a trade good, just changing shape, and keeping the same value.

Actually, technically speaking, it takes the exact same amount of time for both. Because you start with X value of precious metal, and Y value of the second precious metal. To make the Silver ball, if you rule it is a level 1 item, made by a level 1 crafter, it takes them 4 days. And they pay 100% of the material cost. [because they are just casting the material in to the shape] The case of the gold ball, is the same, it takes them 4 days, they pay 100% of the raw materials of the gold, and they are done.

The reality of the situation is that you haven't changed the value of the trade good, so really making the ball isn't a craft an item check in the traditional sense. It might be a craft check to modify the trade good in a way without losing value. So I'd rule if it needed to be done, it would take some arbitrary amount of time, require tools, and on a failure or critical failure they risk loosing some of the metal value.

So I would argue, the 2nd edition is better than the 1st edition alternative version, due to its capital multiplication issue.

Right now, 2nd edition only has a 'batch' option to create a batch of smaller consumable items. This shows the potential issue with your paperclip issue. Some option to be able to create something of small value in less time than a whole downtime, since it's that simple to make. Actually, in the alternate rule, even there creating a paperclip still took 4 hours? Am I correct?

I'd ask/wonder/suggest, if you calculate you can create 2sp in 'progress' each day crafting, and the item you are crafting has a value of 1cp. (the paperclip) I'd be perfectly fine with you paying 1/2cp for the materials cost and producing the paperclip in a fraction of the day. [maybe I rule it is a batch type item, and so you have to use the time to minimum time to make 4 paperclips, or 1/5 of 8 hours, or we'll just say a round 2 hours for a batch. and you can thus make up to 4 professional paperclips in that time paying 1/2 cp per paperclip made in terms of materials.

So technically, I think we are better off with 2nd edition's rules as a base, but potentially, instead of the rule about base time, making the minimum days rule only apply to items if you are going to try use extra materials to shorten the time. Otherwise, have the progress always depend on your level and rank per day based on your craft roll.

I also contemplate the idea of the a crit on the craft roll, instead of boosting you up a level, instead have it boost you up a Rank. That would however, would require expanding out the table to make rank improvements values start earlier. Without redoing the table, we can stick with the boosting level however, I'd honestly contemplate boosting the level progress by more than one level as a potential alternative.

For instance, half-plate is 175sp and would take a 1st level crafter 175 days to make (or 88 days on a critical). Of course a 3rd level crafter make it in 44 days, or 35 days on a critical. (I dislike that a 3rd level Expert crafter can't make it faster than a 3rd level Trained caster, this seems wrong, admittedly, but lets keep going anyway)

So, I agree there is room for improvements on the 2nd edition system, but I still consider it a better then either of the 1st edition methods.

I also readily see some options that I think might be some potential optional rules would be having capital type items (masterwork forge) that depending on specifics might boost a crafter's progress by a specific amount a day (bonus potentially maxed by the person's own production). Such that that perhaps a fist level crafter, with a full masterwork metal forge would get an item bonus on their craft roll, but also would get a bonus to their daily production, instead of getting 1sp per day, they would double it to 2sp per day. Perhaps on critical the 2sp would be boosted to 4sp per day. (perhaps the forge might be +5sp/day max bonus = crafter's own progress. You could add additional specific options for capital improvements, such as an expensive 'adamantine forge' which require master in crafting and would specifically boost progress on adamantine items by a hefty amount, but would be pretty expensive investment. It would provide a bigger boost on Adamantine items specifically.

Such adamantine forge would increase the value of adamantine items a crafter could create, but they would still be limited by the supply of adamantine raw materials, and would either just be making things for themselves, or needing to find buyers that are interesting in commissioning them for specific items adamantine items, for instance.

I don't really know where you got those numbers from. Elixirs of life go 1d6 --> 3d6 --> 7d6 --> 10d6 --> 14d6, which still falls behind healing potions in terms of healing, but nowhere near as bad as only +1d6 per tier. Elixirs more potent than 'Lesser' also end the effects of toxins lower than their level.

Your correct I must read the wrong thing I have corrected the chart.

Healing Potion--Life Elixir
Cost______________Healing amount
3g--3g____________1d8--1d6
8g--12g___________2d8+4--3d6
20g--?g___________3d8+8--??
60g--60g__________5d8+12--7d6
250g--250g________7d8+20--10d6
1,200g--1,200g____9d8+30--14d6

So that makes me feel a little better about things.

logalog wrote:

Concerns

So having identified the fact that elixir and potion use different things to activate and empower them so lets look at similar elixir and potions. Healing potions and life elixir. This comparison shows how much more power magic has over alchemy.

Healing Potion--Life Elixir
Cost______________Healing amount
3g--3g____________1d8--1d6
8g--12g___________2d8+4--2d6
20g--?g___________3d8+8--??
60g--60g__________5d8+12--3d6
250g--250g________7d8+20--4d6
1,200g--1,200g____9d8+30--5d6

So it seems that the only reason you would want to be an alchemist is maybe a little generality or flavor but a wizard focusing on potions and scrolls would be a lot more powerful. I believe I have a few ideas of alternatives that would improve the alchemist which I'll post in a bit when I have more time to explain it fully.

Note that Elixirs also have rider effects of improving saving throws or relieving one from the effects of Toxins, for instance. They are by design, slightly different from one another, but not intended to necessarily have one be inherently completely better or worse than the other.

I'm not exactly sure at this point what your goal is however now. Yes, by definition, the cost goes up faster than the more linear growth of effect.

As an example, someone buys a car. It goes so fast, and hold some four people in it. If someone pays twice the price to get a masterwork car, it doesn't go twice the speed. It goes some 10% faster, maybe. Ok, maybe you buy the expert car for 10x the cost, it might actually go twice as fast, but ends up holding only two people.

The fact that a potion that does double the healing of the first potion, isn't completely unbelievable that it would cost three times or more than the original potion. The more powerful ones are a premium, and you pay for premium.

All that said, I"m still curious what your thoughts were. While I think economy actually improved in 2nd edition, I'm still very interested in seeing how it can improve. And alchemy, being a new thing is something I also think has potential as it has changed a lot in 2nd edition, and I"m looking forward to seeing what it actually will look like.

I'd love to see some concepts like capital and income potential could be better integrated into this, so that adding teams of employees and buildings can be readily and hopefully simply added into the rules to make adventurers who invest in something like that can reap some reasonable downtime rewards and growth in that area. [hopefully with means to help keep it from causing problems with adventure play]

logalog wrote:

In Response

So after thinking and looking at the data we are working with I realized that the main problem is that while price is on an exponential curve the power of the item is on a linear growth. Which would explain why players reach a limit on the level of item they use.

This is a classic problem in Pathfinder. In 1st Edition the price is on a quadratic curve and the power is on a linear curve, so the diminishing returns occurred there, too. The missing factor that made players willing to use the more expensive item was time. One double-strength item took half the time as two single-strength items, and in combat time was critical.

However, for healing after combat, time is no longer critical. Thus, the party would prefer to use two wands of Cure Light Wounds rather than one wand of Cure Moderate Wounds. The two wand were cheaper for the same amount of healing.

Paizo attempted to fix this by having wands use resonance. The resonance limit would mean that the party could use only one wand, and a 72-gp Wand of 2nd-level Heal was better than a 27-gp Wand of 1st-level Heal. Resonance did not survive the playtest.

Note that since hit points increase linearly with level, damage from spells would overwhelm hit points if allowed to increase faster than linearly. And healing spells increasing linearly are enough to keep up with the hit points.

On the other hand, having experience points increase exponentially leads to the most satisfying leveling up. And since the number of monsters of a fixed level would increase exponentially, too, to give that XP, the treasure from the monsters grows exponentially, too.

We simply have a mismatch between the two best curves for the game.

logalog wrote:

Back to the Principles

Okay so I wanted to start out with trying to define the difference between alchemy and magic. Because we know that they are different because alchemical items work when magic items do not (non-magic field). So I put forth a few basic principles to look and think about.
• If we relate things to real world-ish an item has two general qualities energy(electric charge) and mass (basic compounds/elements).
• So that would seem to relate to magic relating to energy and alchemy relating to mass. Which seems to follow lore. With magic being the controlling of "arcane" energies. As well as alchemy being the founder of modern day chemistry.
• Now relating this to our crafts I venture that potions and scrolls are about a basic material that can hold different magical energy. Which would mean we could relate it to a battery.
• Looking into books about the concepts of alchemy it was about refining or purifying essence of an item as well as combining two things to add or remove essence.
• So if we accept these two concepts for this world or just in general then the limiting factors are: a persons individual ability to contain arcane energy(why we have spell slots would be that an individual can only hold so much energy which refills while sleeping), alchemy's limit would be the purity of material or refinement time.
• When people talk of the science of magic in Pathfinder, I remember one of my favorite descriptions from the introduction to The Order of the Stick: Dungeon Crawlin' Fools by Rich Burlew:

Illustration: A smiling scientist in lab coat holding a flask of red liquid together with a serene spellcaster in robe holding a flask of green liquid.
Caption: This world of fantasy operates on three sets of principles. Not only does it obey the familiar laws of physics and the less-familiar-but-requiring-no-less-calculus laws of magic ...

Illustration: The scientist and spellcaster glaring angrily at an approaching gamer wearing a baseball cap and carrying dice bag and rulebook.
SCIENTIST: Great.
SPELLCASTER: There goes the neighborhood.
GAMER: WOOT!
Caption: ...but it also holds adherence to the most capricious form of universal order: the laws of GAMING!

The laws of physics and magic in Pathfinder are a thin veneer of plausibility over a gaming system. The developers of Pathfinder did come up with some basic principles of magic: the four branches of 2nd Edition magic are arcane, divine, occult, and primal. Those are based on deeper magical essences: Mental, Material, Vital, and Spiritual, with each branch assigned a pair of essences. Alchemy is not in any of the branches. It tends to be elemental: acid, cold, electricity, fire, and sonic.

But nothing can be deduced from the principles of magic. They are a style to create a detailed setting rather than a science.

Mathmuse wrote:

The laws of physics and magic in Pathfinder are a thin veneer of plausibility over a gaming system. The developers of Pathfinder did come up with some basic principles of magic: the four branches of 2nd Edition magic are arcane, divine, occult, and primal. Those are based on deeper magical essences: Mental, Material, Vital, and Spiritual, with each branch assigned a pair of essences. Alchemy is not in any of the branches. It tends to be elemental: acid, cold, electricity, fire, and sonic.

But nothing can be deduced from the principles of magic. They are a style to create a detailed setting rather than a science.

While I do agree that magic and game rules are not necessarily tight I still feel we can deduce some principles of magic for the setting. Like the fact that alchemy can work in a non-magic with no decrease in ability or quality means they work with/on two separate traits. I still feel that the RPG community or at the very least DND has put magic into the energy trait because of wording like arcane energy.

But lets get back to crafting economics.

Percentage chart
Alright so I was looking at DC chart and converted it into percentages.

All numbers are in ##% form.
P.= Proficiency modifiers so +1 at 3rd, 7th, and 15th lvl.
I.= Is the Proficiency modifier and a creature with intelligence 18

LVL_Easy_P._I._Medium_P._I._Hard_P.__I._Incredible_P._I._Ultimate_P._I.
_1__65__65__85___40__40__60__30__30__50____25_____25__45___15____15__35
_2__||__||__||___||__||__||__||__||__||____||_____||__||___||____||__||
_3__||__70__90___||__45__65__||__35__55____20_____||__||___||____20__40
_4__||__||__||___||__||__||__||__||__||____||_____||__||___||____||__||
_5__||__||__||___35__40__60__25__30__50____15_____20__40___10____15__35
_6__||__||__||___||__||__||__||__||__||____||_____||__||___05____10__30
_7__||__75__95___40__||__||__||__35__55____10_____||__||___||____||__||
_8__||__||__||___||__||__||__20__30__50____||_____||__||___||____05__25
_9__||__||__||___||__||__||__15__25__45____05_____15__35___||____||__20
_10_||__||__||___||__||__||__||__||__||____||_____10__30___||____||__15
_11_||__||__||___||__||__||__||__||__||____||_____||__||___||____||__||
_12_||__||__||___||__||__||__||__||__||____||_____||__||___||____||__||
_13_||__||__||___35__35__55__||__||__||____||_____05__25___||____||__10
_14_||__||__||___||__||__||__||__||__||____||_____||__||___||____||__05
_15_||__80__100__40__||__||__10__||__||____||_____||__||___||____||__||
_16_||__||__||___35__40__60__||__||__||____||_____||__||___||____||__||
_17_||__||__||___||__35__55__||__20__40____||_____||__||___||____||__||
_18_||__||__||___||__||__||__||__||__||____||_____||__20___||____||__||
_19_||__||__||___||__||__||__||__||__||____||_____||__||___||____||__||
_20_||__||__||___||__||__||__||__||__||____||_____||__||___||____||__||
_21_||__||__||___30__30__50__||__15__35____||_____||__15___||____||__||
_22_||__||__||___||__||__||__||__10__||____||_____||__10___||____||__||
_23_||__||__||___25__25__45__||__||__||____||_____||__05___||____||__||

Sorry for the wobble this was the best I could do.

Okay hopefully this should be correct I've checked it a few times but who knows. I'm tired so I'll let you all look over this but if my math is right you would need to be a lvl. 7 alchemist to make a comfortable living (with the rule of 2 sp a day living expenses), while making your 5 sp a day, and have a hireling to run your shop, while working every single day. If you are lvl. 3 you can live comfortable but you are making only 9.5 cp a day.

logalog wrote:
While I do agree that magic and game rules are not necessarily tight I still feel we can deduce some principles of magic for the setting. Like the fact that alchemy can work in a non-magic with no decrease in ability or quality means they work with/on two separate traits. I still feel that the RPG community or at the very least DND has put magic into the energy trait because of wording like arcane energy.

The modern concept of energy was developed in the early 18th century by French mathematican and physicist Émilie du Châtelet (full title, Gabrielle Émilie Le Tonnelier de Breteuil, Marquise du Châtelet). The word "energy" comes from the Latin word for activity, and was adopted in English to mean having the vigor for lots of activity, so it long predates the physics concept of energy.

logalog wrote:

But lets get back to crafting economics.

Percentage chart
Alright so I was looking at DC chart and converted it into percentages.

<chart skipped due to size, but I appreciate the good job in aligning the columns>

Okay hopefully this should be correct I've checked it a few times but who knows. I'm tired so I'll let you all look over this but if my math is right you would need to be a lvl. 7 alchemist to make a comfortable living (with the rule of 2 sp a day living expenses), while making your 5 sp a day, and have a hireling to run your shop, while working every single day. If you are lvl. 3 you can live comfortable but you are making only 9.5 cp a day.

Months ago I did the work of figuring out whether a commoner could live comfortably at low levels. I didn't save my work, so let me try again.

A 2nd-level alchemist with Int 18 wants to make a living selling alchemical elixirs at full price. THe Infused Reagents from Alchemist class features are not saleable, so he has to make his products with regular Alchemical Crafting. His trained Crafting proficiency is +6.

Minor Elixir of Life is a level-1 alchemical item and costs 30 sp. The rules don't give the DC for crafting it: for a level-1 item, the easy DC woul be 8, the medium DC would be 13, and the hard DC would be 15. I doubt that an item an alchemist sells routinely would have an incredible or ultimate DC. Let me use the medium DC 13.

Thus, his probabilities for the Crafting check would be 5% (nat 1) critical failure, 25% (2-6) failure, 50% (7-16) success, and 20% (17-20) critical success.

Failure takes 3 days and yields nothing.
Critical failure takes 3 days and loses 1.5 sp of ingredients.
Success means that after the initial 3 days, he takes 15/2 days to finish the elixir for a 15 sp profit.
Critical success means that after the initial 3 days, he takes 15/4 days to finish the elixir for a 15 sp profit.

The average time is (5%)(3 days) + (25%)(3 days) + (50%)(10.5 days) + (20%)(6.75 days) = 7.5 days.
The average profit is (5%)(-1.5 sp) + (25%)(0 sp) + (50%)(15 sp) + (20%)(15 sp) = 10.425 sp.
His average earnings per day is (10.425 sp)/(7.5 days) = 1.39 sp per day. And this is working 7 days per week in a rent-free workshop. (Golarion uses a 7-day week: Sunday, Moonday, Tollday, Wealday, Oathday, Fireday, and Starday. My wife once named a creepy halfling sorceress character Wealday Addams.)

Fortunately, the alchemist is hired at 5 sp per day by an adventuring party to make infused elixirs of life for them in the field. After nearly dying more times than he wants to remember, he reaches 3rd level and returns to his shop. His expert proficiency in crafting gives a +8 bonus. His probabilities for the Crafting check of minor elixir of life become 5% (nat 1) critical failure, 15% (2-4) failure, 50% (5-14) success, and 30% (15-20) critical success. The initial time for crafting the elixir shrinks to 2 days.

The average time is (5%)(2 days) + (15%)(2 days) + (50%)(5.75 days) + (30%)(4.5 days) = 4.625 days.
The average profit is (5%)(-1.5 sp) + (15%)(0 sp) + (50%)(15 sp) + (30%)(15 sp) = 11.925 sp.
His average earnings per day is (11.925 sp)/(4.625 days) = 2.58 sp per day. If he reduces his workweek to only 6 days per week, that reduces the average to (6/7)(2.58) = 2.21 sp per day. He can now live comfortably.

However, Int 18 is rare. A more typical NPC alchemist would have Int 16. Let me go over the 3rd-level numbers with that intelligence.
The average time is (5%)(2 days) + (20%)(2 days) + (50%)(5.75 days) + (25%)(4.5 days) = 4.5 days (shorter average time due to more frequent profitless restarts).
The average profit is (5%)(-1.5 sp) + (20%)(0 sp) + (50%)(15 sp) + (25%)(15 sp) = 11.175 sp.
His average earnings per day is (11.175 sp)/(4.5 days) = 2.48 sp per day. Working only 6 days a week would reduce that to a comfortable 2.13 sp per day.

Intelligence does not seem to make much difference.

No-one would hire this alchemist as an assistant because he would earn only half his 5 sp-per-day pay. Abandon the idea of a guildmaster alchemist able to earn extra money by hiring low-level alchemists.

Note that Crafters also have the choice of making a Practice a Trade action to earn income, as well as a specific crafting check.

As far as I can tell, it is equivalent to the crafting progress table, but includes a category for a minimal income if you failed your check.

When doing that form of check, you make it and that is your income from then on, as long as you succeeded. So the alchemist can make that income consistently, and doesn't have to 'reset' and spend X days preparing a specific other item to craft.

Another quick point to note. The crafting progress give you how much you can turn your time into a discount for making an item after the 50% default base raw materials cost. If someone just makes crafting, practice a trade rolls, they make the income, for that time, and can trade that income for the end product, without having actually needed to have raw materials for the item itself.

Note: this is one reason why I am at least a bit inclined to feel that you should be able to complete items in a shorter time than that if your daily progress would have it completed prior to that minimum time, at least if it is something you have made before. With this in mind, it becomes a minimum time if you are paying off the rest of it by spending more raw materials, to complete it instead of time. That way, you have a pretty simple idea of how much someone would make for a particular day. Namely look it up on the table, and that should be a rough estimate of a typical expected income for someone. Understanding there should be instances where something happens and they lose some income, or they accept a job that belongs at a lower level. (so first time you ever make paperclips might take you a while to get them the way you need them, but after that you can crank them out reasonably fast enough, based on what they are)

Granted, if dedicated crafting, naturally produces less income than a practice a trade roll, then you can argue there is a disconnect on how the rules work. In a way, if you have to pay X days of Zero income/progress each time you start a new project on a new object you've done before, I see that as problematic, considering I'm sure in the intended settings people aren't supposed to be little factories cranking batches of a single object constantly.

I'm willing to concede that perhaps ignoring that reset cost when changing what items you are making might 'require' the availability of a decent sized workshop to work in, and not just a traveling crafting toolkit. That means things might work sort of like as written for your average early adventurer. But one who invests in facility to do their crafting in might get a bonus, allowing them to better earn a living more consistently. (but of course have a potential recurring maintenance cost they would have deal with) This works out kind of well with it being the core rules, but opening up some chances for people who build a business having ways of bettering their income with more consistent resources being invested.

 Designer

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Mathmuse wrote:
I have been thinking about the crafting rules as written in the Playtest Rulebook and its updates and trying to analyze its patterns.

I don't think it's even mathematically possible to figure out the formula we used for item value / crafting, especially after the rounding (as you posited later), but even without the rounding, it's a piecewise-defined function on a logarithmic y axis, so one function won't cut it.

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Mark Seifter wrote:
Mathmuse wrote:
I have been thinking about the crafting rules as written in the Playtest Rulebook and its updates and trying to analyze its patterns.
I don't think it's even mathematically possible to figure out the formula we used for item value / crafting, especially after the rounding (as you posited later), but even without the rounding, it's a piecewise-defined function on a logarithmic y axis, so one function won't cut it.

I was able to figure out the offset exponential formula, (5000×1.3^n - 8000) gold pieces, for the wealth-by-level curve in Pathfinder 1st Edition, and that was far from obvious. The motto of an office where I once worked was, "The impossible we do immediately, the miraculous takes a little longer." I figured that in Pathfinder 2nd Edition some piecewise mechanics would have to take place at the levels where proficiency ranks shift gears from trained to expert to master to legendary. And some numbers might not be from a formula, and instead were selected as the numbers that worked best in playtesting.

I can deduce some patterns from not just the numbers, but also from the design principles. Dungeons & Dragons 3.5 used quadratic curves. Switching Pathfinder 1st Edition to exponential curves for levels and challenge ratings reflects genius-level awareness of meaningful challenge. Switching item costs to an exponential curve in Pathfinder 2nd Edition stabilizes the mathematics of buying items by level, because the levels are exponential. Crafting is tied to item cost, so exponential also works for crafting, too.

Also the Paizo designers cleverly matched crafting rates to the pay rates of the new Practice a Trade action. Pathfinder 1st Edition sometimes had a intra-party conflict about paying wizards for their magic item crafting for other PCs. The other PC would willingly pay the material cost, but people disagreed about the pay for the labor cost of the wizard's time and expertise. By giving the other PCs a matching way of earning money with their time via Practice a Trade, Pathfinder 2nd Edition makes the labor cost evident and should resolve those disagreements. That aspect is probably incorporated into the numbers, too.

I don't need my deductions to be perfect. My Iron Gods players routinely performed mundane crafting as part of their character concept as inventive tinkerers. The Pathfinder 1st Edition crafting system was unworkable for them, so I switched to the Making Craft Work system. They also become more involved in the day to day activities of regular townsfolk than most players, so such details matter even if their next character does not craft. Pathfinder 2nd Edition's crafting system is workable, so I might switch away from Making Craft Work to the crafting rules in Pathfinder 2nd Edition. I wish to analyze the playtest system well enough that I can quickly evaluate the final 2nd Edition system and judge whether to leave it unchanged or tweak it.

I think having there be a consistent 'increase in value' which is based on level and rank is a clear winner in the most basic sense. I may disagree with some details, such as the fact that someone with a rank increase, at the level where the increase becomes available, doesn't get a boost in productivity as a result of it until later levels. But the basic premise, as Mathmuse pointed out, created a problem defining the value of the magic crafter's time. Party members 'expecting' to pay only materials as that was the only viewed 'cost' as they ignored the crafter's time as a cost.

I hadn't really thought about that side of the equation of the problem. Instead I'd seen the difference in how much conventional crafting made things. (what was it 20-40gp per week progress, vs magical, gun, or trap crafting which made 1000gp crafting progress per day) And after that giant jump was made, suddenly people were asking why they couldn't sell their brand new items for full price at market, like the established merchants.

In this 2nd edition, there is a clear expectation of what the top likely income such a person will get, and it is base d on level and rank for the work they are doing. There is some GM expected modifiers or limiters, for instance, if you are a 12th level historian or lawyer by trade, and you are in a tiny poor fishing village. You might have trouble finding @level work there. The legendary fisher might be able to rake in awesome takes, but also might make the locals rather jealous. I see that most likely as being a sort of level cap on many incomes based on settlement size, which might explain in part why larger settlements would attract higher level 'heroes', 'villains' and other NPCs.

I assume that this income is probably somehow related to expected wealth by level, making a guess, but I haven't even looked at that to try to compare it. (I suspect Mathmuse, you would be able to look at it and likely see a relationship quickly) However, this stable sort of income level then also gives us a sort of standard we can hold up to potentially build up a concept of how much income an investment might be able to offer. You might be able to treat an investment as a sort of NPC that can earn an income either with your 'aide' or potentially even independently. It could be categorized by level, and if they investment hits a level higher than its 'owner' it might start hitting a natural ceiling, potentially limiting its income, unless a higher level npc administrator is engaged (who would likely take much if not all of the increased income it would earn).

I hadn't really noticed it, but I recently noticed that with expert diplomacy and Bargain Hunter, you can basically earn a discount on an expensive item you want to purchase equal to your practice a trade's daily check as long as it doesn't take the price of the item below half price. Again, this is adding the value of your time, by way of searching for a good deal.

I could see offering the reverse too, perhaps a skill feat perhaps in general sales (or maybe in a limited scope action for free for items via a particular relevant Lore skill). Taking an object you want to sell, and realizing you by default only get 1/2 price for it. Spend a day, and on a success you can add your daily earnings to the price you get for it as long as it doesn't take it past the normal 'list' price for the item. I.e. can't go over double the base half-price amount.

Thinking about it that seems pretty reasonable facsimile to established economics. A crafter makes stuff and has an inventory. On days when people come into the shop, they have the opportunity to sell at items. They are normally have a variety of options, having drawn people into their shop due to reputation and advertising, and have time set aside for their week to apply towards sales, thus generally getting a boost on their sale income with a sale roll, boosting their income via salesmanship in addition to craftmanship. Thus you would seldom be able to buy an item from a shop for half price, because they are always prepared to 'sale' you earning money on the sale. In fact, perhaps established shops have the ability to 'stack' sales-work such that when you came into town and were asking for a magic sword, everyone in town pointed you to the vendor who had it, due to the vendor having 'mixed' with the locals making sure that anyone looking for something they would have would be sent to them. Thus you paid full price for the sword, and the shop owner was very happy with the free ales they had purchased for a dozen people who frequently talk to strangers coming through town.

As such, if you have a magic sword, you want to sell, but you want to sell it for what you view it is worth. (or lets just say you want at least 75% price for it) Well, you start with 50%, and do practice a trade using your diplomacy, you can earn your daily amount based on your roll. It would determine how many days of searching for a buyer would take before they could be successful finding someone who would be willing to pay the given price. Note this would still probably be limited price wise to the limits defined for the settlement you are in at the time you are doing the searching.

I think another thing that might be worth noting is that perhaps not all things need to have the same 50% materials base cost that is the 'default'. Trade goods for instance are an item that effectively have 100% raw materials cost, and likewise return a pretty consistent raw value, allowing them to also generally get their full value for them in trade. Crafting on a raw material doesn't really probably increase its value much if any, just potentially, for instance changing its shape or block size.

I think things like armor and weapons and other typical craft items, the 50% rule seems pretty reasonable. However, I could see some things, perhaps including sculptures, paintings and some other items that I could imagine potentially having a different base material cost. If we changed the base material cost for those things to be significantly less (say 10% instead of 50%), leaving most of the cost being 'labor', it may also mean the base, 'quick sale' price of the given item might be based on the lower base price. Meaning, selling a painting that technically is worth 100gp, based on a 10gp materials cost, and 90gp of painting/crafting time, the base sale might be 10gp, rather than 50gp, but none the less having a potential value of 100gp. Paintings that are well known, by famous paintings, and/or known origin and demand, or course could be seen more like regular items or even trade goods depending on their known/accepted value. Again, this would be an optional rule that might allow the existing of some things of a more soft value, which if players and GM are interested in, would thus have the decision to offload the items right away, or try to find more interested buyers themselves and get more of their potential value out of them.

Anyway, that turned out longer than I'd expected. But it demonstrates how I think there is a lot more things we can do with the new method, which seems to offer a potentially more consistent economic model between crafting and general work. So I'm inclined to prefer starting with the new model, at least as the base.

What do you think Mathmuse? Can you see the potential in it that I see?

Loreguard wrote:
What do you think Mathmuse? Can you see the potential in it that I see?

Yes, I do.

Loreguard wrote:
I hadn't really thought about that side of the equation of the problem. Instead I'd seen the difference in how much conventional crafting made things. (what was it 20-40gp per week progress, vs magical, gun, or trap crafting which made 1000gp crafting progress per day) And after that giant jump was made, suddenly people were asking why they couldn't sell their brand new items for full price at market, like the established merchants.
Loreguard wrote:
I hadn't really noticed it, but I recently noticed that with expert diplomacy and Bargain Hunter, you can basically earn a discount on an expensive item you want to purchase equal to your practice a trade's daily check as long as it doesn't take the price of the item below half price. Again, this is adding the value of your time, by way of searching for a good deal.

Bargain Hunter is a bargain only in that it does not require a 4-day preparation period like Craft, Practice a Trade, and Stage a Performance require. Like those activities Bargain Hunter converts a PC's time (one day) into a standard wage (result from TABLE 4–4: SKILL INCOME on page 153). I think the 4-day period is designed to limit the use of the skill income. Bargain Hunter already has a natural limit set by the number of items the party wants to buy.

Loreguard wrote:
I could see offering the reverse too, perhaps a skill feat perhaps in general sales (or maybe in a limited scope action for free for items via a particular relevant Lore skill). Taking an object you want to sell, and realizing you by default only get 1/2 price for it. Spend a day, and on a success you can add your daily earnings to the price you get for it as long as it doesn't take it past the normal 'list' price for the item. I.e. can't go over double the base half-price amount.

We could easily extend the skill income to cases like trying to sell an item at closer to full price. A Peddle Goods activity could allow stopping at several markets during the day in order to add the skill income to the selling price, up to a maximum of its full price. A Run a Shop activity could allow Peddle Goods from a single shop so that the shopkeeper could routinely sell goods at full price at a rate determined by his or her skill income. And then Pathfinder 2nd Edition would have an explanation why merchants can sell their items at full price while adventurers can't.

The skill income does not fully explain the setting. For example, it cannot create low-level wealthy people with a steady high income, such as a 4th-level wealthy landowner earning money from renting land to peasants. If we add an additional rule about income from investments, based on the rules for creating a business from Ultimate Campaign, and another rule about long-distance trade, we would have most of the economy covered.

At the beginning of Forest of Spirits, 4th module of Jade Regent, I had the party earn money their caravan selling trade goods, because in The Hungry Storm, the prior module, they had set up and guarded a trade caravan traveling over the north polar ice cap. I made up the numbers on the spot based on what the party needed, because The Hungry Storm provided little cash and they needed to upgrade their gear. Having rules for income from trade would make such endeavors easier for other GMs.

These rules would not be worth putting in in the Core Rulebook, but Paizo could fit them into the 2nd Edition of Ultimate Campaign. My Iron Gods campaign tapped heavily from Ultimate Campaign, so I hope the 2nd Edition version comes out within just a few years.

Loreguard wrote:
However, this stable sort of income level then also gives us a sort of standard we can hold up to potentially build up a concept of how much income an investment might be able to offer. You might be able to treat an investment as a sort of NPC that can earn an income either with your 'aide' or potentially even independently. It could be categorized by level, and if they investment hits a level higher than its 'owner' it might start hitting a natural ceiling, potentially limiting its income, unless a higher level npc administrator is engaged (who would likely take much if not all of the increased income it would earn).

This is close to what is in Ultimate Campaign. In the Downtime chapter, it defines how a business is set up as a Building or Organization, constructed out of individual Rooms or Teams that are purchased or hired or created by the PC's own effots. A Manager runs the business while the PC is out of town, because adventurers are out of town most of the time.

In my Iron Gods campaign, three party members had the Local Ties campaign trait that linked them directly to the starting town Torch. They took to adventuring under false names (the evil Technic League frowned on their activities) and then returning home to Torch for relaxed downtime under their real names. Their character concept included crafting and an desire for progress, so they invested in Torch, too. They started several businesses in Torch: the Waterfall Workshop as a private workshop for themselves, B&B Alchemical Smelting which was a cover story for all the skymetals they sold which was really discovered while adventuring, and a nameless caravan as an way to enter the capital city Starfall was legitimate businessmen. They also purchased the local gambling hall and re-modeled its rooms into a dance and music hall. And they built a house for their friend Dinvaya Lanalei when she moved to Torch.

And I read Ultimate Campaign for my players and advised them on the options and how much time and money those options would cost. It was a lot easier than inventing the business rules myself and a lot more controlled than letting them set up the businesses without constraints.

However, the skill income has a little problem (and "little" is a pun). Let's look at 8th level. A master at his trade earns 30 sp a day. An 8th-level consumable costs 60 gp, 20 times as much. An 8th-level durable item costs 500 gp, 167 times as much. For example, crafting an 8th-level Elixir of Life takes 14 days and still costs 30 gp. Crafting a +2 weapon potency rune (a 400-gp part of a +2 weapon) takes 71 days and still costs 200 gp.

In contrast, an 8th-level wizard requires 8 days to enchant a masterword sword to +2 and would require 2 days to craft a Potion of Cure Critical Wounds if potions of 4th-level spells were allowed. That is about 1/8 the time.

Do players and GMs really want the party to take 8 times as much downtime in Pathfinder 2nd Edition as in Pathfinder 1st Edition?

Looking at a single level does not give a complete picture. Fortunately, I can compare the curves I created to check all levels. Consumables cost (2.8×1.4678^n) gp, where 1.4678 stands for the sixth root of 10. Durable items cost (22×1.4678^n) gp. Note that these are the curves for the highest-priced items. Some items cost only 75% of the maximum price for their level.

I haven't made the full curve for skill income. That curve needs to switch proficiency columns: from trained to expert at 3rd level, from expert to master at 7th level, and from master to legendary at 15th level.

The expert curve from 3rd to 7th level is 4 sp, 6 sp, 10 sp, 14 sp, 20 sp. If we pretend it is geometric with base 1.4678 (really, its base is 1.5), it becomes (0.135×1.4678^n) gp, which would be 4 sp, 6 sp, 9 sp, 13sp, 19 sp. For consumables, level-matched crafting would take 14 days. For durables, crafting would take 85 days.

The master curve from 7th level to 15th level has a true base of 1.43 and can be approximated by (0.116×1.4678^n) gp. For consumables, level-matched crafting would take 16 days. For durables, crafting would take 99 days.

Magical and alchemical crafting proceed at the same pace as mundane crafting. And the playtest lacked feats that would speed up crafting (the playtest did not test crafting, so maybe the feats exist and were left out).

With the longer crafting times, the non-crafting PCs will want to earn some downtime money while waiting. The Practice a Trade activity seems designed for that, but past 3rd level is gains a disparity. The crafter boosts his crafting income by advancing his proficiency to expert. But Practice a Trade relies on Lore skill, and characters have no reason to become expert in Lore. The disparity becomes worse after 7th level after the crafter becomes master in Crafting proficience. Only the bard, who will keep up his proficiency in Performance and can earn downtime income with Stage a Performance, will be able to keep up with the crafter.

Thus, when the 8th-level wizard finishes the 400-gp +2 weapon potency rune for the fighter, who paid 200 gp for materials in advance, and holds out his hand for the rest of the payment, the fighter will say, "Um, I earned only 133 gp while you were working. Can I make up the other 67 gp later?"

The trained skills via Rules Update 1.6 for fighter are Acrobatics or Athletics, so we can assume that the Fighter might make one of those expert. But I don't see wage-earning opportunities with that skill. The alchemist (Crafting) and bard (Occultism and Performance) can earn as much as the crafter. The barbarian (Athletics), cleric (Religion), druid (Nature), fighter (Acrobatics or Athletics), monk (Acrobatics or Athletics), paladin (Religion), ranger (Survival), rogue (Stealth or Thievery), sorcerer (varies), and Wizard (Arcana) might have to dig into their savings. In the setting, a ranger earning money by trapping furs and a rogue earning money by theft would seem plausible, but the rules don't allow it without roleplaying through all the details.

So yes, the new system, presuming you want to only pay 50% in materials, is going to be significantly slower than the old magical rate. However, I still feel like the new system allows normal crafting to progress much faster as your level goes up than the old system. In the new system, the crafter could complete that +2 item in 4 days, but it would chew up a good deal more material requirements.

I like your comparisons to get the price in time for a consumable, vs. for a durable item. This is really a pretty good thing to consider, in my opinion. Basically, sounds like by your calculation, a consumable takes ones earning for some two weeks worth, while a durable item takes some 3 months or a quarter of a year. Actually, this helps give the impression of how frequently a non-adventuring individual might conceivably expect they might use a consumable item for instance.

Whether 2 weeks/3 months is an appropriate specific amount of time to accrue wealth to get something like that is a different question however.

When I first read the downtime rules in Ultimate Campaign for P1, since I wanted to be able to build some buildings and hire some workers to work in them, but I have to admit I really ran into issues when I realized they didn't have any means of specifying the costs associating with paying your workers. They simplified things, by saying, we are only going to tell you your profit, we already took out their pay. Then they told you, if you hire them to serve you rather than the public, they don't make any profit. (however, there is still no pay you owe for them, since the pay was a hidden part of the profit calculation) Later I also kind of felt like it all added up to a really complicated way of getting an income +- 1gp and didn't do a good job of presenting expenses and such. I loved the idea, and really wanted it, but felt it din't deliver what I'd hoped. I also remember doing some calculations and realized that you made more income from having a little two person house, than a person was expected to pay for living expense for the same period. All those issues got me looking more to the Investments chapter as a more reasonable set of rules, despite my finding them less interesting and engaging. They at least felt more balanced, thought it had its own issues.

Sorry, anyway back to P2. I'd like to see some rules so we can have ways for characters to build up some investments and get some boosts to their incomes due to this potentially, but not cause game breaking issues in doing so.

But I see a few different ways that assets could produce additional income in P2.
1. by adjusting the income roll made by the character. There are a few sub-options:
a. Adjusting the die roll helping to improve their roll to turn failures into success or success into critical
b. Adjusting the income produced directly by some given amount when the conditions are met (like success at applicable income roll)
c. Adjusting the actual row/column used to determine your income.
2. alternately income from assets might be handled almost as if they are a form of NPC that gets to make an income roll,
a. either as simple as making its own practice a trade income roll for the business as if it is an NPC with a Rank and Level determined by some criteria.
b. as above but have some adjustment to the table to reflect size somehow (so that if the inn is considered a level 3 business of size 2 in expert shape/reputation, it gets income as level 3 expert, and multiply's it by two because of the defined 'size'.
c. have some completely separate sort of system/method for calculating income. Perhaps some percent of the 'investment value' producing a return on a successful business roll of some time, producing that amount on a success, more on a crit, half on a failure and none on a critical failure, or something like that.

Also, it is a somewhat reasonable question in P2 do you let a second level wealthy noble, control/utilize all their families wealth while they are second level. Or for game balance reasons do you allow the family wealth only provide an extra income in a factor more in line with a second level resource, even if it might qualify as large enough to be in its entirety something more like a 10th level resource?

Anyway, if we consider the practice a trade table, something close to a 'value added per day' table. And reduce the frequency of saying 4 days of zero value add (just catch up to paid resources) I think we get an income that might be a workable base to work from. We could also then offer some rules that allow having an actual workshop, or kitchen, or other facility allows you to somehow multiply or improve your income by a designated way.

I'd imagine such resources would have a significant cost, and would probably have some sort of maint cost to them. But people who have the capital to spare may find them a valuable way to boost income if they aren't raking in the money via other means. I can't help but think that the expectation should be that adventuring should produce significantly more when successful than conventional business investments.

Oh, as far as ranks in lore. Good enough point, although I believe the Additional Lore skill feat gets you another trained in Lore, and that skill automatically advances as you hit the various expected levels. So for 1 feat they could probably get a very viable business lore to practice, if that is what they want.