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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.

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.

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.

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.

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.