Assumptions:
1) Spend a day adventuring or crafting Magic Items
2) All start up costs are paid, adventurers and crafters have all necessary gear
3) A given caster has the skills/prerequisites to do either task
4) All Magical goods have an integer multiple of 1000 gp for their price, even those produced by very low level characters.
5) Characters can produce magic in any multiple of 1000 gp value. They can spend 1 day or 20 – and produce saleable items worth 1000 gp/day
6) Level transitions are ignored
7) Only encounters of matched level to the character occur, and there are 13 and 1/3 encounters per level
8) Expected treasure per encounter (3-3, DMG) and Wealth Comparisons (Pg. 54) are taken as given for the Dungeons and Dragons world
9) Character cares only about profit (their valuation of equipment and experience is assumed to be zero)
10) Character can sell their product at market price without expending a premium to find a buyer
A rational spell caster would then maximise their profit.
Revenues per day:
Crafting: 1000 gp, Magic Items take 1 day for every 1000 gp of Market Price.
Adventuring: EeTi-error, where Ee is the expected encounters per day, and Ti is the expected wealth gained per encounter at the character’s level i. Error denotes extra expenses such as spellcasting services, research, bribes etc. Using the wealth comparison chart on page 54 of the Dmg, we can compare expected wealth gain versus expected treasure gain. The expected wealth gain is adjusted for consumables and services, the error. Thus revenue is EeDi where Di is the expected wealth gain per encounter.
Costs per day:
Crafting: You create Magic Items for ½ Market Price in Materials. Magic Items have Market price of 1000gp/day. Therefore Cost/day = 500gp.
Adventuring: rEeDi. Because you face increasingly powerful monsters, adventuring requires a reinvestment in equipment. This is a fraction, r of your Adventuring revenue EeDi.
For a given level i.
Profit I = 1000dc + Ee*da*Di – 500dc – r*Ee*Di*da
Where dc is days used in crafting, and da is days used in adventuring.
Profit I = 500dc + (1-r)Ee*Di*da
Constraints:
Time: For annual profit, 30 days/month – 12 months per year – 360days per year.
dc+da = 360
Experience:
Experience earned adventuring ≥ Experience Spent Crafting.
Experience Adventuring:
Ee*Ei*da where Ei is the experience per encounter at level i.
Experience Crafting:
1000/25 (1/25th daily market price) = 40
= 40dc
Ee*Ei*da ≥ 40 dc.
If we rewrite the profit function to display dc as a function of da for a given profit P,
We get linear Isoquants:
dc = (Pi – (1-r)Ee*Di*da.
Higher Pi values shift the curve out, and since the character values higher profits, the character will gain the most benefit from the most outward shifted version of this curve subject to the constraints.
There are three different cases to consider:
1) The profit curve is parallel to the time constraint. Since the time constraint is Dc +Da = 360, the slope is equal to 1.
Therefore: [(1-r)Ee*Di]/500 = 1.
Profit will be maximised at any combination along the time
constraint, so long as dc is below the experience constraint. dc ≤ (Ee*Ei*da)/40.
Using Both constraints;
360 ≥ da ≥ [ 14400/(Ee*Ei – 40)]
360 – [14400/(Ee*Ei-40)] ≥ dc ≥ 0.
Case 2)
Profit Curve has a slope Steeper than time constraint.
[1-r)Ee*Di]/500 ≥ 1. This results in a corner solution at da = 360, dc = 0
Case 3)
Profit curve is more shallow than budget constraint
[1-r)Ee*Di]/500 ≤ 1. This results in a solution at da = 14400/(Ee*Ei – 40) , dc = 360 – da. Which is the maximum amount of time spent crafting at the time constraint.
Therefore the choice to craft or adventure is based on the variable
[(1-r)Ee*Di]/500.
If this choice value is greater than one, the character favours adventure for profit.
If this choice value is less than one, the character favours crafting for profit
And If this value is equal to one, then the character is indifferent to any possible combination.
To get some more insight we compile a table of Ee*Di
(I have included the tables as attachments. If they don't work I apologise. [Re-submit them as replies to this thread and I will post them – Regdar.])
Using this table, we multiply by (1-r) and divide by 500. We subtract one so that craft choice values are negative, and adventure choices are positive.
For a medium – high reinvestment rate of 75%:
(Table 2 Appended)
Where Blue Choices Indicate an All adventuring Choice, and Red favour a Maximum Crafting Choice.
For a Medium – Low reinvestment rate. R = 25%
(Table 3 Appended)
In comparison CV is increasing in Ee, and Di. CV is decreasing in r.
For a constant reinvestment rate r, characters are more likely to adventure the higher level they are and the more frequent the encounters.
If we drop the assumption that an adventurer does not consider equipment wealth profit, then we can calculate with the equivalent of r = 0.
(Table 4 Appended)
Relaxing assumptions 4/5, First and Second Level Casters can only produce scrolls. Since the scrolls they make are far below 1000gp/day, it seems reasonable to eliminate them from consideration for the choice.
Then in regards to Ee
Ee: Will Craft
0: 3rd – 20th
0.5: 3rd – 9th
1: 3rd – 6th
1.5: 3rd – 5th
2: 3rd
Above: Never
Conclusion: In regards to profit maximisation, there are a range of levels where a caster will choose to do any crafting at all. This range decreases as the frequency of encounters increases.
Please note that this is a first draft. Questions and Insights are appreciated.
There are a bunch of other things that you haven't factored in, as far as I can tell, and some of them are very significant. Even though some of them are campaign dependant I felt that they needed to be mentioned.
The first can probably be ignored as trivial (you ignored it with assumption 4): the cost of masterwork materials for crafting. The profit margin on a +1 bastard sword (1,335 gp to create, 2,335 gp market price) is actually less than that of a scroll with 5 silence spells (500 gp to create, 1000 gp market price) as you must spend additional time & XP to "pay" for the masterwork quality. Ergo, no one would ever bother to make +1 weapons, as they are the least profitable magic items in the game.
The second is that the gain of xp from adventuring vs the loss of xp from crafting in very significant. It doesn't affect your crafting profit, because any 1st-level character can make a scroll full of 1st-level spells every day (though I'm not sure who would buy it), but it does affect your long-term adventuring profit. More XP = higher levels = tougher challenges = more XP/challenge. The easiest benchmark I can think of is 5 gp/XP, the amount spellcasters pay when they when they don't spend gp for various spells, but this would require at least one more table and probably more.
The third is downtime, whether due to time in transit, seeking out adventures, scouting missions, etc. Obviously, downtime varies heavily by campaign but I'd guess that it's at least 1/2 the time for adventurers and frequently a lot more. When you craft, on the other hand, there's only downtime when you want it. This adds up quickly, as you could realistically spend as many as 300 days a year crafting but the typical adventurer is only going to get perhaps 30 days of actual combat. When you end up adjusting Di for this adventuring becomes much, much less profitable.
The final factor is the threat of death. This is another thing that it is nearly impossible to put a price on as both the frequency and permanency of death are campaign dependant. It is also unclear from the rules whether or not the "error" variable, as you call it, covers any and all required raise dead/resurrection/true res spells. But in any case there is no threat whatsoever of death from crafting which means that, in the very long run, you have an increased chance of making a larger total profit from crafting.
Finally, I was a little disappointed to see that you ignored what may be the most profitable way of all for high level casters to make cash: simply cast spells for gold. Compared to the other two methods it would seem harder to do successfully simply because of the limited market but if you tailor your spells to non-combat magics (wall of iron, wall of stone, fabricate, etc.) you can make far, far more money than with either of the methods that you covered.
Again, it was a very interesting post and I applaud you for crunching the numbers. Nice job. Just define all the variables in one place, please.
-Shaftiel
What about long term investment vs sales? Create a permanent magic item and sell the use of the item instead of the actual item? For example a bed of healing made by a cleric. Instead of selling the bed to somebody, charge a little bit of money for each person to lie down and be cured.