I'm having trouble gleaning this from the Covenants book. How much does it take to build a lab with different Upkeep from +0? Does it cost silver to install new virtues/flaws, and if so, how much? Can you take Missing Ingredients for every Te/Fo not being used for a season, then switch it instantly when you move to another TeFo combination?
Generally speaking, it takes time. The original Size doesn't really have a cost so much as the building has to be there with the room within it. Once you've got that, it takes two seasons and 5 or 10 lb silver (forgot which). New Virtues cost silver if they have a non-zero Upkeep; they nearly always cost seasons (one for minor, two for major), though some "free" ones can be picked up without seasons. Similarly, getting rid of Flaws generally takes seasons, with some exceptions. Of course, these need not be your seasons if you have a specialist on hand who has a high enough score in Magic Theory. As for taking a Flaw multiple times, that is possible only if it is marked with a star. Switching bonuses takes a season of Refinement, even if not moving to a higher Refinement score. Even then, that's switching bonuses for the same Virtue/Flaws you already have, not switching between ones you have and ones you don't have.
Specific to Missing Ingredients: It has an asterisk, so you can have it multiple times. But it does not provide a switchable bonus. Of course, you can get rid of it without a season by spending the silver. So, I suppose, theoretically, you could keep throwing out ingredients to get new Missing Ingredients and buy off the Missing Ingredients you no longer want, which is what you ask. So, yes, it looks possible. But I highly recommend you compare the cost to increase Upkeep (buy off the one Missing Ingredients you no longer want) to the cost to maintain a lab. I think you'll find it's cheaper to just maintain the lab at the higher Upkeep, and as an SG watching you try to game the system I might take a little sadistic glee watching you spend more than you save instead of telling you - just rewards for gaming the system. Only if you want to work solely on certain Arts for many seasons before switching to other ones will this method actually save you money.
The chart on page 64 of Covenants has the Upkeep cost for labs, but it is also used to calculate the costs when upkeep changes, and it can be used to reference the starting cost of labs. Putting in a lab where none existing before costs 10 upkeep points, since there wasn't anything there before, you have to pay the difference in upkeep in silver, in this case 10 pounds of silver for a brand new shiny standard Hermetic lab.
To increase upkeep it's the difference between the old upkeep and the new upkeep score, so if you are installing something that takes the lab from 0 upkeep to 2 upkeep, you have 30-10=20 upkeep points, which costs 20 silver to install.
To answer the specific question about missing ingredients, and the constant switching around, I would impose a penalty of increasing the Upkeep, at a standard lab with missing ingredients that would be from -1 to 0 (3 points, or 3 pounds of silver), despite the upkeep level never changing. Because gaming the system like that should be discouraged somehow. It doesn't track that you suddenly acquired the necessary ingredients to reduce the penalties for one Technique or two Forms while also losing the ingredients you had for a different Technique or two different forms (unless the magus simply throws them out when done with a project, and then it's a personality quirk that needs to have a consequence). Note, this penalty gets much higher, if for example the lab's upkeep is +2 and fixing missing ingredients makes it a +3, that's 30 silver, every time you switch out. It's just better to bite the bullet and not have missing ingredients, although it's a suitable flaw to take temporarily while installing another virtue into the lab that pushes the upkeep past an acceptable level...
Ah, I found the lab point/upkeep/installation section, thank you.
That is a good point. RaW, having a pile of Missing Ingredients except for the TeFo you're using would mean you would pay the +2 Upkeep difference if you switched since you'd lower it by 2 with a set of Missing Ingredients (at no savings) and raise it again when you buy off the other Missing Ingredients.
Additional question: a house is £1 and is about 500sqft (Size 0 lab) from what I can tell on 12th century peasant architecture on Google. How much bigger would a Large, Huge, or even Stupendous house be in comparison to Lab Size? Would making it Large/Superior (£4) be sufficient to make the whole thing stone and add a second floor for the bedroom?
Well, I typically don't care about silver. It's just a pain to track. My approach would be to consider how many people could (not will) live in it, and calculate the cost based on that using the guideline from Buildings section of expenditures.
The covenant builds a house big enough to house 4 magi and their servants, they build it with an eye towards the future, as they have a bit extra money, so it will house 40 points in magi and say another 8 points in servants, and round it to 10 for servants for a total of 50 points. The cost would be 50 silver. It's probably a bit much, but it's for magi, who expect fine finishes. Alternatively a spring covenant would only be 25 pounds (20 for magi and 5 for servants).
A 500 square foot house is a pretty simple afffair, stick frame, wattle and daub walls, thatch roof. The £1 cost probably represents the money the homeowner lost out on making by building the house and bartering for supplies, and not any actual expenditure. Magi, or nobles building large houses are employing expert craftsmen and acquiring exquisite materials...
Small correction to JL's commentary on how much increased lab upkeep costs: Taking a lab from 0 Upkeep to 2 costs 10 pounds, not 20, because according to the Upkeep subsection (pgs. 110-111) you pay one pound per two Upkeep points changed, rather than paying on a one-to-one basis.
You are correct! I was conflating the x10 for the cost of increasing the lab.
(First, note there are some oddities in Upkeep costs, things like candles being far more expensive if you have a building of your own versus having an otherwise identical - including drafts and need for lighting - room in a larger building. All that aside...)
Anyway, what can be examined is the cost each season to buy off this Flaw multiple times versus the cost to just maintain the higher Upkeep lab.
Unless a given project has a lot of requisites, Missing Ingredients could theoretically be taken 8 times. I would recommend a practical limit of 7 if trying to game the system. That would give you two Techniques and two Forms, which would allow things like MuCo(An) while still allowing Cr(Re)An without having to do all sorts of stuff gaining and losing number of Missing Ingredients. Practically, most likely the three that aren't taken would be swapped for three that are, though carefully moving between projects could keep that down to two. Let's go with three to maintain a certain amount of practicality.
So, without 7x Missing Ingredients the lab has an Upkeep of U. After 7x Missing Ingredients the lab has an Upkeep of U-7. When swapping the lab has to be improved up to U-4, and some other ingredients are then thrown out to bring it back to U-7. So the costs are:
No Missing Ingredients: maintenance on U
7x Missing Ingredients: maintenance on U-7 and payment to improve from U-7 to U-4.
We're looking for break-even points. How often can you swap and have this worthwhile? (This may also depend upon the value of U.) Unfortunately, I don't have the scale on hand so I'm stuck here until I get back to my book. Knowing how costs tend to explode for Upkeep, I'm guessing this is actually worthwhile but probably wouldn't be with a single Missing Ingredients, but I would like to check.
Since Upkeep bottoms out at -5, U can't be lower than +2 if we want to avoid 'wasted' savings. No Missing Ingredients: £3 per year
7x Missing Ingredients: £.1 per year and £2 to switchThis is a net positive so long as you swap no more than once per year. Let's look at a higher end, Igor Rastvan's lab (+16 Upkeep).No Missing Ingredients: £136 per year
7x Missing Ingredients: £45 per year and £230 to switchYou need to switch a little less often than once every two years for this technique to be viable.