This question comes from the comments on my previous question.
In short, if I have for example a Belt of Incredible Dexterity +2 (4,000 gp), and I want a Belt of Incredible Dexterity +4 (16,000 gp), can I simply go to a wizard and pay the difference and wait for the necessary days to have the item upgraded?
In this case, since the cost goes from 4k gp to 16k gp, I'd have to pay the wizard 12k gp and wait 12 days, while s/he would have to spend 6k gp to perform the task and keep the other 6k gp as profit.
However, the only example I found in the rules, is of a wizard upgrading his/her own item:
Example: Patrick's wizard decides to use his downtime to increase the
armor bonus on his bracers of armor +1 to +3. The price difference
between the two types of bracers is 8,000 gp, so Patrick's wizard must
spend 8 days and 4,000 gp (half the 8,000 gp price difference)
upgrading his bracers' magic. If he has fewer than 8 days before the
next adventure, he'll need to finish his crafting while traveling or
use accelerated crafting in town to speed up the process.
Best Answer
Paying the full price
If you decide to pay the difference of magic item's Price, then this difference already includes both the magical components and his spellcasting services. The magical components cost is always half the market price of the item, everything else is profit for the creator/seller.
If you have a Belt of Incredible Dexterity +2 (4,000 gp), and want to upgrade it to a Belt of Incredible Dexterity +4 (16,000 gp), the 12,000 gp difference already includes the components and services.
But if you want to save some money, you could buy the required reagents for 6,000 gp and look for a spellcaster to upgrade the item for you.
You can simply go to a wizard with the reagents...
and pay for his services
Yes, unless said wizard is a friend and wants to work for free, the Cost of a magic item is simply the Magical Components required to craft the magic item, or upgrade the item.
Now, if you read the rules for cooperative crafting magic items (on that same page), you will see that for each day spent crafting, one of the creators (or yourself) must provide the spell required for that magic item, or suffer an increase of +5 to the spellcraft DC per spell missing.
For convenience, i will quote those rules here:
When you ask someone else to craft or upgrade an item for you, you can provide all the components, but that doesn't mean he will work for free (unless you convince them somehow), and you will have to pay for the spellcasting services(normally Caster level × spell level × 10 gp), which may or may not be available on that town, based on it's population and size.
This cost must also be paid when you request a npc cleric to cast spells on you, or when you ask a npc to use a divination spell to ask questions about your quest, or when you need a npc wizard to enchant your masterwork sword with a +1 enhancement bonus.
Of course, if you are the creator, and provide all requeriments, you do not have to pay for any extra service. But if you need the aid of someone else, they may charge for their availability.
Example
On your example, you can pay 6k gp for the materials, provide the base item (Belt of Incredible Dexterity +2) and would still need to pay for it. "How much?", you will ask your GM.
To craft this item you must be at least 8th caster level and be able to cast cat's grace, either that or have enough ranks in spellcraft to beat a DC 18 (not that difficult), but for the sake of this example, let's say they only need to be able to cast cat's grace and be 8th level caster (could be a wizard, or cleric, or anyone able to meet those requeriments, really).
So 160 gp is the average cost for each cast of cat's grace from a generic spellcaster. Since the upgrade has a cost of 12,000 gp, that means he will spend at least 12 days working on your belt, so he may charge you 1,920 gp for all the trouble.
Note that this is still cheaper than buying 12 scrolls and cast the spell yourself if you don't have that spell.
This example is probably the most expensive you could go, working with your GM and rolling Diplomacy, you could make this go lower. If you have the feats but not the spell, you could find a 3rd level spellcaster to cast it for 12 days and pay only 60 gp per day (720 gp total) instead.
The spellcasting service's formula is an average market value for that kind of service, the GM can lower or increase that cost based on any circunstances he sees as necessary. But this cost should never be the same as what he would profit from using his own money to craft the item and sit it on his shop waiting for someone with enough money to buy it (that could take months to happen).
Usually, spellcasters that work on a town, are more than happy to sell his spells and time, as the average earnings for downtime is about 2-4 gp a day. Unless, of course, he is already working on another project and cant cancel it (or all his progress is lost)