###There is not, and really couldn’t be—if it existed, it would be wrong

How wealth affects a party’s power in D&D 3.5e is extremely complicated, and it depends so much on the party’s composition, level, the foes they face, and so on. Some classes are, even at high levels, inconvenienced at worst—a cleric might really like their greater metamagic rod of quicken spell, but if forced to live without it, it’s not exactly going to make or break them. The same can’t be said of a fighter’s magic weapon—a large number of foes are all-but-literally untouchable without one (and some are actually-literally untouchable without one). A fighter without a good magic weapon has little chance of contributing in combat against mid-to-high level foes. A cleric is almost never going to be unable to contribute.

If we’re considering a party completely stripped of gear, of course, that implies that a wizard is without a spellbook, a cleric is without a divine focus, and both are without spell component pouches. That, of course, can render them functionally unable to contribute. Plenty of spellcasters can get around that—Eschew Material Components is a thing, spell-like and supernatural abilities à la warlock and binder don’t use those to begin with, and of course most classes lack any item as key to a character as a spellbook is to a wizard.

The wizard example is instructive, I think, because with even the tiniest wealth—their starting spellbook and a spell component pouch—they are arguably the most powerful class in the game. Lack of magic items is at worst and inconvenience, they don’t need armor or weapons, and so on. So long as they’ve got their spellbook and spell component pouch, they are always going to be ahead of the game. In fact, assuming everyone’s in the same situation, less wealth will make the wizard even stronger relative to others, because the lost wealth affects him so little while it affects many other characters massively.

Until the spellbook and spell component pouch go away. At that point, the wizard becomes a commoner with an abnormally high Intelligence score.

How would one even begin to quantify that? There certainly can’t be a one-size-fits-all approach; we aren’t going to be able to define any kind of “function of wealth” that covers everyone. The wizard and the fighter simply aren’t affected the same way. And since a party can be all wizards or all fighters, parties aren’t going to be affected the same way.

Ultimately, though, none of this matters. D&D 3.5e is not a remotely balanced game. How strong a given level character is, how strong a given CR monster is, vary wildly. Even the rules we have got for figuring out party strength vs. encounter threat are lucky to even find themselves in the same ballpark. Ultimately, a DM has to just know their party, know their encounters, and have a strong sense of how a fight is likely to go, to have any hope of consistently challenging the party.

There is not, and really couldn’t be—if it existed, it would be wrong

How wealth affects a party’s power in D&D 3.5e is extremely complicated, and it depends so much on the party’s composition, level, the foes they face, and so on. Some classes are, even at high levels, inconvenienced at worst—a cleric might really like their greater metamagic rod of quicken spell, but if forced to live without it, it’s not exactly going to make or break them. The same can’t be said of a fighter’s magic weapon—a large number of foes are all-but-literally untouchable without one (and some are actually-literally untouchable without one). A fighter without a good magic weapon has little chance of contributing in combat against mid-to-high level foes. A cleric is almost never going to be unable to contribute.

If we’re considering a party completely stripped of gear, of course, that implies that a wizard is without a spellbook, a cleric is without a divine focus, and both are without spell component pouches. That, of course, can render them functionally unable to contribute. Plenty of spellcasters can get around that—Eschew Material Components is a thing, spell-like and supernatural abilities à la warlock and binder don’t use those to begin with, and of course most classes lack any item as key to a character as a spellbook is to a wizard.

The wizard example is instructive, I think, because with even the tiniest wealth—their starting spellbook and a spell component pouch—they are arguably the most powerful class in the game. Lack of magic items is at worst and inconvenience, they don’t need armor or weapons, and so on. So long as they’ve got their spellbook and spell component pouch, they are always going to be ahead of the game. In fact, assuming everyone’s in the same situation, less wealth will make the wizard even stronger relative to others, because the lost wealth affects him so little while it affects many other characters massively.

Until the spellbook and spell component pouch go away. At that point, the wizard becomes a commoner with an abnormally high Intelligence score.

How would one even begin to quantify that? There certainly can’t be a one-size-fits-all approach; we aren’t going to be able to define any kind of “function of wealth” that covers everyone. The wizard and the fighter simply aren’t affected the same way. And since a party can be all wizards or all fighters, parties aren’t going to be affected the same way.

Ultimately, though, none of this matters. D&D 3.5e is not a remotely balanced game. How strong a given level character is, how strong a given CR monster is, vary wildly. Even the rules we have got for figuring out party strength vs. encounter threat are lucky to even find themselves in the same ballpark. Ultimately, a DM has to just know their party, know their encounters, and have a strong sense of how a fight is likely to go, to have any hope of consistently challenging the party.