Mystic Theurge and other classes in the like

[Alucard S]

The mystic theurge gains +1 level of existing arcane spellcasting class/+1 level of existing divine spell casting class. Does this also increase the caster level of the character. For example, will his fireballs increase in damage, or does the caster level not increase with the mystic theurge, only the spells per day?

 

[Patlin]

Yes, caster level is increased. a 5 Wizard/5 Cleric/2 Mystic Theurge would cast 7d6 fireballs unless modified by feats, for example.

 

[Pinotage]

The mystic theurge gains +1 level of existing arcane spellcasting class/+1 level of existing divine spell casting class. Does this also increase the caster level of the character. For example, will his fireballs increase in damage, or does the caster level not increase with the mystic theurge, only the spells per day?

No, caster level increases as well. Here's the relevant text, emphasis added.

Spells per Day

When a new mystic theurge level is gained, the character gains new spells per day as if he had also gained a level in any one arcane spellcasting class he belonged to before he added the prestige class and any one divine spellcasting class he belonged to previously. He does not, however, gain any other benefit a character of that class would have gained. This essentially means that he adds the level of mystic theurge to the level of whatever other arcane spellcasting class and divine spellcasting class the character has, then determines spells per day and caster level accordingly. If a character had more than one arcane spellcasting class or more than one divine spellcasting class before he became a mystic theurge, he must decide to which class he adds each level of mystic theurge for the purpose of determining spells per day.

Pinotage

 

[Thanee]

+1 (effective) level in a spellcasting class gives you more spells per day, more spells known (or 2 free spells in case of a wizard), and caster level. You can also use the spell swapping ability of the sorcerer, and other spontaneous casters, as if you had gained a level of the base class, since it is assumed to be part of the spellcasting progression.

Bye
Thanee