Is the husband obligated to give his wife a private allowance if he is well-off?

It is not obligatory for the husband to give his wife a private allowance. Rather, what is obligatory is to provide maintenance (nafaqah) in a reasonable manner that suffices her, taking into consideration the circumstances of both spouses. However, it is recommended for him to give her a private allowance if he is well-off and the wife requests it for permissible matters, as this falls under good companionship and the kindness enjoined by Islamic law.