"if I work an hour for a client in a day, the day is shot for any other client. My hourly would have to be 8x my daily, my 4-hourly 2x my daily, &c"
If they are paying at least your daily rate, why would you mind that your day is shot for your other clients? They are, effectively, hiring you for the entire day and paying what you've determined you deserve for it.
If they are inattentive/crazy enough to actually pay you more than your daily rate for an hour (or any number of hours up to the maximum number of hours you'd work in a day anyway), then that's just pure gravy. Same for the case when it takes you less than a day to do the work you're getting paid at least your daily rate for.
In your original post, you'd said "I can't effectively work for any other client that day, so my minimum billable increment is a person-day" so in recommending the raising of your hourly rate to more than your daily rate, I was going on the assumption that your daily rate would have been sufficient for you to accept the job in the first place.
Of course, if you can't afford to work a day for your new client because of other commitments, you'll either have to refuse the job or raise your rate to the point that it is worthwhile for you after all. Perhaps that's what you were referring to when you cited the 8x daily rate.
If they are paying at least your daily rate, why would you mind that your day is shot for your other clients? They are, effectively, hiring you for the entire day and paying what you've determined you deserve for it.
If they are inattentive/crazy enough to actually pay you more than your daily rate for an hour (or any number of hours up to the maximum number of hours you'd work in a day anyway), then that's just pure gravy. Same for the case when it takes you less than a day to do the work you're getting paid at least your daily rate for.
In your original post, you'd said "I can't effectively work for any other client that day, so my minimum billable increment is a person-day" so in recommending the raising of your hourly rate to more than your daily rate, I was going on the assumption that your daily rate would have been sufficient for you to accept the job in the first place.
Of course, if you can't afford to work a day for your new client because of other commitments, you'll either have to refuse the job or raise your rate to the point that it is worthwhile for you after all. Perhaps that's what you were referring to when you cited the 8x daily rate.