Recently offered a promotion, but now at less of a net pay raise than I expected

I'm currently working part time, making $14.50. I was recently offered a promotion to a full time position that would earn $16.00 an hour, a $1.50 increase.

However, my employer is giving all part time employees a $1.00 raise to $15.50 starting this week, to keep pace with the California minimum wage going up. However, it is my understanding that the position I have been offered will remain at $16.00 for now, as full time positions get raises at a different rate/amount.

I had previously indicated that I would accept the position before learning of this pay raise to my current position, but have not formally signed any paperwork or anything yet. Now I feel like there is less incentive for me to accept, as it would only be a 50 cent raise over what my current position has now been raised to, with a considerable increase in responsibility. I am getting basically full-time hours every week, so going from part time to full time would give me access to benefits, but my hours worked will remain about the same. If they had offered me this position this week instead of last week, at only a 50 cent increase, I feel like I would have declined it.

Would it be appropriate for me to ask for $17.00 to keep the $1.50 pay raise over my current position that I expected? Or should I not consider the increasing pay rate of my current position, since I had been okay with $16.00 beforehand?

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