Is there anything that says when your promoted to Supervisor should you get higher pay? Paid hourly 40 hrs week. In NB.

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I am sorry to hear of this difficult situation.

Are you in a union?

There is no law law that says you need to get higher pay when you're promoted but you don't have to accept the promotion if you're not going to get higher pay.

If they require you to take this promotion and don't give you a higher pay than this would be a case of constructive dismissal.

When an employer does something that fundamentally changes the nature of the employment so that it drives the employee to quit, this may be a case of constructive dismissal. This is usually the case when the employer reduces wages, cuts hours etc. It is also the case where the employer's conduct makes it intolerable for the employee to continue working.
If an employee does quit under these circumstances then the law is that constructive dismissal is wrongful dismissal and the employer will be liable for damages.
If you are considering this option it is crucial that you first consult with an employment lawyer so that you can get a legal opinion from an expert both about whether the facts amount to constructive dismissal and, as well, about what damages you may be entitled to.
Generally the damages would be equal to what you would receive had you been dismissed without cause. If that had been the case you would have been entitled to receive "reasonable" notice or pay in lieu of notice.
Generally, in determining what is reasonable notice Courts look at several factors including the length of time you worked for the employer, your age, your position, the likelihood of finding new employment etc.
At the high end, if you were in a managerial position, the Court would likely order one month's notice or pay in lieu of notice for each year of employment. If you were not in a managerial position the Court would order somewhat less.

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Debra