In general, most business experts would say that it's important for businesses to consider raising pay to keep up with the rising cost of living. Employees who don't see their wages increasing in line with inflation may become dissatisfied and may seek employment elsewhere. Of course, it's important to consider the financial health of the business when making these decisions. There are also other ways to show appreciation for employees besides pay raises, such as flexible schedules, opportunities for advancement, and recognition for good work.
The same thing that business A is facing is the same thing that business B is facing. There's no guarantee that the new job that you're seeking is paying their workers increased salaries. Are they not facing the same sting of inflation in the country? There's even a good chance that you wouldn't see a new job quickly when you quit your job.