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Actually demanding low/high salary involves risk of losing a job you are strong candidate for. therefore, what i would suggest is to go with the policy of the company saying: i would be happy with salary grade policy because the salary is usually based on the scale/grade/category of the position. in Non-for-Profit organizations the salary range of the staff is mentioned at the time of writing proposal for funding. it shows how perfectly you respect the policy and dont care about the salary.
it's well served if it meets one's expenses and savings and accordance to work at hand
the level of position does matter. if you think it is manager level position and JD has some description such as: salary negotiable than it is good to negotiate.