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I guess the fair way to approach this would be to take the average YEARLY salary and cross it against the increase in hours worked.
Using your example:
Average salary = $51,000 yearly
Increase of 2% = $52,122 yearly an increase of $1,122.
Increase in hours worked proposed was 40 minutes per work day X 260 days of actual in school work (Roughly does vary across the nation) = 174 hours (Rounding up) extra hours worked.
$51,000 / 365 = $139.72 per each day of the year regardless of whether they're actually in school working.
$139.72 / 7 = $19.96 per hour.
$52,122 / 365 = $142.80 per day worked.
$142.80 / 7.7 = $18.54 per hour worked.
Conclusion effective pay rate decreases per hour worked.
Exactly. There are numerous ways to illustrate that point. I tried to take the simplest, a strict hourly approach.
However, if the 2% increase is tied to the effective hourly rate of the teachers then the salary would be more than $51,122 as noted above. I did not read how the 2% increase was factored in. If factored into the hourly rate, then obviously the salary would increase and this whole conversation is moot.
In that case, I agree that it would be a moot point. However, as they receive an annual salary, one is dealing with a 2% increase from current compensation, not a 2% increase in the effective hourly rate that would be tied to the expanded work days.
Having said that, I recognize that Chicago faces some major fiscal challenges. The union will need to compromise, but the City will likely have to increase its offer. Its current offer is a 5-year contract with a guaranteed 2% raise in the first year. That's inferior to the last contract that was agreed with the police (10% increase guaranteed over 5 years). There's no indication that the City will even attempt to offer its police officers terms similar to what it is offering its teachers (guaranteed 2% raise over the next 5 years), much less ask them to increase their workdays by 10% in exchange for that compensation.
I am not in any way suggesting that the City concede the union's maximum position. Far from it. The City should offer reasonable terms consistent with its financial realities in exchange for agreement on reasonable reforms (preferably focused on increasing student learning outcomes that are truly controllable variables).