I'm about to start the negotiation process for a new position. I expect the offer to be in the area of $72,000 - 76,000 / year. If the offer is higher than $73,800 should I negotiate to have my starting salary slightly decreased so that I pay 15% income tax vs. 25%? I'll be filing married-joint.
No, absolutely not. Income tax rates are marginal. The tax bracket's higher tax rate only applies to extra dollars over the threshold, not to dollars below it. The normal income tax does not have any cliffs where one extra dollar of income will cost more than one dollar in extra taxes.
Moreover, you are ignoring the personal exemption and standard deduction. A gross salary of $72,000 is not the same as taxable income of $72,000. The deduction will generally be $12,200 and the exemptions will be $3,900 for you, your spouse, and any kids. So married-filing-jointly with the standard deduction will get an automatic $20,000 off of adjusted gross income when counting taxable income. So the appropriate taxable income is actually going to be more like $52,000.
Note that getting your compensation package reshuffled may result in different tax treatment. But simply taking a smaller salary (rather than taking some compensation as stock options, health insurance, or fringe benefits), is not a money-saving move. Never do it.
No. In a marginal tax system, only additional dollars that push you into a higher bracket are taxed at that higher rate. If you would pay 15% on $73800, then when you earn over $73800, you will still only pay 15% of the $73800, plus 25% of the extra amount over $73800. As far as a marginal income tax affects things, you cannot decrease your net income by increasing your salary. (There can be other potential reasons to keep your income down besides income taxes, as asked in this question, but as the answer there suggests, these often aren't great reasons either.)
As far as I know, every income tax system that has differing tax rates works this way. That is, I'm not aware of any country with an income tax system where you can decrease your net earnings by moving into a higher bracket.
I think Feral Oink said it well here when someone asked if they should negotiate for additional benefits in lieu of a portion of salary.
"You never want to take a lower salary, especially not in exchange for something that is conditional e.g. benefits. Your salary is the only thing that is guaranteed as a condition of employment. Other things can be changed by the employer at a future point in time."
If your employer offers a 401k retirement plan then you can contribute a portion of your salary to your retirement and that will lower your effective income to remain in the 15% bracket (although as others have pointed out, only the dollars that exceed the 15% bracket will be taxed at the higher rate anyway).
AND if your employer offers any kind of 401k matching contribution, that's effectively a pay-raise or 100% return on investment (depending on how you prefer to look at it).