For officials in some communities, the calculus seems simple: Either give companies a break on their tax bill, or don’t get any tax revenue at all.

This fall has seen a flurry of towns and cities chasing new development through tax increment financing — or TIF — plans that temporarily reduce property tax bills for businesses that agree to complete projects adding local jobs. Within just the past few weeks, Lexington, Marlborough, and Needham have approved or announced plans to seek approval for TIF agreements.