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Why do the 1 and 2 euro cent coins exist and why are they used?
While dealing with US pennies and not 1 and 2 cent euro pieces, you may find this Wikipedia article of interest and analogous: Penny debate in the United States This article briefly summarizes both the arguments for and against retaining the one cent piece.  The arguments against include: Arguments for preservation include: Already a number of countries have removed their equivalents of the one and two cent coins, including New Zealand, Sweden, Australia, Israel, and Brazil (to name a few).