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I oppose elimination of the cent as it will only encourage further inflation.
Too late. Inflation will continue to happen with or without the cent. Also, rounding does not cause inflation.
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The government simply does not have to make so many each year.
Yes, they do, because the demand is there.
Reducing the mintage will have the same effect as eliminating it because demand will outstrip supply and there will be shortages.
Actually, this sounds like a good idea.

The mint should reduce the mintage to one tenth or so.

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It also should not be minting so many dollar coins that the public clearly does not prefer to use over the one dollar bill.
The dollar coin is already NIFC and minted for collectors only.