In 2005, the Scottish Government issued a full environment impact assessment report. The report includes the following finding (at page 31):
Paper bags are anywhere between six to ten times heavier than lightweight plastic carrier bags and, as such, require more transport and its associated costs.
More paper bags = more gas consumption.
We can present this graphically as follows, assuming that paper bags are only six times heavier.
Delivery of PLASTIC bags at $2.60 per gallon for diesel fuel

Delivery of PAPER bags with same grocery carrying capacity at $3.00 per gallon for diesel fuel
The price of diesel fuel has dropped by about 50% since the summer of 2008, but it will undoubtedly rise again in the future.
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