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The best justification for such a tax would be an externality-reducing one (although for some reason the revenue is intended to go to the supermarkets, so it is not technically a tax but a price floor). What externalities are there from plastic bags? They are not very biodegradable, so they hang around in landfills for a long time. It is probably a bit of a push to describe this as an unpriced externality, as we actually pay for the maintenance of the landfills through local body rates. It might be reasonable then to use the money to run the landfills, as it is probably very hard to charge people per plastic bag they throw out, yet heavy plastic bag users impose higher costs on the landfills. However, this is not the plan. Furthermore, I am led to believe that our landfills are far from overflowing. So I don't see any pressing environmental hazard from having them fill up with plastic bags.
Perhaps the externality comes from people that throw them away outside landfills? I don't see this is a major environmental problem facing people - I certainly don't notice clouds of plastic bags clogging up downtown Wellington. Perhaps I am missing them. Certainly plastic bags can harm animals. Google image search plastic bag pollution and you will see some horrific photos of animals being smothered by bags. However I am not sure that this is a huge (in terms of scale) problem (although if I am wrong please correct me). As a lifeguard I only very rarely see plastic bags in the ocean, and they are usually very easy to pull out and get rid of. If the problem is more widespread then this is a reasonable justification for the plan. But my intuition is that it is relatively small, and that there are measures in place to prevent this already (to the extent that it can be).
There is certainly carbon in plastic bags, and seeing as landfills occasionally engage in controlled fires (I believe), perhaps this is the start of a carbon tax. However I would be greatly surprised if the Government (especially this one) plans to implement a carbon tax one good at a time. Furthermore we aren't taxing (or raising the price of) the carbon producing action (the burning) so this would be a relatively inefficient way of correctly pricing this externality.
So I don't think there is an externality-based justification for taxing plastic bags. The final option is simply that the Government considers them a demerit good, that people just should be discouraged using for the sake of it. This seems to be the tack Nick Smith is taking in the article I linked previously. I am unsure as to why this would be, and it is certainly a surprising approach from a Government that railed against paternalism while in opposition.
I suspect it is simply to make themselves appear 'pragmatic' and 'centrist', and I imagine it will probably work in that sense.