The modelling is in gross revenue estimates – it shows how much revenue a higher GST and carbon price would raise, including revenue from the sale of carbon permits, before given any consideration to compensation packages for households.

But a carbon price of $28 per tonne would cost households less than both options – just $10-15 a week on average – while raising the same amount of revenue for the government, it shows.

The modelling also shows if the GST base was broadened it would cost the average household about $48 a week, and if the rate was raised to 12.5 per cent it would cost households less, at $23 a week.

The analysis, which was commissioned by the Australian Greens, comes after the Australian Council of Social Service (ACOSS) released modelling this week showing the current 10 per cent GST consumes 13.4 per cent of disposable income for those in the bottom fifth of households, which would rise to more than 20 per cent if the rate were lifted to 15 per cent, as is favoured by some within the Coalition government.

The ACOSS modelling, carried out by the respected National Centre for Social and Economic Modelling (NATSEM), went a long way to explaining Labor's trenchant opposition to any GST increase and suggested that any compensation built in to ensure the poorest are left "no worse off" – as the Prime Minister has pledged – will require an enormous "churn".

Greens Treasury spokesman, Adam Bandt, said the modelling shows that "dollar for dollar," it would be fairer to bring back the carbon price than to lift the GST, and it would cut pollution as well.

"This research exposes the Alice in Wonderland logic of the Liberals, where a price on pollution is a great big new tax that will wipe cities off the map, but a new tax on almost everything we buy is a fair and reasoned proposition," Mr Bandt said.

"Treasurer Scott Morrison's vague suggestion of compensation [for a GST increase] misses the point. If a higher GST demands much more compensation than a carbon price but both can raise about the same amount of gross additional revenue, it must be better and fairer to go with the carbon price, especially as it will also cut pollution."