Even if a poor household "makes" $50 or even $100 a year from a rebate scheme, it could still be worse off from the higher energy and transportation prices it must pay due to the carbon tax.
Proponent of Alberta Carbon Tax Misleads the Public
One of the problems with a carbon tax is that it hits poorer households particularly hard. By raising the prices of electricity, heating, and transportation--which is the whole purpose, not an unintended side effect--a carbon tax falls disproportionately on lower-income people, not in absolute dollar terms but as a proportion of their monthly budget. The advocates of a carbon tax try to fix this problem by recommending a "rebate" of its proceeds, and in some cases (such as Alberta) they even target the rebate to poorer households. They present calculations showing that poor people "make money" from a carbon tax, and so are allegedly better off.
Even if we accept these figures at face value, they don't prove what they claim. I explained this fallacy with regard to comparable claims from the U.S.-based Climate Leadership Council (CLC). Namely, even if a particular household pays less in carbon taxes than it receives in dividend rebates, it could still be worse off, because the carbon tax makes energy (and other goods) more expensive. (That's what taxes do, folks.) A poor household can reduce the amount it pays in carbon tax by changing its behavior, such as using less electricity and taking the bus instead of owning a car. The calculations depicting a household as a "net financial winner" from a carbon tax assess the money flows after the household adapts to the higher prices (particularly for electricity and gasoline) due to the tax.