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Prime Minister Justin Trudeau speaks with reporters as he makes his way to Question Period, in Ottawa on Oct. 31.Adrian Wyld/The Canadian Press

The genius of the carbon tax is that it works on the principle of polluter pay. That’s also its political Achilles’ heel.

Everyone’s in favour of polluter pay when the target is assumed to be cartoonish enviro-villain Snidely Whiplash. But when it comes to a lot of Canada’s carbon emissions, there is no Snidely. There’s just us. We’re the driver gassing up the tank. We’re the homeowner heating the house.

Which brings me to the pretzel shape the Trudeau government has contorted itself into by abruptly exempting home heating oil – and only home heating oil – from the federal carbon tax, while rolling out a subsidy program giving up to $20,000 to families currently heating their homes with oil.

The Liberals watered down the principle of polluter pay because it was causing them political pain in Atlantic Canada, where many homes use heating oil. But once you say the carbon tax applies to all fuels except the most polluting one, you’re cutting the legs out from under the argument for the carbon tax – which is the intuitive fairness of the more you pollute, the more you pay.

I support carbon taxes, especially when paired with the federal rebate of those taxes. It’s sound in principle, and mostly fair in practice. It isn’t perfect, and there are places and cases where it may not be the most efficient way to lower emissions. But it is a pretty good system for cutting pollution, and for allocating the cost.

It’s also clear that many of those pushing for the elimination of consumer carbon taxes aren’t half as interested in coming up with an alternative. I’m looking at you, Conservative Party of Canada.

Along with the temptation to replace the carbon tax with nothing, there’s also the urge to substitute polluter pay with polluter gets paid. That’s what the Trudeau government is doing on home heating oil. Instead of punishing families to lower emissions, they’ll pay (some) families to lower their emissions.

Carbon tax supporters have to concede that a tax isn’t always the best tool for the job. Think of the regulations that forced light-bulb manufacturers to switch from old incandescent technology to new LED lights, which use around 85 per cent less energy.

The Liberals’ heating-oil gambit blows up in their face. The carbon tax may be collateral damage

And in the case of heating oil, a tax of a few hundred dollars a year may not be the most efficient way to push homeowners to spend $20,000 on an electric heat pump, even if it would more than pay for itself over its life. Companies calculate things like that down to the last penny; most families don’t.

And in politics, a subsidy – free carrots instead of a whack with the stick – is almost always the preferred choice. That’s because, instead of polluter pay, it can be sold as nobody pays.

The Joe Biden administration has an ambitious carbon-reduction plan, with no consumer carbon tax and lots of subsidies. Financing comes from what seems like free money: adding to Washington’s massive deficit, which at US$1.7-trillion is about four times Ottawa’s deficit, relative to the size of the economy.

But whether it’s the punishment of a tax or the reward of a subsidy, somebody’s paying. The world is double-entry bookkeeping. All those credits come from somewhere.

Consider Ottawa’s newly enriched program to subsidize switching to electric heat pumps from heating oil. A home that does so instantly goes to low from high emission. But the upfront cost of a heat pump system runs around $20,000. Who should pay?

The answer the Trudeau government has settled on is: not the homeowner. At least not if they’re lower to middle income. They will be offered a subsidy, in Atlantic Canada at first, but with the other provinces invited to join the party. An existing program offering $10,000 federal dollars and $5,000 from the province will see the feds add another $5,000 a home to the pot.

Ottawa says that means “making the average heat pump free.” In Nova Scotia, a family of four that heats with oil is eligible for a free heat pump if they have an after-tax income of $105,000 or less. In Ontario, Alberta and British Columbia, the ceiling is just over $120,000.

The feds have not yet released the price tag, so allow me to take a stab at it.

There are more than 15 million Canadian households. Three per cent heat with oil. Let’s assume that half of those oil-using families are income-eligible for this subsidy. That’s a quarter-million free heat pumps. At $20,000 a pop, the cost to taxpayers is around $5-billion.

That’s a rough guesstimate, and my point is not to nail the precise price. It’s simply a reminder that giving away free heat pumps isn’t free.

Taxing people to encourage them to pollute less has a visible cost. But flipping the script, and giving them a subsidy – financially rewarding emissions reduction, rather than financially punishing emissions – has similar costs.

What changes is who pays. Instead of taxing Peter to lower Peter’s emissions, it’s taxing Paul to pay for lowering Peter’s emissions.

Is that fair? As with many issues, where you stand may depend on where you sit.

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