Thousands of Albertans queued at service centres across the province on New Year's Eve with the goal of filling up their gas tanks before the province's new carbon tax kicked in at midnight.

Few if any pennies were saved. Prices at most pumps didn't shoot up the next morning and gasoline is now cheaper across much of the province nearly a week after the tax's introduction.

That goes against many expectations, but much about the Alberta levy – who will win from it, who will lose – remains unclear, and the question of whether carbon pricing is effective for the environment gets lost to politics.

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That political backdrop includes using the tax to transfer wealth to the less fortunate, using the tax to generate revenue akin to a sales tax long verboten in Alberta, and using it as part of Premier Rachel Notley's stated ambition to gain social licence in exchange for greater pipeline acceptance.

Unsurprisingly, the political criticism has been shrill: Federal Conservative leadership contender Kevin O'Leary has called Alberta's tax a horrendous mistake in an open letter to Ms. Notley. "You will officially be guiding Alberta into an economic blizzard with the implementation of the carbon tax. A disaster Alberta won't be able to dig itself out of," he wrote.

Alberta's economy-wide carbon tax now prices carbon at $20 per tonne, before increasing to $30 per tonne of carbon-dioxide emissions in 2018. That matches the nearly nine-year-old carbon tax in neighbouring B.C. While the proceeds from B.C.'s carbon tax were used to reduce that province's income taxes, Ms. Notley has rejected that approach.

As of 2018, Alberta's carbon tax would bring in about as much as a 3-per-cent sales tax – a comparison the NDP has sought to avoid. While most of the tax will be spent on government programs, more than $2.3-billion will be spent over the next five years on rebates for lower income families.

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The carbon tax's arrival has caused many worries in Lloydminster, a bi-provincial city of nearly 30,000 cut in half by the Alberta and Saskatchewan boundary. While the city has one municipal government, it has to contend with the political currents of two different provinces. For decades, Lloydminster's politicians have sought to limit the differences between the two sides, ironing out problems over clashing provincial regulations, different school rules, hospital care and diverging taxation.

Where Ms. Notley has embraced a carbon tax, Saskatchewan Premier Brad Wall has been the harshest critic in Canada, threatening to take the federal government to court over a proposed national carbon price.

The Saskatchewan side of the city has long had an exemption from that province's sales tax so that businesses would not flee to sales-tax-free Alberta. While the city's leaders have asked the provincial government to exempt its side of the city from the carbon tax, to avoid driving gasoline sales to the other side, no exemption has yet to be granted.

"It infuriates people in Lloydminster," said Richard Starke, the area's Progressive Conservative MLA. He raised the issue in the legislature recently, only to be told by Finance Minister Joe Ceci that Albertans still have lower taxes than any other province.

"Saskatchewan waived the PST on their side of the border because they knew that all business would go to Alberta if they didn't," Mr. Starke said. He says he's hopeful Ms. Notley will eventually give the city an exemption. "What we're asking for isn't unprecedented. It just requires a government to be flexible."

Ms. Notley's wide-ranging climate agenda, with its carbon tax and limit on oil sands emissions, has had its supporters. Prime Minister Justin Trudeau credited her plan for his recent approval of an expanded pipeline from Edmonton to Vancouver.

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However, groups across the province have raised concerns about the new tax and the government's unwillingness to grant many exemptions. School districts have complained about the increased cost of operating buses and heating classrooms. Municipalities have raised similar concerns about increased costs without funding increases. In Calgary, an arena has warned parents to dress warm and pack a blanket as it says it might have to turn off the heat due to a jump in natural-gas prices.

"This is something that is crucially important to our climate," Deputy Premier Sarah Hoffman said on Thursday as she announced that the first rebate cheques were being deposited into bank accounts.

Individuals making less than $47,500 will get a rebate of $200 this year while a family with two children would need to earn less than $101,500 to get a $360 cheque. "Two-thirds of Albertans will get a rebate," Ms. Hoffman said. "Ordinary families, two-thirds of us, will be receiving one. If you have a higher income, you won't."

University of Calgary economist Trevor Tombe, however, said that only about one-third of Albertans will receive a rebate for the carbon tax.

The difference is in the language used. While someone in about 66 per cent of households will receive a rebate, that doesn't necessarily mean the entire house will get one. As an example, he said a 19-year-old living at home might get a small rebate while their parents might not.

Along with rebates and grants for non-profit organizations, the government has promised that it will unveil a new energy-efficiency program in the spring. But it has yet to reveal many details about the program or who will be eligible.

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One industry that successfully lobbied the government for a carbon-tax refund is the province's greenhouse operators. They learned only weeks before the tax took effect that they'll get an 80-per-cent refund on their carbon-tax costs, according to Debbie Foisy, the president of the Alberta Greenhouse Growers Association.

"We don't know the details yet. We don't know why it's only up to 80 per cent, but we're still hammering out the details," she said. The rebate amount does match a similar one given by the B.C. government to that province's greenhouse operators.

"It makes sense. Plants have this natural way of cleaning the air. It's a great cycle," Ms. Foisy said. "Some of our trees will live for 80 or 100 years. They'll absorb carbon dioxide for longer than we'll be here."

The tax is expected to increase heating costs for greenhouse operators by 30 to 50 per cent annually. While the greenhouses get good light in sunny winters and blazing summers, it's expensive to heat them through the prairie winter.

"We needed the government to understand that in a northern climate our plants help remove carbon dioxide from the air. We aren't an industry where there are big stacks of pollution going into the air," said Mohyuddin Mirza, a consultant who helped the greenhouse association in negotiations with the Alberta government.

Over the next two years, he'll help as the association studies whether plants grown in Alberta's greenhouses capture more carbon than the greenhouse industry generates. "We don't have good scientific data on that yet," he said.