The beverage industry has already spent about $14 million to defeat three controversial soda tax measures on Bay Area ballots next month, and almost all of their ads use the phrase “don’t tax our groceries.”

The advertisements claim that not only will sugary drinks cost more if the measures pass, but so will everything else at the market. But is it true that everything from paper towels to broccoli will be more expensive?

Probably not.

Two separate studies being conducted in Berkeley, where a soda tax passed two years ago, show that grocery prices have not gone up. Interviews with grocers in San Francisco also cast doubt on the business strategy of raising all prices to compensate for more expensive soda.

Sam Mogannam, owner of Bi-Rite, said the idea he would voluntarily raise prices on everything in his store is ludicrous.

“No retailer would ever do that,” said Mogannam, who supports the soda tax and called the soda industry’s claims that it is a “grocery tax” a scare tactic intended to cause confusion among voters.

“Nobody’s going to want to raise the price of a loaf of bread or a box of cereal to offset the cost of soda,” he said. “Then the price of cereal wouldn’t be in line with the competition.”

The soda tax measures on the ballot in San Francisco, Oakland and Albany all work essentially the same way. They would levy a 1-cent-per-ounce tax on sodas and other sugary drinks at the distributor level, with the proceeds going to those cities’ general funds.

City officials say they’d spend the money on programs to combat diabetes and obesity, though they wouldn’t be compelled to do so. Berkeley was the first city to pass such a tax, in 2014, and Philadelphia has since followed suit. Mexico also has a soda tax. In addition to the three Bay Area measures, another is on the ballot in Boulder, Colo.

Jim Krieger, executive director of Healthy Food America, said the soda industry is using the “grocery tax” claim to scare people. California law prohibits taxing many items in grocery stores, including unprepared food, he pointed out.

“It’s Big Soda using a time-honored tactic of taking a lie and saying it loud enough and enough times that people think it’s true,” he said. “The wording is crystal clear. It’s a tax levied on distributors of sugary drinks, and not on grocers and not on groceries.”

Last month, an Alameda County Superior Court commissioner sided with the pro-soda tax side over the “grocery tax” issue. The soda industry had challenged wording in Oakland ballot materials saying “the tax is not paid by your local grocer,” but the commissioner said the wording was accurate.

Unlike, say, state taxes on cigarettes, state law prohibits a city from taxing just one product directly. But cities may tax the distributor of the item, which is how soda taxes work. The distributor is the first person to bring the item into the city’s borders.

In the case of stores like Bi-Rite or Safeway, that’s usually a distributor who serves as the middleman between a soda producer like Coca-Cola and the grocery store. In the case of a small mom-and-pop grocer, that’s often the owner who goes, for example, to Costco in South San Francisco, buys the soda and sells it at a higher price at his or her store. In that case, the owner would have to pay the tax.

If the soda taxes pass, distributors can decide whether to pass on the higher price to grocery stores, which in turn can decide whether to pass on the higher price to customers. In theory, the grocers could decide to raise the price of everything slightly to recoup their costs rather than make only soda more expensive. But in practice, at least in Berkeley, that hasn’t happened.

Jennifer Falbe, a UC Berkeley postdoctoral researcher in public health, has interviewed 33 owners of supermarkets, small grocery stores, convenience stores, liquor stores, restaurants and a drugstore that sell beverages in Berkeley.

Of those, none reported raising the price of anything other than beverages since the soda tax went into effect. Nineteen said they raised the price only on those sugary drinks that are subject to the tax. Three said they also raised the price of diet soda, which isn’t taxed. Two said they raised prices on all beverages, including bottled water. Nine didn’t raise prices at all.

“We’re just not seeing the prices of non-beverage items, like produce, going up,” Falbe said. “We would expect similar results in other places that implement sugar-sweetened beverage taxes.”

A separate study being conducted by the Public Health Institute and the University of North Carolina has researched grocery bills from two major chains that have stores in Berkeley and elsewhere. Andronico’s identified itself as one of those chains, but the other chain has not been named.

In preliminary data from the first six months of the soda tax being collected in Berkeley, the study found people are buying fewer sugary drinks and more untaxed drinks, like bottled water, making sales totals for drinks about stable. Overall grocery bills have also stayed the same.

“The industry has been calling this a grocery tax,” said Lynn Silver, a senior adviser at the Public Health Institute. “In our preliminary six-month data, we didn’t find any evidence to support that.”

The campaign to defeat the soda tax measures, funded solely by the soda industry, says it has 1,000 small business and restaurant owners on its side. It has recruited many of them to star in television and radio ads and to appear in campaign mailers for no compensation.

There’s plenty for grocers and restaurant owners to dislike about the soda tax. It makes the product more expensive in an already expensive region, and many of those kinds of businesses already make very little profit. The California Grocers Association, the Golden Gate Restaurant Association and the Hispanic Chamber of Commerce in San Francisco all oppose the tax.

Joe Arellano, spokesman for the campaign to defeat the soda taxes, said the tax could be especially bad for mom-and-pop stores that are already on the verge of closing in the pricey Bay Area. Raising prices across the board may be a necessity if the tax passes, Arellano said.

“A lot of our grocers have told us it doesn’t make sense for them to raise the price of one thing 50 to 60 percent when they can raise everything across-the-board just a little bit to make it less impactful,” he said.

But interviews with a handful of the grocers used in the soda industry ads showed some confusion about the notion of grocery taxes.

Humberto Felix, owner of Casa Lucaz in the Excelsior district, stars in a campaign mailer reading “Don’t tax our groceries.” But asked if he would raise the prices of all groceries in his store if the soda tax passes, he said, “No, no, no. Only the one with the taxes, you know?”

Still, he was clear that he opposes the soda tax because everything in San Francisco costs so much already.

Abdul Taleb, owner of Mi Carnal Market in Oakland, said he definitely plans to raise the price of all items if the tax passes.

He said he currently sells a 2-liter bottle of soda for $2. If he offset the soda tax by increasing the price of just the soda, that same container would cost $2.68. He said he’d certainly lose customers, so he’s more likely to consider the tax an additional overhead cost, like rent and utilities.

“I would spread it out 5 cents here, 5 cents there,” he said. “That way it doesn’t seem as obvious to you as a customer.”

Suzy Monford, CEO of Andronico’s, has already been faced with the question of whether to raise the price of sodas or other items, too. She runs stores in San Francisco, San Anselmo and Los Altos, plus two in Berkeley where the soda tax already exists.

Her Berkeley stores have added the exact amount of one penny per ounce to the drinks subjected to the tax, and have not changed prices on anything else.

“You see a six-pack of soda in Berkeley, and you go, ‘Holy cow! One more of those, and I could get a bottle of wine!’ That’s where I choose to get my sugar,” she said with a laugh.

Of the 15,000 to 20,000 items an Andronico’s store sells, the soda tax applies to just 50 to 60 of them, Monford said. The tax has worked out just fine for Andronico’s, because shoppers are following the trend nationally of buying less soda — and instead buying more expensive drinks like Kombucha tea, coconut water and bottled water.

Of the industry’s claims that a soda tax means more expensive groceries of all kinds, Monford said, “It’s an absolute fallacy.”

Though he runs a very different kind of store, Fouad Hussein agrees. The owner of Family Market on Broad Street in San Francisco, Hussein said he’ll add the exact amount of the tax to sodas to offset the cost.

He’s fed up with the city’s overflowing trash cans, dirty streets and insatiable hunger for taxes, but he said that’s no reason to make everything more expensive for his customers.

“If they raise 40 cents on soda, I’ll collect it from the customer,” he said. “That’s how I’d do it.”

Heather Knight is a San Francisco Chronicle staff writer. Email: hknight@sfchronicle.com Twitter: @hknightsf