Despite price reductions on kale, bananas and more after Amazon.com officially took control of Whole Foods this week, the grocer has long touted the superior quality of its food and retains an upscale vibe. So for the time being, shoppers are likely to find better deals elsewhere, including at industry giants Wal-Mart and Kroger. In a survey of 18 items, Bloomberg found Whole Foods was 50% more pricey on average than Wal-Mart.

Amazon put the grocery industry on notice in June, when it announced it had agreed to buy Whole Foods for $13.7 billion. And with the deal now complete, attention has turned to how the e-commerce giant will operate its newly acquired grocery stores as it tries to convince more shoppers to buy food online. Fears of a profit-crushing price war have weighed on stocks in the cutthroat grocery industry, which survives on famously thin margins.

While Amazon is expected to bring down prices as it tries to move beyond Whole Foods’ rarefied reputation, said Mikey Vu, a grocery expert at Bain, so far the reductions have been more about generating buzz than changing the perception that the chain caters to wealthy shoppers.

“Unless they slash prices, they’re not going to dramatically expand the income band of customers they go after,” Vu said. “It was a bold statement on the first day, but it wasn’t that many items that were moved.”

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The Bloomberg price survey was conducted on Tuesday at Whole Foods and Wal-Mart locations in Bellevue, Washington. Some items — canned tomatoes, black beans and corn for instance — compared Whole Foods house brands with the Great Value Wal-Mart store brand. Wal-Mart had lower prices for brands carried by both retailers, including Florida Natural orange juice, KIND snack bars, Nature’s Own whole wheat bread and Blue Diamond almond milk. Kettle Sea Salt chips were the one exception, costing $2.69 at Whole Foods compared to $2.98 at Wal-Mart.

The fruit, vegetables and canned goods were all cheaper at Wal-Mart, with the exception of bananas, which cost 49 cents per pound at Whole Foods compared with 56 cents per pound at Wal-Mart. The biggest price difference was for boneless, skinless chicken breasts, which cost $1.99 per pound at Wal-Mart and $5.19 per pound at Whole Foods.

Whole Foods sells only natural products that are fully compliant with animal-welfare standards, while Wal-Mart sells a range of groceries that don’t all meet Whole Foods’ lofty standards. Still, it could be tough to persuade cost-conscious shoppers to pay $1.99 for a can of Whole Foods corn that they can get at Wal-Mart for 68 cents.

Two other independent surveys found that prices at Whole Foods had barely budged since the Amazon takeover earlier this week. A Whole Foods in Princeton, New Jersey, reduced prices by an average of 1.2% compared to a week earlier, according to a Gordon Haskett Research Advisors review of 115 items. A separate review of prices at a New York City Whole Foods by Telsey Advisory Group determined Whole Foods prices remained higher than those at Wal-Mart and Kroger despite Amazon’s cuts. And Amazon has also raised prices: the cost of the salad bar at at least one location in Manhattan jumped from $8.99 a pound to $9.99 a pound this week.

It’s easy to understand the grocery industry’s pessimism. After all, Amazon has disrupted much of the retail landscape and made clear that it has groceries in its sights. The company offers Amazon Fresh grocery delivery in many cities and has even been testing out a convenience store concept. The Whole Foods acquisition gives it the brick-and-mortar presence it lacks to make a stronger play in the grocery market.

Still, taking on the entrenched players may well be harder than becoming an online leviathan in books, apparel and electronics. Most customers still prefer to shop for groceries in stores, and delivering fresh food is a tricky and expensive proposition that has vexed Amazon for a decade. Plus, even with Whole Foods, Amazon remains a small player, controlling less than 2% of of an $800 billion market dominated by Wal-Mart, Kroger and Albertsons. According to Moody’s, combined sales for Amazon and Whole Foods will be well below $20 billion, or less than one-tenth that of Wal-Mart.

Bezos has acquired a chain mired in a deep slump, with customers decamping for mainstream rivals offering better deals on natural and organic products. If Bezos was willing to break even at Whole Foods, taking margins on the chain’s high-end products to zero, Amazon could reduce prices across the board by as much as 15%, according to an estimate by Bain’s Vu.

But shifting the entrenched perceptions of Whole Foods, and bringing customers back in a bid to boost sales, will take time.

“Amazon won’t go kamikaze,” said Roger Davidson, a former grocery executive who runs an industry consulting business. “Over time the prices will surely go down, but those initial cuts were more about the media than actual pricing.”