Whole Foods is debuting lower prices in its stores Wednesday, and former Walmart U.S. President and CEO Bill Simon doesn't expect that the strategy will boost its sales. Whole Foods, known for its organic selection and premium prices, last made major price cuts in November 2017 after being acquired by Amazon. Simon said the new lower prices on select items, announced earlier this week, likely show the retailer is working through the kinks of the competitive grocery market. The recent price cuts are probably an "indication that [Amazon's strategy] hasn't worked the way they expected it to," Simon, a frequent critic of Amazon, told CNBC's "Squawk on the Street" on Wednesday. In response to a request for comment on Simon's remarks, an Amazon spokesperson said: "That's simply not true. Price reductions at Whole Foods Market have been successful and feedback from customers has been overwhelmingly positive — in fact customers have already saved hundreds of millions of dollars through lower prices and Prime member deals." Even with the announced average 20% off certain items, Whole Foods still has higher prices than other national grocery retailers. A recent analysis from Morgan Stanley revealed that a basket of items at Whole Foods costs $198, while it's $172 at a conventional grocery store and $157 at Kroger.

Average online grocery prices rise

A separate analysis from J.P. Morgan, which looked at online prices for a shopping list of 117 items, said prices in March broke a three-month streak of month-over-month declines, with the average price change up 1.8%. That makes it the highest price increase since the survey began, according to the report. Companies with price increases in the past month included Kroger, Sprouts, Publix, Amazon Pantry and Albertsons. However, two large retailers reported decreasing prices: Walmart and Whole Foods. More decreases could be ahead in April's report given Whole Foods' price cuts. In March, Whole Foods' pricing was down 1% month over month, according to the report. It follows February's 4% price increase. Walmart showed the most consistent decline in online pricing. Online costs were down 1% this past month, and J.P. Morgan said it has been steadily declining over the past year. "No other grocer in our survey has invested so consistently in pricing," according to the report. Walmart did not immediately respond to a request for comment. Prices for Target were reportedly down slightly, but no specific percentage was reported. Kroger saw its pricing rise 2%, which "wiped out the past 4 months' price investments," the report said. Retailer Sprouts also hiked prices by 3%, and analysts said that was as its price increases normally follow declines. Spokespeople for Kroger and Sprouts did not immediately respond to requests for comment.

A difficult market