The question has dogged the company (GOOG) in recent years. Investors have been concerned that advertisers pay less for mobile ads than they do for Web ads, and analysts have warned that searches could become less important in a world dominated by apps.

But a new report by Marin Software, which manages digital advertising campaigns worth billions of dollars on behalf of marketers, suggests that fears are overblown.

“The market has been a bit pessimistic as to how Google would fare in the mobile migration,” said Chris Lien, Marin’s chief executive. “The data here demonstrates that they are managing the migration to mobile in a way that is sustaining their business and adding to it.”

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When it comes to search advertising, Google’s core business, Marin found that mobile accounted for 34% of all clicks on ads in December, up from 21% in January. Marin projected that by 2015, half of paid search clicks will be coming from mobile devices. Importantly, the gap between the price marketers pay for desktop and mobile ads has narrowed significantly. On average, advertisers paid $0.83 every time someone clicked on a desktop ad in 2013, compared with $0.58 on a smartphone ad and $0.76 on a tablet ad. Marin said that the cost of an ad click on a tablet should surpass that of a desktop ad this year. The report is based on data from a mix of large advertisers who collectively spend about $6 billion a year in search ads.

The figures cloud help ease concerns that advertising on mobile is inherently less effective than on desktop. Indeed, Marin found that prices for mobile search ads grew more than twice as fast in mobile than on desktop. Overall, Google has reported slight declines in the cost-per-click of ads over the past two years, but Lien says those declines include all types of advertising, not just search ads.

The survey by Marin, whose business depends on the effectiveness of digital advertising, also found that mobile ads lead to purchases about as often as desktop ads do. “Conversion rates have increased dramatically on mobile,” Lien said.

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Despite ongoing concerns from investors, big Internet companies like Facebook and Google appear to have managed the shift to mobile better than most. The new report suggest that some efforts, like Google’s new “enhanced campaigns,” which blend mobile and desktop ads, are paying off even faster than anticipated.

“Google is successfully migrating their ad units and business model to better meet the needs of advertisers and consumers,” Lien said. “Consumers are responding well to the mobile ad placements.”

Over the past year, Google shares have soared from about $800 to more than $1200 as the company successful diversified its business in areas like video advertising and mobile content. Google shares closed Tuesday at $1211.26, up 1.6% for the day.