Delta's strategy to increase its offering of higher-end seats is paying off. 

For the second quarter, Delta reported a 4.6% increase in the average fare that passengers paid per mile -- a key airline industry metric known as yield. The bump was driven by an 8% increase in premium seats in the second quarter, Delta president Glen Hauenstein said during the carrier's earnings call Thursday. Those seats drove a 20% increase in premium revenue. 

Delta counts as premium all seats located in its domestic first class, Delta One international business class and new Premium Select cabin that for now is available almost entirely on transpacific routes. The carrier also counts its Comfort Plus extra legroom product in the economy cabin as a premium offering. 

Delta flies just one transatlantic route with Premium Select, but plans to offer the product throughout its international fleet by 2021.

"Our fleet sets up nicely over the next few years to continue to expand those number of seats," Hauenstein said. 

Strength in the transatlantic market also boosted Delta's results during the second quarter. Yields on transatlantic flights were up 11.1% compared with just 2.5% in the domestic market. 

"With higher fuel prices, you're going to continue to see ticket prices go up, as well," Delta CEO Ed Bastian confidently predicted during the call.

His comments came on the same morning that the Department of Labor released its monthly Consumer Price Index, which showed that airfares dropped 0.9% between May and June, the third straight month-to-month decline. 

For the second quarter, Delta reported net income of $1.03 billion, down 14% year-over year. 

The carrier's revenue for the period jumped 10%, to $11.78 billion. That increase was more than countered by a 15% jump in expenses, more than half of which was due to a $578 million, or 33%, increase in fuel costs. 

Delta reported earnings per share in the second quarter of $1.77, beating analyst expectations by a nickel, according to the website Seeking Alpha.

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