The Biden super PAC has actually outspent the campaign on the airwaves in Iowa — but that money buys far fewer ads than the campaign’s cash can because federal law allows political candidates to buy advertising at the lowest available rates.

The disparity is jarring, with the Biden super PAC paying four times as much for the same ads as the campaigns, blunting the advantage of having a super PAC.

Mr. Sanders, for instance, paid $375 for 30-second ads on the 6 a.m. news on KCCI in Des Moines last week; the Biden super PAC paid $1,800. To air one ad during the Grammys, Mr. Sanders paid $1,350 and the Biden super PAC paid $5,500.

“The cost difference is real,” Mr. Schale said. “At the same time, it is the most obvious gap we can help fill.”