West Lafayette, Ind.

Mitch Daniels teaches a course on World War I at Purdue University, where he is president, and loves to talk about Woodrow Wilson. Wilson left the presidency of Princeton in 1910 and was elected governor of New Jersey the next year—“sort of the opposite of the thing I did,” says Mr. Daniels, who served two terms as Indiana’s governor (2005-13) before taking his current job on campus: “Explaining his decision to abandon the academy for a statehouse, Wilson said, ‘I can’t take the politics anymore.’ ”

I’ve just asked Mr. Daniels—who, unlike Wilson a century earlier, decided against seeking the U.S. presidency in 2012—how running a university differs from running a state. The silver-tongued Mr. Daniels offers a quip that must play well at the meet-and-greets that clog up a college president’s calendar. “I use an old line,” he says without missing a beat, “which is that in my last job it was dog-eat-dog, and here it’s just the opposite.”

Mr. Daniels, 69, is the most innovative university president in America. Like his counterparts at other schools, he believes higher education has been “a competitive advantage” for the U.S.—“a nice little export industry, if you add up all the dollars that come here to purchase the education of students from other places.” He regards the rumbling in Washington about curbing visas for foreign students to be “very shortsighted.” But he also thinks American higher education has grown fat and complacent. He’s making inventive, even radical changes in the way his institution finances itself and imparts an education.

Mr. Daniels kicks off our conversation with a morality tale: “I’ll speak to an audience of businesspeople and say: Here’s the racket that you should have gone into. You’re selling something, a college diploma, that’s deemed a necessity. And you have total pricing power.” Better than that: “When you raise your prices, you not only don’t lose customers, you may actually attract new ones.”