“The president likes me as a media communicator,” Mr. Kudlow said, “so I will be more than happy to oblige.”

Most recent directors of the National Economic Council have not been academic economists, but the role has traditionally demanded more policy advice than salesmanship. The director is in effect the point person in the White House for economic issues, coordinating advice from across the cabinet and the West Wing. Mr. Trump’s advisers generally agree on tax issues, but they often diverge on trade, with warring factions between the traditional free-market group and a more populist group that reinforces Mr. Trump’s own inclinations and campaign talk.

Mr. Kudlow is a longtime advocate of free trade, seeing it as critical to America’s economic growth. He criticized Mr. Trump’s recent plan to levy global tariffs on aluminum and steel, but has since endorsed a slightly more tailored version of the tariffs that Mr. Trump announced this month. His predecessor, Gary D. Cohn, announced that he would step down after losing the battle over those tariffs.

Wall Street researchers were skeptical that Mr. Kudlow could persuade Mr. Trump to back away from his anti-trade agenda.

“We expect that the president and Mr. Kudlow will be at odds over trade policy,” analysts at Keefe, Bruyette & Woods wrote on Wednesday, “but that the president’s view will prevail.”

In the CNBC interview, Mr. Kudlow distilled the economic philosophy — including his love of tax cuts — that has animated him for four decades.

“I believe, first of all, the greatest and most important thing for this or any other country is rapid prosperity for everyone,” Mr. Kudlow said. “If you keep tax rates minimal, if you keep regulations and government spending minimal, if you keep the dollar sound and steady, you are going to have a terrific economy.”