Andrew Young's brand of outspoken diplomacy made him a household name after President Carter appointed him ambassador to the United Nations this year, but Young is running short of cash. Which is why he may be one of the few cabinet members in recent history permitted to write a book while still in office.

Young's new visibility may eventually pay off in the form of book sales, but right now he's making less money as an ambassador than he did as a congressman. In 1976 his House salary was $44,600 and he picked up $16,525 in lecture fees. Now his gross pay is a few thousand dollars less: $57,500. The expenses of four children and living well in Manhattan prompted him to ask Carter's permission to begin a book immediately, according to Scott Meredith, his literary agent. Meredith says before Young accepted his current job, Carter gave him "a tacit promise" he could earn some outside money with a book. Meredith says Young has the book proposal "written in his mind." Now he just has to write it on paper, and Meredith will begin selling.

Footnote: Another member of the administration, national security adviser Zbigniew Brzezinski, postponed publication of a book he had written for a subsidiary of Harper & Row before he went to work for Carter. The editor-in-chief at Harper & Row, Erwin Glikes, says he hopes to have first crack at Brzezinaki's memoirs when he retires, but that it will be Brzezinski's decision.