In 1977 the American Enterprise Institute has established itself as a prosperous think tank that serves partly as a Republican shadow government in Washington. At its helm is the patriarch of a little-known Republican family, William Baroody Sr., the son of a Lebanese immigrant stone-cutter, who is grooming another generation of Baroodys to provide government with the benefit of his conservative political philosophy.

Baroody joined AEI in 1954 and coaxed the non-profit, public policy research organization to promonence. Now its $6 million budget and an impressive roster of scholars, economists and political thinkers makes it the Brookings of the right. His oldest son, meanwhile, went to work for Melvin Laird in Congress, then the Pentagon, and eventually served as President Ford's public liaison man - the position Midge Costanza now holds. This year Baroody Sr. put both his son and Gerald Ford and AEI's payroll.

"I had studiously avoided coming over here at first," admits the younger Baroody. But after seventeen years of working for the government, he compared his earning potential with the cost of putting his nene children through college and decided it was time to work for dad. He is now AEI's executive vice president.

Says his father: "Part of his reluctance was the fact that AEI is a non-profit institution. But his better judgement took hold and he realized his contributions would do more for the future of his children than moving into the corporate world where he might have to concentrate on making washing machines."

What AEI tries to make is public policy by conducting seminars, funding studies and publishing magazines and newsletters. The two Baroodys (dad is 62, son is 40) work one door away from each other in modern offices near 17th and M Steets; both earn a salary in the high-$50,000 range - at the White House, Bill, Jr.'s salary was in the low-$40s. Their first joint decisions was to name Gerald Ford AEI's "distinguished fellow." Which means the former President receives $35,000 from AEI which books him on at least ten campuses annually in conjunction with AEI programs.

Other Republicans currently thinking writing or lecturing for AEI: economists Paul McCracken and Milton Friedman, essayist Irving Kristol, attorney Robert Bork, speechwriter Raymond Price and others. Democratic strategist Ben Wattenberg and political strategist Austin Ranney, among others, keep AEI bipartisan.

The elder Baroody happily admits outside interests, such as several college trustee positions, may lead him eventually to take a less active role at AEI; that his eldest son is the think tank's heir apparent is, well, quite apparent. When his son was at sea in the Navy in 1959, Baroody put him on AEI's mailing list; he knew his son had little else to read. "By virtue of coincidence, it all worked out fortunitously," says Baroody Sr., with undisguises self-satisfaction.

Footnote: another Baroody son, Joe, is part owner of the firm that handles AEI's public relations, another is, as his father puts it, "director of research for a small political party called the Republican National Committee."