In the land of the free and the home of the brave, these developments took place last week:

* Auditions began in New York for a Broadway musical called "Mayor." It is written by Warren Leight, with songs by Charles Strouse, and is budgeted at $228,000. It is based on the book of the same title by Edward I. Koch, the city's mayor.

* Geraldine Ferraro's participation in a television commercial for Diet Pepsi was predicted by Advertising Age and confirmed by The Washington Post. Ferraro, who was the Democratic nominee for the vice presidency last year, will be paid more than $500,000 for the commercial, in which she is shown chatting with her two daughters and advising them that "there are lots of choices for women and one of the choices is that you can be a mother," the precise pertinence of which to Diet Pepsi presumably will be revealed at some future date.

* Ralph Nader sent a letter to President Reagan urging him, as "custodian of matters relating to presidential taste and decorum," to "urge that businesses rein in their promotional addictions and permit the historical record, not advertising sleaze, to speak for our past presidents and founders." Nader's ample supply of indignation was in this instance set off by TV commercials depicting the likes of Thomas Jefferson, Benjamin Franklin, George Washington and Abraham Lincoln peddling everything from banks to (Japanese) automobiles.

Not for the first time, Nader thereby put on public display his bottomless capacity for naivete'. Surely he cannot imagine that a man who came to the White House by way of fronting for General Electric is going to be offended at the sight of presidents leaving the White House and fronting for other enterprises -- even if those presidents are many generations dead and are portrayed in these commercials by actors, for whom as a breed, as it happens, the incumbent has deep affection. Surely, by the same token, Nader cannot imagine that much of anybody, in this age of sleaze, is going to be offended by yet another exploitation of public position for private gain.

The surprise isn't that Tommy Jefferson is hustling banks but that Ralph Nader is surprised. The ad agency that came up with the idea of using George Washington -- "Nutty George," as Bob Newhart used to call him -- to push Nissan automobiles was just playing by the rules of the game, as the game is now played. In the United States of Glitz, the ultimate mark of prestige is not election to high public office but the opportunity to prostitute one's dignity and integrity -- if, that is, one ever had any of either -- in a television commercial. In going show biz the politicians, both dead and alive, are merely doing what politicians always do: following the crowd.

What did Sam Ervin do after lecturing the nation, month upon month, about momentous matters of ethics and morality? He signed himself up as a shill for American Express. What did Gerald Ford do, after two years of healing our national wounds? He signed up for those two indistinguishable, interchangeable American institutions, the celebrity golf tour and the college lecture circuit. What do all White House custodians, United States senators and Foreign Service plenipotentiaries do the moment the opportunity presents itself? They write books, or, with the aid of ghosts, they "author" them.

Public service isn't public service anymore, if ever it was. It's the springboard to Fat City, the land of grab and grasp, where sly fellows turn the notoriety acquired through public office into the real coin of the realm, plugola. Edward Koch may have assumed office with every intention of being the best mayor since Abraham Beame, but it didn't take him long to grind out a book -- the most unlikely best seller of recent vintage -- and then to suggest that it would make a dandy Broadway show; Geraldine Ferraro may have accepted her nomination with every expectation of speaking for newly liberated woman, but when Bantam Books ($1 million) and Pepsi ($500,000) came courting, she was as willing as a southern belle being romanced by Rhett Butler.

Money, money, money: Can you use any money today? That's the question Ethel Merman asked in "Call Me Madam," and it's the question to which the guys and dolls of politics respond with a thundering chorus of "Gimme!" Never in our history has the line between grasping for political power and grasping for personal riches been more difficult to distinguish. A presidential adviser writes a diet book while in office, and no one seems offended by what gives every appearance of being an effort to capitalize on the prominence of his public position; no one seems to be offended because no one isoffended in a capital city where such exploitation has become a fact of daily life.

Where's Ralph Nader been all this time, anyway? As usual, the guy simply is out to lunch. Instead of saving the world, he ought to be strip-mining it. He's got a name, and it's a cinch the fellows in ad alley would say he's got credibility. Surely there's a spot for Ralph in the Miller Lite gang, maybe filling in for Rodney Dangerfield from time to time. Don't you know Lee Iacocca would love to get his hands on Ralph? "Hello there. I'm Ralph Nader. When I go out for a day of raiding, I go in my Chrysler. I wouldn't drive anything else. It's got seat belts, air bags and a registered nurse in the trunk. It's safe at (wink!) any speed!"

Run that through the Super Bowl a couple of times and before you can say "Ed McMahon" Ralph Nader would be famous. Not Jack Kemp famous, or Bob Dole famous, or Cap Weinberger famous, but famous. You know: Dinah Shore famous, Chuck Yeager famous, Robert Young famous. And soon to enter the club, Gerry Ferraro famous. Soon the kids will be saying about her, "I never knew the Diet Pepsi lady ran for vice president," just the way they already say, "I didn't know Mr. Coffee used to play baseball."

It's the new American immortality, and Nader is just whistling Dixie if he thinks anyone in Washington, dead or alive, is going to say no when it beckons. "Howdy! I'm Honest Abe! You'll find the cheapest deals in town under the sign of the stovepipe hat! Seventy-nine Malibu, four on the floor, make me an offer! I don't split rails, I split the difference! Got an '82 Mustang that's screamin' to leave the lot! It's got YOU written all over it! At Honest Abe's, no offer is too low and the customer is king! Come on out to Honest Abe's and I'll give you a special T-shirt just for takin' a test drive! I'm Honest Abe, and I ain't got NO malice towards noooooooooBODY!"