Students of Parkinson's Law - work expands to fill available time - will be happy to know that a new corollary thrives in Washington: public bureaucracy breeds private buraucracy.

The more government expands, the more it stimulates a vast supporting apparatus of trade associations, lawyers, lobbyists, research groups, economists and consultants - all trying to shape the direction of new federal regulations and spending programs. At last count, about 2,500 major trade associations had their headquarters in the Washington area, roughly 27 percent of the national total. In 1970, that was only 20 percent.

The public and private bureaucracies are both adversaries and allies. Superficially, they fight; in reality, they need each other. They engage in mutual flattery, shuffle paper among themselves and talk incessantly. Washington has more telephones per capita (145 for every 100 people) than any other city.

It is doubtful that any other city in the world spends so much time and money producing so little as Washington. The biggest manufacturing operation is The Washington Post, which simply reports everybody else's non-productive work.

But if all this is often a wasteful, chaotic and absurd business, it is not evil. It is called democracy, and it reflects the waste, chaos and absurdities of government which - in striving to make life better for everyone - is often asked to do too much for too many.

None of this is "news"; it has been going on for years. But it is useful to remind yourself that the evolution is continuing: that more and more private groups find they must have a presence in Washington to defend their interests.

This is the meaning of a "mixed economy" in the United States. Economic success is determined not only by market power and efficiency, but also by political effectiveness in Washington.

A recent item in the mail provided just such a reminder. It came from the Associated Retail Bakers of America. The bakers are latercomers to Washington. Indeed, until last year, they didn't have a Washington Office. The association's general counsel - working out of Annapolis, about 45 minutes away - handled most government problems. But, according to Jerry Panaro, the new associate director for government affairs, the problems multiplied too fast.

"The Food and Drug Act affects our members with packaging and labeling requirements, and all our members are small business employers. We follow fair labor standards, minimum wage and occupational health and safety (requirements). Also, more recently, social security and job tax credits," he said.

The bakers latest complaint involves the food stamp program. The headline of the bakers' Government Bulletin, sent to its 2,000-plus members, makes the problem clear:

RBA Needs Your Help to Assure Food Stamps Eligibility of Retail Bakers

It is hard to imagine an issue that better magistrates the silliness of much on the struggling and feuding that occurs between the public and private bureaucracies.

Food stamps, of course, are one of the government's most massive programs. In the current fiscal year, Treasury will spend more than $5.1 billion for food stamp benefits, now being received by about 16 million to 17 million people. Naturally, the retail bakers want their piece of the pie.

And that is just the trouble. Congress doesn't necessarily believe that food stamp recipients should be gorging themselves on pies, cakes or chocolate chip cookies.

The food stamp program allocates a family just enough money to achieve a nutritious diet under the Agriculture Department's "thrifty food plan." But that assumes the food stamp beneficiary spends the money wisely. This means cheese, milk and vegetables, not strawberry shortcake or Twinkies.

So, naturally enough, Congress wanted to eliminate the stigma of shoveling out taxpayers' dollars for sweets and junk food. Unfortunately, that's easier said than done.

"Ever since 1964, they've tired to come up with (a definition of) eligible food that would result in recipients buying only nutritious food," said an aide at the Agriculture Department's Food and Nutrition Service. "But even nutritionists disagree. And then you have the administrative difficulty of stores determining what recipients can and can't buy." Although some items (such as liquor) are ineligible, Congress abandoned this approach as impractical.

It is the new strategy that offends the bakers. Under its amendments to the food stamp law last year. Congress said that only food stores whose sales consist at least of 50 percent or more of "staple" foods could qualify to accept food stamps.

Staple foods were defined to include "meat, poultry, fish, bread, cereals, vegetables, fruits, fruit and vegetable juices and dairy products," but to exclude "accessory food items such as coffee, tea, cocoa, carbonated drinks, candy, condiments and spices . . ." The bakers' group figures that bread does not constitute half of most bakery sales, and, consequently, most bakeries will not qualify. This means that the government won't give them cash for their food stamps.

Tough luck for the bakers? Look at it from their perspective. The new law doesn't say that food stamps cannot be used to buy "non-staple" foods. Recipients still can go into grocery stores to stock up on cupcakes, coke and candy. Understandably, the bakers feel cheated.

There is a certain pointlessness in this sort of legislation and regulation. It is unlikely that the restriction will cause food stamp recipients to improve their diets. The only result is to anger a few bakers. And, although the example is trivial, it is precisely the sort of irritation that accounts for much of business' rabid anti-Washington attitude.

But the growing blanket of regulation and legislation also has spawned a corresponding opportunism among business groups. There is still a lot of rhetoric about "free enterprise," but most of it is hypocritical.

Business may not like much of the new regulation, but, it has decided that if it has to live under the federal whip, it might as well feed at the federal trough. There is hardly a major business group that doesn't want some form of government subsidy, trade protection, loan guarantee or handout.

Parkinson would love it.