FOR 29 CENTS each -- less than a cup of coffee costs you in most places these days -- about 500 people bought round-trip airline tickets from Boston to New York last Sunday. A Washington's Birthday sale? No. It was New York Air's way of announcing its arrival in Boston.

New York Air, an offspring of Texas International, is one of the new airlines created as a result of deregulation. Before moving into Boston, it was already challenging the hold that Eastern on the Washington-New York traffic. It doesn't expect to sell tickets for 29 cents again, but it does expect and thus win a share of the passengers.

This kind of competition -- Eastern countered with a weekend excursion fare as soon as its new competitor showed up at National Airport -- is giving the well-established airlines fits. There have already been some mergers, and there are likely to be more. A few airline officials were saying just last week that if pilots went on strike next month, as they were then threatening to do, some companies might just go out of business. The competition is that fierce on some routes where deregulation has meant travel bargains for passengers. On other routes, however, the primary result of the end of governmental controls has been higher air fares.

The economics of deregulation, in other words, is making life hard for many big companies in this industry. Further moves toward deregulation could have a similar effect in other industries, although some of the early proposals of the Reagan administration do not indicate that is precisely what it has in mind; cutting back OSHA and enforcement of the antitrust laws will not cause problems for big business.

Government regulation, after all, has a double function, protecting consumers and workers against business abuses on one side and protecting business from competition on the other. As the new administration unfolds its version of getting government off the back of business, it should keep in mind the relationship between these two functions. Not all the regulations that need to be undone are strangling business; some of them are unnecessarily pampering it.