Who pays piper? Who calls tune?

''All contributions are tax-deductible.'' The inducement is familiar. But in the area of subsidized arts institutions, some benefactors are more equal than others. According to a new Twentieth Century Fund study, the wealthy benefit disproportionately more than the less affluent under the present system of tax-deductible giving. The report asserts that the rich also exert an undue influence on the policies of arts institutions.

Copiously supplied with charts and tables, the 163-page study is entitled ''Patrons Despite Themselves: Taxpayers and Arts Policy.'' It was prepared by Alan L. Feld of Boston University, Michael O'Hare of Harvard, and J. Mark Davidson Schuster of the Massachusetts Institute of Technology. It is published by New York University Press.

The report claims that almost two-thirds of government support received by the arts is provided indirectly through tax deductions taken by rich donors. The taxes such well-heeled individuals do not pay (big donors get proportionately larger tax breaks than small contributors) must be compensated for by higher payments on the part of all other taxpayers.

In 1973 (the most recent year for which complete data are available), direct government arts aid through the National Endowment for the Arts and other agencies totaled $200 million. Indirect aid (through tax deductions) amounted to about $460 million.

How do wealthy donors seek to influence arts policy? Here are some illustrations cited in the report:

* A $6 million gift to the expansion program (launched in 1977) of Harvard University's Fogg Museum stipulated that the expansion include an entire new building. Harvard insisted that in order to accept the gift, the Fogg must raise an additional $3 million to cover the new building's carrying costs.

The Twentieth Century Fund study notes ''philanthropists' preference for bricks and mortar rather than endowments or operating costs,'' and further observes: ''The professional staffs of art institutions are not immune to this 'edifice complex.' ''

* Numerous Metropolitan Opera productions are financed by the Opera Guild, the National Council, ''or any other individuals or corporations willing to make gifts for this purpose . . . some for surprising reasons. Cornelius Starr, a New York insurance executive, commissioned a new production of 'Madame Butterfly,' citing his impatience with the old production's unforgivable anachronisms: cherry blossoms (a spring flower) and chrysanthemums (an autumn flower) side by side on the same stage.''

* ''Corporations . . . have political interests: One of public television's most important sponsors, the Mobil Oil Corporation, set many teeth on edge when it publicly attempted to have a program likely to offend the Saudi Arabian government canceled.''

* The Joffrey Ballet cut its ties with the Rebekah Harkness Foundation, ''a source of considerable support, when the foundation requested that the ballet change its name to the Harkness Ballet and allow the foundation officers an unspecified amount of control over the artistic decisions of the company.''

The new report ran into immediate challenges when it was introduced at a press luncheon at the Twentieth Century Fund's posh town-house headquarters here. Even though most of those present had not had time to read the study, its authors were sharply questioned as they summarized and defended their findings.

A persistent critic was Thomas P. Hoving, former director of the Metropolitan Museum of Art. The study's recommendations, which tend toward a more populist approach, would ''wreck the art institutions,'' according to Mr. Hoving.

Messrs. Feld, O'Hare, and Schuster offer various reforms of the present system. They would replace income-tax deductions with tax credits. They suggest ''sunset'' legislation that would remove restrictions on charitable gifts ''after a reasonable period, perhaps 25 years.'' And they would eliminate property-tax exemptions for cultural institutions. In seeking moderate reforms, they put forward seven questions to ask about any subsidy program: Who pays for it? How? How much? Who decides how the money is spent? Who benefits from it? How? How much? The answers they leave to public debate.