There is hereby created a body politic and corporate to be known as the "Educational Facilities Authority for Private Nonprofit Institutions of Higher Learning," hereinafter in this chapter called the Authority. The Authority is constituted a public instrumentality and the exercise by the Authority of the powers conferred by this chapter shall be deemed and held to be the performance of an essential public function. The Authority shall consist of the members from time to time of the State Budget and Control Board, ex officio; and all the functions and powers of the Authority are hereby granted to the State Budget and Control Board as an incident of its functions in connection with the public finances of the State.