Elderly and Handicapped Persons Transportation Act - Amends the Federal Aviation Act of 1958 to authorize reduced air fares on a space-available basis for persons 60 years of age or older and for handicapped individuals and their attendants. Directs the Civil Aeronautics Board to conduct a study and to report to the Congress on the feasibility and economic impact on air carriers of providing such reduced rate transportation for persons 21 years of age or younger.