Pan Am Corp.'s directors, impatient with union opposition to cost-cutting, took the drastic step of authorizing the liquidation of its ailing Pan American World Airways. Pan Am, whose first-quarter operating loss widened to $62 million from $51 million in 1987, has unsuccessfully sought wage concessions from its flight attendants and mechanics and had threatened "radical changes" if its union workers did not cooperate in cost-reduction efforts. The board gave Pan Am's management authority to sell the airline's assets, "including route segments and divisions, maintenance and terminal facilities, aircraft, engines and other equipment," the spokeswoman said, reading from a letter sent to employees.