Painting a bleak picture of the economic fortunes of Detroit and its newspapers, the city's two competing dailies yesterday officially asked the Justice Department to allow a joint operating arrangment under the Newspaper Preservation Act.

Submitting the detailed request almost a month after announcing their plans, Gannett Co. Inc., which owns The Detroit News, and Knight-Ridder Inc., which owns the Detroit Free Press, argued that economic problems in Detroit helped cause operating losses totaling almost $63 million at the two papers over the last five years.

The application said the Free Press is losing in the city's newspaper war and thus qualified as a "failing newspaper" under the act. The law permits papers to combine their business operations to preserve editorial competition that would be lost if one paper went out of business.

The document argues that operating losses of $39.1 million over the last five years at the Detroit Free Press "far outstrip the losses of any prior" applicant for a joint operating arrangement. Jointly operated newspapers in 21 other communities already have won antitrust exemptions under the act.

The losses for the News were listed as $23.8 million for the last five years, although the report showed that the company earned a profit of $667,000 in 1985.

The document said losses stemmed in part from the "combination of high inflation and a severe economic recession that struck particularly hard at the automobile industry" in the Detroit area.

It also argues that losses at the Free Press are "emphatically not a case in which the failing newspaper's losses have been created through 'creative bookkeeping' or resulted from 'culpable mismanagement.' "

The proposed antitrust exemption already has stirred strong feelings in Detroit, where journalists from both papers said they felt the agreement would sap their urge to compete vigorously. Donald Kummer, administrative officer of the Detroit Newspaper Guild, said shortly after the plan was announced that the union was studying the possibility of trying to block the agreement either in the courts or through the Justice Department.

Detroit Mayor Coleman Young also has spoken out against the agreement, which many believe would end the stark differences between the two newspapers. Others have argued that Knight-Ridder should offer the Free-Press for sale before setting up the agreement.