Production problems with the guidance system of the MX intercontinental ballistic missile will cost taxpayers millions of dollars in unexpected expenses, according to the General Accounting Office.

The agency found that problems with the critical guidance system drove Northrop Corp.'s first production contract up by $30 million -- about 10 percent more than the original $338.8 million price tag for 52 guidance systems.

The Air Force will pay $21 million of that because some of the problems in the guidance system, called the inertial measurement unit (IMU), have been attributed to parts the government supplies Northrop from subcontractors.

House Armed Services Committee Chairman Les Aspin (D-Wis.), who released the GAO study, said problems in the production of the MX missile are more serious than originally believed. About 40 percent of the 30 MX missiles now in underground silos are unable to go on alert because Northrop has fallen so far behind in delivery of the system, according to Air Force officials.

"My impression is that the firm is taking the problems very seriously, and addressing them with their best people," Aspin said in a statement. "But it appears the problems are more intractable than thought." Both Northrop and Air Force officials say they expect the company to begin meeting schedule deadlines before the end of this year.

The $20 billion MX program is the land-based leg of President Reagan's strategic defense buildup. Another cornerstone of the triad, the B1 bomber, also has been plagued by serious problems that have limited the capability of the bomber force. The third leg is the Trident submarine.

Northop has been issued three production contracts and three other development and spare parts contracts on the MX guidance system, totaling $1.6 billion. The 10 percent cost increase cited by the GAO involves one of those contracts.

"It is premature to estimate the total cost resulting from late IMU deliveries and Northrop's efforts to recover contract schedule until Northrop is back on schedule and has demonstrated the ability to consistently deliver IMUs on schedule," according to the GAO, the congressional watchdog agency. Northrop Corp. has been trying to correct numerous problems with the guidance system for several years and is working on the ninth variant of the guidance system.