Trade problems between the United States and Mexico, this nation's third largest trading partner and a growing influence among developing countries, are expected to dominate talks in Mexico City next week between Commerce Secretary Malcolm Baldrige, U.S. Trade Representative William E. Brock and Mexican trade officials.

At the first session of the Joint Mexico-U.S. Commission on Commerce and Trade, the two governments will devise the framework for later lower-level discussions and attempt to offset future trade problems with the politically sensitive Latin American nation, U.S. government officials said. The joint commission was set up this spring by President Reagan and Mexican President Jose Lopez Portillo at Camp David. Greater North American harmony has been one of Reagan's stated goals.

Although there will be time during the two-day session for talks with U.S. businessmen in Mexico, and a possible visit to a horse show by champion cowboy Baldrige, U.S. and Mexican negotiators are expected to get into heavier subjects such as the Mexican automobile decrees, Mexican membership in the General Agreement on Tariffs and Trade, easing restrictive Mexican trucking regulations, energy concerns and possibly immigration problems.

Mexico is expected to push for retention of favorable trade benefits reserved by the United States for developing countries and were planning to try to dissuade U.S. officials from selling silver -- one of Mexico's prime commodities -- from U.S. strategic mineral stockpiles. However, the General Services Administration announced yesterday that it will sell 1.25 million ounces of silver weekly from the stockpiles beginning sometime in mid-October.

Although relations between Reagan and Lopez Portillo are warm, the Mexican president recently emphasized in a speech his growing foreign policy differences with Washington. In particular, he criticized the administration's touted Caribbean Basin economic policy.

The Mexicans, like the Canadians, are particularly sensitive to what they perceive as U.S. efforts to tell them what to do. For example, Lopez Portillo has repeatedly stated his support for Cuba, Nicaragua and leftist insurgents in El Salvador, and condemned intervention by the superpowers in Caribbean matters.

Although Mexico has the world's fourth-largest supply of proven oil reserves, it has high unemployment and a $24 billion trade imbalance with the United States. It maintains protectionist trade practices to offset its development problems and to build base industries such as textiles and autos. Mexico's first priority is developing the food processing industry, which produces more than 40 percent of its total manufactured output, followed by the capital goods industry -- mainly manufacturing of food-processing equipment.

Although Mexico's auto industry is about one-fourth the size of Canada's, it has grown tremendously during the last decade. The auto decrees, which benefit the small but burgeoning Mexican auto industry while restricting U.S. imports, are high on the list of U.S. negotiators' topics. The Reagan administration isn't necessarily looking for elimination of the decrees, but possible management of what could become an even touchier problem, according to administration trade sources.