Mexico reopened a free exchange rate for its currency today, and the cost of a U.S. dollar on the legal market immediately doubled for most people here from 70 to 150 pesos in those few locations where dollars could be found at all.

The measure is part of an increasingly complex monetary package still taking shape under the 20-day-old administration of Mexican President Miguel de la Madrid in an effort to recover tens of billions of dollars in vital capital that has left the country over the last 18 months.

At the beginning of this year the peso was trading at around 28 to the dollar. With major devaluations in February, August and today its value had dropped by 81 percent on the open market.

The immediate goal of the new free-market rates, according to government officials, is to bring the business of the black market and exchange houses operating just across the border into Mexico and under government supervision.

Businessmen and even casual tourists were trading their dollars for pesos in the United States before arriving here since the rate for pesos in the U.S. markets was free floating already and had reached well over 140 pesos. Meanwhile, Mexicans facing severe limitations on the number of dollars they could obtain legally ($250 a year in most cases) opted to put their pesos on the black market or take them out of the country and use them to buy dollars at whatever price they could.

But the so-called free rate for tourists and most Mexicans and businesses is only one of three parities that went into effect today, and an additional futures market is also planned.

Many import-export transactions are to take place on a "controlled market." A third category of exchange, a "preferential rate" for debts payable in foreign currency, was also announced yesterday by the central bank.

Technically, 95.10 "controlled" pesos or 70 "preferential" pesos will buy a dollar. But all these exchange levels will be allowed to "float," according to a Bank of Mexico statement. The bank anticipates, for instance, that the controlled peso will decline in value by an annual rate of 50 percent against the dollar over the next few months.

Until today a Mexican who wanted to take a Christmas trip abroad could only buy a few hundred dollars legally in Mexico, but they cost him only 70 pesos.

Today bank customers were told that for the moment not only is 150 the going rate but the purchase of dollar bills remains limited to the border or the airport after passing through customs. Money orders and travelers checks can be bought at banks, but only at certain branches, and supplies are restricted.

Banco Cremi, according to managers in its central office, will sell only as many dollars in a day as it takes in that same day. And today it wasn't selling any.

A few doors down Reforma Avenue, however, the Banco Internacional sold travelers checks and money orders to all comers up to the temporary limits ($1,000 for individuals, $5,000 for institutions in a single transaction).

Tourists coming here discovered that their luxury hotel rooms cost about $20 a night, but as a clerk at Eastern Airlines put it, "We Mexicans won't be traveling much anymore." International air tickets are set in dollars and converted to pesos at the 150 rate.