MEXICO CITY, NOV. 25 -- The Mexican peso today appeared to stabilize somewhat in free market dealings just a week after it plummeted nearly 50 percent in a fall that added new uncertainty to the nation's troubled economy.

"People were psychologically very, very shaken by this," said Jonathan Heath, senior economist at the forecasting firm of MACRO Asesoria Economica.

"The government had promulgated the idea that the economic crisis was starting to be under control," Heath said.

The Bank of Mexico, the nation's central bank, last week stopped trading the peso in the free market, sending the currency into a slide. Before recovering a bit, it had skidded nearly 46 percent.

The Bank of Mexico said it decided to stop supplying dollars to the free market to conserve its foreign reserves of $14 billion to $15 billion.

It said it had been supporting the currency on the heels of an increased demand for dollars, spurred by private firms wanting to pay their foreign debts and speculators in the U.S. currency.

The free market rate is used in tourism and most transactions along the U.S.-Mexican border.

The government regulates a second rate, called the controlled rate, which was not affected by the plunge. That rate, which is used in 75 percent of commercial transactions, has slipped from about 1,697 pesos to 1,735 pesos to the dollar in the past week.

Private exchange houses in Mexico City today offered customers 2,050 to 2,100 pesos for each dollar and demanded 2,125 to 2,200 pesos for clients wanting to buy a dollar.

A week ago, those same trading firms were offering 2,200 pesos for a dollar and demanding as much as 2,700 pesos for clients wanting to buy a dollar.

Along the U.S.-Mexico border, rates were off even more, weakening to 3,000 pesos to the dollar.

Many exchange houses ran out of dollars, adding to the panic caused by the currency's rapid free-fall during two days.

The decline came after a period of stability in the exchange rate. Moreover, economic indicators have in recent months been pointing to a healthy rebound in the economy after last year's sharp downturn.

The most worrisome economic problem this year has been inflation, and analysts expect the peso turmoil to add to the price spiral.

Residents reported that merchants, as soon as they realized the peso's value was falling, quickly raised prices. Some said they saw prices on some items increased by as much as 30 percent in a day.

Heath predicted that with the peso slide the inflation rate would end the year at slightly more than 150 percent, surpassing last year's record of 105.7 percent.

Even more troubling, analysts said, was the government's apparent inability to set an anti-inflation policy.

The government's newly released budget plan for 1988 projected an inflation rate of 95 percent. But it offered no details on how it would bring it down to that level.

Private analysts predicted a pace next year of nearly 200 percent.

Meanwhile, the stock market's main indicator, the Index of Prices and Quotations, fell for the third day in a row. It dropped more than 9 percent, to 116,799 points.

The index soared a record 26.6 percent on the day the government bowed out of the free market.

The stock market, one of the world's best performers, had been badly hurt by the Oct. 19 global market collapse.