outh Africa's government, faced with sharply declining revenues from gold sales, has unveiled a Reagan-style budget that some observers believe could exacerbate racial tensions and diplomatic problems in the troubled, white-ruled nation.

Finance Minister Owen P. Horwood earlier this week announced he was slashing government spending rather than sharply raising taxes to reduce the deficit caused by the plunging price of gold, one of South Africa's most profitable minerals.

Some observers are hoping this approach will ease the budget's recessionary impact. But others fear it will not and warn that a steep recession would lead to large-scale black unemployment and new social unrest among the black majority.

There are also fears that prolonged hard times would harden attitudes among low-income whites and increase support for the right-wing group that broke away from Prime Minister Pieter W. Botha's government earlier this month and formed a new political party.

Observers believe increased polarization could also worsen prospects for a political settlement leading to independence for neighboring Namibia. The Western powers, led by the United States, are seeking such a settlement.

Horwood's budget revealed an awareness of the racial dangers that lie ahead as South Africa enters a recessionary cycle. Although he opted for an austerity approach, he did so with what some economists described as a surprising degree of concern for the poor.

South Africa has little in the way of social welfare, especially for blacks. But within its limited context Horwood made some improvements. He increased pensions and exempted both the poor and the elderly from proposed tax increases.

"I regard it as a shrewd, subtle budget drafted in difficult circumstances," said Merton B. Dagut, economic adviser to one of South Africa's biggest banks, Nedbank.

South Africa produces 75 percent of the non-Communist world's gold and has been enjoying the greatest boom in its history as a result of high gold prices, which touched $820 an ounce early in 1980.

The government takes 44 percent of gold earnings, and it used the bonanza to slash taxes for both businesses and individuals. Most of the wealth went to the country's 4 million whites, but employment and wage levels among the 21 million blacks also rose. Partly as a result, South Africa has enjoyed relative racial calm.

But the gold boom has ended. Heavy selling by the Soviet Union and Iran, both of which are strapped for hard currency, has caused the world price to plummet to about $320 an ounce.

For every $10 the price goes down, South Africa stands to lose $200 million a year.

Two years ago, South Africa's revenues from gold sales were about $4.5 billion. In the fiscal year now ending, revenues are estimated at $2 billion. Next year, Horwood said this week, they are expected to reach no more than $900 million.

To make up the shortfall, Horwood ordered government expenditures to be held to an increase of 11.5 percent. With inflation in excesss of 14 percent, that represents an actual cut of at least 2.5 percent.

The finance minister also ordered a 1 percent sales tax increase and slapped a 10 percent surcharge on exports. He also increased business taxes 10 percent and raised excise duties on luxury goods.

But he held tax increases for individuals to a modest 5 percent, and cast them in the form of a compulsory loan to the treasury repayable after four years.

Whether the government can hold down spending to the budgeted level remains unclear. In the current year it has overspent its budget by 2.5 percent under much easier circumstances than it now faces.