Every time the price of gold goes up by $10 an ounce on the money markets of Zurich, London, Hong Kong, and New York, South African gold producers become richer by more than $2 million.

It is not all profit, of course, for the operators of the 38 big mines in South Africa. At the current price of gold -- it has been around $700 an ounce recently -- 67 percent of the increased revenue goes to the government in taxes.

Still it is boom time in South Africa. In Johannesburg's venerable Rand Club, mining executives talk business with a tingle of exuberance added to their normal mood of prosperity and confidence. The talk is of expanding the present mines, sinking new shafts and even reworking old dumps.Using the more modern techniques for extracting pure gold from the ore, enough of the precious metal can be gotten on the second go-around to make a profit -- at the present price for gold.

"One of our mines cleaning up their railroad lines between shafts picked up 80 kilograms of gold," Anglo American Corp. executive Dennis Etheredge exulted. "Some people say it's time to tear up the streets of Johannesburg, but I'm not in favor of that," Etheredge chuckled.

Meanwhile, Anglo-American confirmed last week that it secretly has purchased a major stake in one of its chief rivals, Consolidated Gold Fields, a British-based concern. Anglo-American paid an estimated $345 million for the surreptitious purchases and says that, with an associated company, it now has effective control of 25 percent of Consolidated's shares.

[Anglo-American and Consolidated control a total of about 43 percent of the Western World's gold production, Reuter reported last week.]

[The news agency also said that Britain's Department of Trade will investigate whether Anglo-American had run afoul of any British regulations, and it noted that market analysts are speculating that the South African Monopolies Commission might be concerned about the purchases.]

In the alluvial sands near Barberton, 250 miles east of Johannesburg, where little towns like Eureka recall the early days of panning for gold, hundreds of new small claims are being filed. For an acre to prospect, the claimant pays only 42 cents a month to the government. On weekends the gulleys are filled with enthusiastic amateurs hoping to turn up a nugget.

In neighboring Rhodesia there is the same gold fever. The Department of Mines recently published a list of 1,000 dormant mines in the country. Within a few weeks the initial printing of 500 copies had been grabbed up.

But in the mining houses in Johannesburg's financial district, even the multi-millon-dollar reworking of the mine dumps which stand out on the Johannesburg skyline are "little fellow" operations. Even in his own Anglo American ergo project, where million of tons of old gold tailings are being retreated chemically to recover not only gold but its companion metal, uranium, Etheredge estimated the recovery will be only five a year.

"Still, it's nice gold because it's profitable," Etheredge said. Besides being chairman of Anglo American's gold and uranium division, Etheredge is president of the all-powerful South Africa Chamber of Mines.

Last year South Africa produced 703 metric tons of gold, 51 percent of all the gold that came onto the world market. Gold sales returned $7.3 billion to the companies and the South African treasury last year. The second biggest miner of gold, the Soviet Union, whose trading in precious metals is devious, marketed an estimated 300 tons last year, while the other "big producers" -- Australis, Canada, South America and Rhodesia -- were also-rans.

So it was a banner year -- here -- a "King Midas year." The price of gold averaged $305 throughout the year, rose sharply at the end of 1979 and on Jan. 21 peaked at $825 an ounce. Its "modern" low of $103 was set in September 1976.

Inflation in the West, soaring oil prices, political uncertainty and a weak dollar brought about the frantic demand for gold as a backup against the paper monies of the world. Because the future does not look particularly brighter in any of these political and economically troubled areas, South African economists believe that the value of gold won't fluctuate widly as it has in the past.

Michael F. Brown, chief economist of the Chamber of Mines, believes a conservative base price of $300 an ounce is expectable, and much of the spending policies in both private industry and South Africa government are predicated on a gold price which keeps to this level, or above it.

As a result, even after taxes the South African mining houses will have substantial money available for large-scale expansion of underground operations.

"It gives us a completely new ball park of mining capability," Etheredge said. "Ore bodies which at the gold price of $180 to $220 (an ounce) were uneconomical to mine (too low-grade in gold content and too hard to reach) will at $350 to $400 an ounce become an economic proposition," he said.

But to go after the remote gold seams -- some of which lie more than three miles below the surface -- is an enormous financial undertaking, Etheredge said.

"You can't expect to see a bar of gold from such new enterprises for 5 to 6 years, or maybe 10," he said.

Despite the expenses and the long lead time, plans for three new gold mines have been announced. And "there's not a single spare drill rig" available in South Africa for exploratory probing, looking for new seams of gold, Etheredge said.

The gold deposits in South Africa, which exceed in concentration anything the world ever has know, were almost all discovered this century. They lie in a golden arc stretching 100 miles from Johannesburg south to the Orange Free State. There were once 120 major mines in this golden arc, and 38 still are operating.

But Edgeredge does not expect that the expansion of gold mining will increase production. It merely will allow the industry to prolong its life, he said. Unless new fields of high-grade ore are found, profitable mining in South Africa will end in about 50 years, it is believed.

"Gold has always been a scarce commodity, hence its desirability," Etheredge said. "All the gold mined since 3900 B.C. is estimated at only 116,000 metric tons. If it was all put in a hunk, it would be a cube of gold 24 feet to a side.

And the amount of throw-away in the mining process is one million tons of rock for every ton of gold extracted.

Whatever the future, the present boom is spurring the South African economy, which was in the doldrums during much of the Seventies due to racial unrest as well as for economic reasons attributable to worldwide recession.

But now, due to the rising gold price in 1979 and to the skyrocketing price in recent months, the government has inherited a bonanza. Its share from taxes and reserve bank sales of gold was about $2 billion last year, three times the income budgeted.

For a man who might be thought to have broken the bank at Monte Carlo with such a largess in his lap, Finance Minister Owen Horwood made no Santa Claus promises when he rose in parliament earlier this month with preliminary remarks on how the state plans to spend its new-found wealth. The budget will be revealed March 26.

When the gold price hit $200 an ounce in 1974, "most of us" spent too much and "lived beyond our means," Horwood remembered. He said that even with vast sums on hand this time, the government will continue fiscal conservatism, and said the country's "security needs have to receive priority."