WARSAW -- A newspaper cartoon published here recently showed two proud mothers with their infant children. "Mine already says 'mama,' " bragged the first woman.

"Big deal," answered the second. "Mine already says 'dollar.'"

Such is the power of the U.S. currency in this Warsaw Pact country that Poles have reluctantly come to accept it as an indispensable part of daily life. Traded far more heavily than in many western countries and treasured by consumers for saving, speculation and consumption, the dollar here has outgrown the typical parameters of black market dealing to become Poland's most favored cash.

"In what way does Poland differ from the United States?" the Communist Party weekly Polityka recently asked. "The answer is none. In either country, everything can be bought for dollars."

In fact, dollars buy a lot more in Warsaw than in Washington. Poles armed with greenbacks can buy literally thousands of different consumer items at discounted prices in state stores that accept only western hard currency. Paying dollars is the only way a typical Polish consumer can obtain a car, an apartment, a box of facial tissues or a shower curtain from the state.

Moreover, state-produced goods priced in zlotys are wondrously cheap when paid for in dollars. The price of sirloin steak, for example, was recently increased 40 percent in zloty terms but still costs the equivalent of only 18

U.S. a pound. Polish-made Fiat compact cars retail in state outlets for $1,900.

Fed by such incentives, the use of dollars has spread in the past 15 years here from the usual Soviet Bloc fringe of tourists and taxi drivers to the mass of Polish society. Economists estimate that Poles spent more than $500 million last year in state hard-currency stores alone, while an equal amount was turned over in the illegal private exchange markets.

More than 3 million Poles now hold dollar-denominated accounts in state banks, and the number of accounts is increasing at the rate of 600 a day in Warsaw. The amount deposited in them, more than $2.5 billion, has increased 700 percent in five years and now exceeds the value of public zloty deposits. Economists believe another $2 billion in cash may be stuffed under Polish mattresses.

"The dollar has become a full-fledged Polish currency," said Pavel Wyczanski, an economist at the State Institute of Finance. "It has the role in savings and speculation that gold does in other countries."

The dollar in Poland is impervious to the frailties it knows in the West. Even as U.S. currency has plunged in value on European and Japanese markets in recent months, it has inexorably risen in value in Poland. In November, its black market exchange rate against the zloty leaped from 900 to 1,200, or 30 percent. Last week, following price increases, it rose another 16 percent, to the current float of 1,400.

"Why does Poland remind Americans of 1984?" goes a joke here. "Because the dollar is still rising, and Ronald Reagan could win an election by a landslide."

Though private trading in dollars is nominally illegal, Poles looking for cash have no need to sneak into alleys or seek out foreign tourists. The private exchange market for hard currency is huge and sophisticated: the official press has estimated the number of fulltime professional traders at up to 20,000, including 3,500 to 4,000 who regularly wait outside Warsaw's banks, hotels and hard currency stores.

The classified section of Warsaw's popular newspaper Zycie Warszawy always contains listings of dollar traders. These are usually thinly disguised as offers to buy or sell bony, a dollar-denominated scrip, usable in hard-currency stores, that is issued by the state to some Poles and can be legally traded.

A telephone call to one of the listed numbers is typically answered by a harsh voice barking out the day's exchange rate as aggressively as on any western currency exchange. The dialing customer must merely indicate how many dollars he wishes to buy or sell and is then told where to make the transaction.

Like traders everywhere, Poland's exchange dealers have a few benchmarks. The two most common are the price of vodka and the price of cars -- the two Polish-made items that are sold in both zloty and dollar markets.

For years, the price of a bottle of vodka in the state-run Pewex store has conveniently hovered around $1, while the zloty price has ratcheted upward with inflation. Currently, vodka sells for 1,440 zloties -- not coincidentally equaling private exchange rate, which is more than three times higher than the official rate of 380 zloties to the dollar.

The state's not-so-innocent role in setting the dollar's sky-high private value is one of the several embarrassing aspects of the currency market for authorities. There is also the problem of explaining to consumers why Krakow hams and Warsaw apartments are now sold for dollars, and, to Poland's socialist allies, why a Comecon economy is running on capitalist currency.

Poland's state managers, however, are by now thoroughly hooked on the dollar system. The hard-currency stores and bank accounts provide a badly needed flow of income to the state that can be used for western imports and debt payments. And dollar-based consumer trade provides a vital escape valve for popular frustration with the empty shelves of state zloty stores.

Consequently, the dollar seems to face less threat of extinction than the zloty. "The dollar is probably here to stay," said Wyczanski. "There are too many people and too many institutions by now who are using it. For now, we can't afford not to have it."