HELMUT SCHLESINGER, new head of Germany's central bank, has just been handed the reins of a bucking economy.Inflation is rearing up. Deficit spending is dangerously high. The deutsche mark is misbehaving. The challenge for Mr. Schlesinger, who replaces Karl Otto Pohl as Bundesbank president today, is to rope inflation to the ground, convince Bonn to get its borrowing under control, and steer Germany toward a single European currency without sacrificing the strength of the mark. It's a tough assignment which even this monetary hard-liner may not be able to complete in the given two years. Schlesinger, originally due to retire from the Bundesbank in September of 1992, was designated the new president when Mr. Pohl surprised Bonn and the international community by announcing his early retirement in May. Schlesinger spent 19 years on the Bundesbank's policymaking central council and eight years before that as the central bank's chief economist. In accepting the appointment as president, he will delay his retirement and fill the post for the required minimum of two years. The first order of business for Schlesinger is to tackle inflation - public enemy No. 1 in German eyes - which now lies at 4.5 percent, compared to last year's rate of 2.7 percent. It is widely speculated here that he will use the Aug. 15 Bundesbank council meeting as a chance to convince his 17 fellow council members to beat down inflation by raising interest rates. "The Bundesbank won't let inflation lie at over 3 percent," says Norbert Walter, chief economist for Deutsche Bank, Germany's largest bank. "We assume rates will go up." Such a move would face criticism from the international community, which argues that German interest rates are too high already and complained loudly when the Bundesbank upped interest rates last February. There is also the danger of a backlash, warns Peter Pietsch, an economist with Commerzbank in Frankfurt. If rates are too high, they could quash recovery in eastern Germany or even slow growth more than desired in the western part of the country. "It's a delicate situation," he says. However, Mr. Pietsch still believes there is more than a 50 percent chance that the Bundesbank will decide to raise interest rates. The inflation rate is simply unacceptable, he says, and Schlesinger "has been one of the guarantors of price stability for years." Part of July's preliminary inflation rate of 4.5 percent can be attributed to a mechanical adjustment - the expected result of tax increases which went into effect July 1 to help pay for reunification. But prices were already rising in the months previous to July and the trend is worrisome. The central bank has meanwhile been concerned with another problem, government borrowing to pay for reunification. In June the bank issued a stern warning to Bonn, calling for "clear steps" to cut the deficit by reducing spending and subsidies. The deficit of federal, state, and regional governments for this year is estimated at DM 180 billion (US $103 billion). "Schlesinger looks at the long term and what he sees is that the potential for fiscal deficits is still there," says Paul Horne, international economist for Smith Barney, Harris Upham & Co. in Paris. Schlesinger, however, "can do nothing about this but keep jaw-boning" and applying pressure to Bonn, Mr. Horne says. The media here have drawn parallels between the state of the economy now and in 1980, when Pohl became Bundesbank president. Now, as then, inflation, deficits, and weaker economic growth prevail. But, economists warn, the situation of today is actually quite different. Most of today's fiscal and monetary problems have been brought on by German reunification and do not reflect a fundamental flaw in the German economy. The price being paid now will hopefully come back later in the form of a strong economy in eastern Germany.