CAMBRIDGE, Mass., March 30 (Reuters) - Federal Reserve Chair Jerome Powell speaks on Monday at an introductory macroeconomics class at Harvard University, where his remarks will draw scrutiny for how he may answer the classic textbook question: how does a central bank respond to a shock that simultaneously feeds inflation and slows the economy?

The Fed may face just that dilemma as the Iran war enters its fifth week and U.S. gasoline prices rise to around $4 a gallon.

It has been just a week and a half since the Fed left short-term interest rates steady in their 3.50%-3.75% range.

At the time Powell said he would want to see tariff-driven inflation in goods prices subside before even getting to the question of whether the central bank ought to ignore any rise in inflation stemming from the Iran war, or to respond to it with tighter monetary policy to keep inflation from spiralling upward.

Since then, investors' inflation concerns have contributed to a rise in Treasury yields, and a University of Michigan survey showed a jump in household price expectations in both the coming year and farther out. Other measures, including a widely watched market-based gauge, have been more sanguine.

If the Fed raises rates to get ahead of inflation, it risks slowing the economy and hurting employment. If it leaves rates where they are or even cuts them to protect the labor market, it risks allowing inflation to bubble higher.

"In a very typical Fed model, the Fed's not really happy with that choice," said Pomona University economics professor Michael Steinberger. "The Fed is truly darned if they do, and darned if they don't."

At a Dallas Fed event on Thursday, Vice Chair Philip Jefferson said he feels the Fed's policy stance is now broadly neutral - neither stimulating nor holding back the economy.

That leaves the central bank in a good spot to watch the data and see how best to next respond, he said.

Philadelphia Fed President Anna Paulson told a group of researchers at the San Francisco Fed on Friday that she is worried higher oil and fertilizer prices due to the closure of the Hormuz Strait may feed quickly and durably into higher inflation expectations.

BMO Economics' chief U.S. economist Scott Anderson, speaking from the sidelines of that conference, said Paulson's view jibes with his own.

"We are more concerned about the inflation side of the shock at the moment...prices keep going up and up and up, and that definitely starts to affect behavior and decisions, not just at the consumer level but for businesses as well," Anderson said.

Given that inflation has run above the Fed's 2% goal for the last five years, he said, central bankers "have to be more concerned about the inflationary impact" of the oil shock.

Since the start of the Iran war financial markets have flipped from betting on a couple of interest-rate cuts this year to now pricing in a one-in-three or so chance of a Fed rate hike by year end.

"It's going to come down to the classic trade-off of what are you more worried about - rising inflation or weaker employment," III Capital Management chief economist Karim Basta said, adding that Powell's speech on Monday may indicate his concern leans toward inflation.

That's particularly understandable, Basta said, with the price of oil running far short of levels like $150 or $200 a barrel that would sharply raise recession risks, but - at near $100/barrel - high enough to noticeably increase some prices.

As for a possible rate hike, Basta said: "They have to be ready to do whatever is needed, and one of the things that possibly could be needed is to raise rates. I think it's fair that nothing can be ruled out."

(Writing by Ann Saphir; Editing by Lincoln Feast.)