What should the Federal Reserve be doing?

From Judy Shelton's interesting lunch with economist Robert Mundell:

Currency Chaos: Where Do We Go From Here?
'The most important initiative you could take to improve the world economy would be to stabilize the dollar-euro rate.'

[...] Mr. Mundell has a knack for boiling things down to simple terms. He grew up on a four-acre farm in Ontario, went on to earn a Ph.D. from the Massachusetts Institute of Technology, and would ultimately challenge the renowned Milton Friedman at the University of Chicago during the late 1960s. Both economists were strong proponents of free markets, but Mr. Mundell disagreed with Mr. Friedman's advocacy of floating exchange rates.

The sound of a buzzer indicates lunch has arrived. Mr. Mundell suggests that we continue our discussion at the table and politely invites his assistant Ivy Ng, who has been taking careful notes, to join us.

"We've been talking about the possibility of global monetary reform," I continue, deciding to switch gears. "Let's talk a bit about domestic monetary policy. What do you think the Federal Reserve should be doing right now?"

It's a seamless transition for Mr. Mundell. "The Fed is making a big mistake by ignoring movements in the price of the dollar, movements in the price of gold, in favor of inflation-targeting, which is a bad idea. The Fed has always had the wrong view about the dollar exchange rate; they think the exchange rate doesn't matter. They don't say that publicly, but that is their view."

"Well," I counter, not particularly savoring the role of devil's advocate, "I suppose Fed officials would argue that their mandate is to try to achieve stable prices and maximum levels of employment."

Mr. Mundell looks annoyed. "Well, it's stupid. It's just stupid." He tries to walk it back somewhat. "I don't mean Fed officials are stupid; it's just this idea they have that exchange-rate effects will eventually be taken into account through the inflation-targeting approach. In the long run, it's not incorrect—it takes about a year. But why ignore the instant barometer that something is happening? The exchange rate is the immediate reaction to pending inflation. Look what happened a couple weeks ago: The Fed started to say, we've got to print more money, inflate the economy a little bit. The dollar plummeted! You won't get a change in the inflation index for months, but a falling exchange rate—that's the first signal."

Clearly on a roll, I press a bit. "You mentioned gold?"

'The price of gold is an index of inflation expectations," Mr. Mundell says without hesitation. "The rising price of gold shows that people see huge amounts of debt being accumulated and they expect more money to be pumped out." He purses his lips. "They might not necessarily be right; gold could be overvalued right now."

Sensing that the soup is getting cold, I decide to cut to the chase: "What would be your winning formula today? What advice would you give to Washington that would help turn around our moribund economy?"

He pauses to think, but only for a moment. "Pro-growth tax policies, stable exchange rates." [...]

Pro growth tax polices sound good. I don't know about stable (fixed) exchange rates. I would like to hear Milton Friedman's argument against it.