If Dr. Paul becomes President, then inflation and spending (especially government spending) would go down (I'm guessing the former would go down because of gold and silver no longer subject to tax penalty).
I was thinking that if the general economic boom is still not as big as it was when Harding took office, then the depression wouldn't last longer than 1 year (assuming Restore America Now is implemented). There are so many factors to take into account, but I don't see how it could be more than 3 years until private debt is liquidated enough for there to be prosperity (bankrupt entities closed, new firms propping up). The GD lasted 12 years or so with heavy ass govermental interference for reference. The Panic of 1837 lasted 4 years and I'm not sure why that lasted so long since Van Buren didn't interfere (I haven't read Dr. DiLorenzo's "How Capitalism Saved America", so I'm pretty uninformed on the Panic of 1837).
He wouldn't be in control of monetary policy, tax policy or the budget directly. Those are all left to Congress and the assorted delegated institutions.
He could personally remove troops from Afghanistan and Iraq. He could veto spending bills. He could pardon war prisoners. He could push policy agendas and such but the main power of the President is in the military and the public stump not the public purse.
Now if the Republicans were to keep their majority in the House and get a majority in the Senate then they could push through legislation that Paul might be favorable to. In that case they would be in a position to do something about the spending and the overall tax burden.
It would also be nice to watch RP appoint replacements for Ginsburg and Breyer if they chose to step down from the SCOTUS.
Pardoning all the non-violent drug offenders as Paul said he would sounds like it would clear up a lot of money from the prison industry. Imagine people who were formerly CO's now doing actual productive work.
Ron Paul can only be elected if there is a massive shift in the beliefs(and level of time preference) of society. So if he is elected he will have the power to enact every free market policy that he wants. Unfortunately though, the coming economic collapse is larger than anything we have ever seen in history. It is much worse than the Great Depression. The government has created the so-called "great moderation" by simply printing money and inducing massive capital consumption every time the free market tries to correct the ever-increasing imbalances. We have decades of malinvestment that will be revealed. The government constantly prints money which discourages savings, it has programs like social security which discourage savings, and it gives out employment insurance benefits which also clearly discourages savings. Over time, because of policies like these, we have been consuming our capital and therefore have very few factories left in existance. Meanwhile, we have been building heterogeneous capital in the form of malls, office buildings, restaurants, houses which, for the most part, are mal-investment. If Ron Paul overhauls the entire system we will have an immediate crash so psychologically devastating that everyone will turn against him. But even with full support of Ron Paul's policies the recession could still last a few years. Unfortunately, it is impossible for Ron Paul to get elected and we will get something similar to the depressions of Soviet communism.
Thanks for all the answers everyone. I agree with the person who said productivity will go up if Dr. Paul cuts off the prison and banking complexes... so I guess that if people want to make more money, then they won't be able to do it as much through non-productive speculating and hedgefund management and all of that stuff. Perhaps it would just be a minor recession because anti-market and other mostly useless activity will go down.