This would be really bad. The United States would experience short-medium term economic devastation and be hit by major economic aftershocks for many years thereafter.
Let’s make an assumption that there is broad scientific agreement that the eruption is definitely going to happen with a six month warning period (this is unlikely in practice, but a useful simplification for this exploration).
Given that this is pretty speculative and the geological record is likely to have substantial inaccuracies, we can’t be certain about the size or classifications of the affected areas. For a rough estimation, I’ll use this map:
(It's worth noting that the depiction of ash fall ranges here are not particularly detailed and somewhat optimistic. There's a more comprehensive exploration of potential ash levels in this paper.)
The kill zone covers most of three states. Fortunately these states are relatively sparsely populated, but you’re still looking at almost three million people. This region is going to experience pyroclastic flows and will be almost entirely unsurvivable. This means at least three million people will need to be evacuated with no expectation of their home, business, or town surviving the event.
The broader ash zones are going to experience levels of ash fall that will kill crops and animals, cause widespread roof collapse in buildings, and damage cars to the point of being unusable.
The rest of the country will also be affected with most of it seeing some amount of ash, which even in small amounts can cause electrical damage, invade homes, and contaminate water supplies.
This would be an economic disaster without precedent in recorded history.
Before the Eruption
The forewarning, while likely to save lives, will only compound the economic damage. In the year leading up to the explosion there will be immense anxiety as increasing numbers of scientists agree with the predictions. This will cause some people to flee the entire region in advance. Businesses will cease to open in that area and many might hastily relocate. This could cause the economies in anywhere from three to ten of the closest states to collapse before the eruption even happens.
Then there’s the matter of evacuating three million people. Where do you put them? How do you feed them? The pressure from relocating so many people will increase the load on other state economies. Unemployment will soar. And that only assumes that the three million in the kill zone are evacuated, when many more millions are likely to be mandatorily or voluntarily evacuated from other nearby areas. You’ll also have some people who won’t heed the warning — either they won’t believe that it’s going to happen or are simply unwilling to abandon their property for the life of a homeless refugee in some other state.
At this point there would probably be a nation-wide challenge to feed and house so many displaced people.
It’s worth noting that we don’t know how long a potential eruption might last. A four day event should be simpler to handle than a month-long eruption that’s constantly spewing ash, but both would be devastating.
All non-emergency aircraft in the U.S. and Canada would be grounded for the duration of the event and for some time afterwards. Power outages would be nationwide and systemic damage to power lines could result in months without power for many people, particularly in the core ash fall regions. The areas with the most ash would also see roads and ground transportation become unusable. Forewarning should at least ensure that most are prepared for this, but it will still massively impede emergency services. Another major danger across the highest ash fall regions is roof collapse. The weight of ash will cause widespread damage and loss of life.
Many of these effects will be felt all the way out to the coasts, including in states already hit hard by managing refugees from the interior. Food shortages are almost a guarantee, even with preparation, and now you have to deal with the most catastrophic problem: the eruption and ash fall have just hit America’s heartland. Agriculture will be utterly devastated, with widespread crop failure and livestock death. Water will be polluted with ash and in many states the remaining population will be in full-on survival mode. Starvation is likely in some places along with major unrest. These problems would take years to resolve and the damage to some of these state economies could last decades. A severe economic depression is all but a certainty.
These are more speculative. It is safe to say that stock markets would plunge throughout the forewarning period. This is unlikely to be limited to the U.S. since the forecast would be for widespread devastation of one of the world’s top economic powerhouses. This could have severe consequences on economies worldwide.
Canada would certainly share in some of this misery. Yellowstone is close to southwestern Canada and could see severe damage on par with many of the central states. This is actually pretty noteworthy as it could seriously limit Canada's ability to assist the U.S. in the aftermath.
Worldwide travel would probably be mostly unaffected. There may be cancellations out of an abundance of caution outside of the Americas during the event, but the ash cloud should not pose the same long-term problems it will cause in North America. Much of this depends on the actual ash cloud itself and may be impacted by the time of year.
The most troublesome international effect is the possibility for climate change. Substantially smaller eruptions such as Tambora in 1815 caused major global effects (the “year without a summer”) and Yellowstone would be far worse. Substantial cooling and even global circulation of ash could cause a global agricultural crisis that might exist for years and kill many, many more millions worldwide.
If you’re interested in what the aftermath would look like, I’d suggest looking up images from the 1980 Mt. St. Helens eruption. In short: a flattened, devastated wasteland.