Can someone smarter than I tell me what would happen to U.S. equities if the dollar collapsed? I mean, the companies would still have their underlying value - I presume their prices would inflate? What happened in Japan in the early 90s?
Well, a lot of things happened, but overall, you saw lower prices for many asset classes, particularly real estate and stocks. There was some measure of deflation. A small number of institutions went under, and a large number of them consolidated. Non-performing loans (NPLs) were considerable, and were considered for a while to be the greatest systemic danger.
Many of these loans eventually began to perform again --- a circumstance that I don't think we would see here in the U.S. since we are far faster to clamp down on a non-performing loan than the Japanese.
Other things happened, such as the government borrowed a lot of money; however, they wisely also pushed interest rates very low, and thus borrowed money at very low interest rates (often at 0% in nominal terms) and thus weren't paying a lot in interest on the large sums they borrowed.
The Bank of Japan bought a lot of U.S. dollars to keep the yen down, and now holds around USD $800 billion in foreign reserves, which are held at much higher interest rates than any JGBs are paying.
The Japanese continued their massive acquisition of foreign assets, and continue (as they have since 1991) to have the world's largest international net asset position.