Alex Tabarrok reminded us that Julian Simon's hypothesis was really about increased human welfare:
Resource prices were easy to observe so the famous bet was made in terms of prices. Simon understood, however, that prices are not a measure of welfare or even of scarcity (quantities would have been a better metric but these are much more difficult to observe).And so when I offered David Round the bet about half a year ago, I specified two separate parts: one on commodity prices and one on worldwide per capita GDP growth. David's still not provided me his preferred commodity bundle. I'll take this to mean he's been too busy over the last half year rather than that he's reconsidered his position on the likelihood of the world collapsing.
As Tyler notes, catch-up growth may mean that demand will increase faster than supply at least for some periods thereby driving up prices. But here is the key point, increased demand with a non-decreasing supply means an increase in social welfare. If tomorrow we discover that cold fusion actually does work, the price of palladium will increase dramatically, perhaps never to fall again. Nevertheless, human welfare would dramatically rise not fall.