Tyler Cowen considers the economics of time travel. Actually, he starts with the economics of interstellar travel, but if you take relativity seriously, it’s the same thing. Tyler is most interested in how time travel in the presence of time dilation would affect interest rates (e.g., what happens if someone saves a penny and then travels into the future?; what happens if everyone tries to do that?).
I’m more interested in the effect of time travel on migration and trade. If wages are expected to be higher in the future, then once the cost of time travel falls low enough, we can expect people to start migrating in large numbers into the future – just as they migrated from Europe to the North America from the 1500s onward, and just as they migrate from Mexico to the U.S. today. A simple model of transtemporal migration would therefore predict equalization of wages over time, as wages rise in the present (from reduced labor supply) and fall in the future (from increased labor supply). But wage equalization does not even clearly result from international migration today. New arrivals, aside from increasing the supply of labor, both (a) increase the demand for goods and services, and (b) to the extent they are willing to work for less, lower the price of goods and thus increase purchasing power. The future might be able to absorb the time-traveling arrivals with little impact.
Moreover, there could actually be increasing returns from larger populations, because more people interacting with each other generate more ideas and innovations that can benefit larger numbers of people. Maybe the future would leave the present behind, not just temporally but economically, as its population grows while ours shrinks.
And that’s assuming time travel is only possible in a forward direction. (I think time dilation only makes forward time travel possible, but I confess that I’ve never fully wrapped my head around relativity.) If backward time travel is also somehow possible, maybe firms in the future will choose to outsource some of their operations to the past, locating their manufacturing and other services in lower-wage time periods. This opens the possibility of transtemporal gains from trade... assuming, of course, that governments don’t implement effective trade barriers. Would America-3000 place tariffs on goods from America-2000? Would temporal nativists call for the construction of a time-wall to keep out the trans-temporal immigrants -- even if those immigrants were, in fact, their own ancestors?
* I use ‘transtemporal’ to refer to economic phenomena related to time travel, since ‘intertemporal’ already has an economic meaning without time travel.