Steve Horowitz, Charles A. Dana Professor and Chair of Economics at St. Lawrence University, says no and explains why in this brief, but very informative video.
This is very timely for me, because in my Economic Expansion and Development course we have just got to the section in which we discuss issues of "Sustainable Development." One of the hot issues is resource depletion. Those on what David Osterfeld called "the Catastrophist" side of the argument begin with the assumptions of exponential demand growth and a finite stock of resources and conclude by claiming that the more resources we use, the less we have left; and the faster we use resources, the faster we will run out.
As Horowitz shows, we have good reason to believe this is not the case. As long as the price system is allowed to work, entrepreneurs will have the incentive to produce whatever goods experience relative increases in demand and consumers have the incentive to economize on the same. Both of these phenomena work to increase the quantity of resources available to satisfy our ends.