Since I did a post on increasing returns to devoting resources to producing rice, I think it is time to focus on the opposite. That is, it’s time to focus on resource depletion and decreasing returns.
To do this, it may be useful to introduce some concepts from ecological economics. First there is throughput. Throughput is the amount of energy and matter involved in a production process. A big argument of ecological and biophysical economics is that many of what have appeared as “productivity increases” to economists has historically actually been increasing throughput of energy. Regeneration meanwhile is the idea that when natural resources are left unused they start to regain their original characteristics. Thus the essential distinction between non-renewable and renewable resources is their rate of regeneration. Technically fossil fuels, even considering the greenhouse gas effect, do have a rate of regeneration. However since we are thinking in terms of human resource use the time scale for regeneration, and the level of resource unemployment required to get there, these resources can be called non-renewable given how extremely slow their rate of regeneration is. That last point is worth emphasizing, renewability only matters relative to human time scales. No humans and the time it will take for oil to reform in the ground is irrelevant- at least to us.
This leads us to our final concept: the maximum sustainable scale. This refers to the idea that there is a level of employing a natural resource where the rate of throughput, ie the rate at which this material or energetic natural resource is used, is equal to the rate of regeneration. In other words there is a rate of use where the stock of this natural resource remains constant. A scale of production beyond that will deplete the natural resource and, for our purposes here especially important, lead to diminishing returns over time. This can potentially end with the resource being used up all together. Thus, to simplify here we’re only going to be dealing with homogenous nature. In reality of course, there are many different material forms of nature that are important to different production processes and techniques and have different rates of regeneration.
Thus, rather than dealing with increasing returns in rice, I’m going to deal with decreasing returns in grapes. In this example “Monocropping” grapes leads to an overuse of the soil and less returns each year. At maximum production, Friday produces one less grape meal each year. The less resources devoted to producing grapes, the slower the “decreasing returns” are. For simplicity’s sake I’ve not only assumed the midpoint of the production possibility frontier is the point that maximizes utility but that it is also the spot of maximum sustainable production for Grapes. For those not up on the jargon, I’m assuming that the combination of rice and grape Robinson Crusoe or Friday would choose to produce without specialization both leads to them getting the most enjoyment but also involves producing grapes at the maximum sustainable scale. In other words they would be led by their “short run” self interest to choose to produce the level of grapes and rice that leaves their stock of natural resources constant. With all that in mind, let’s go to the data. I’m starting with the same numerical values as i used in the first post and will try to stick to those numerical values for every Crusoe post I do.
So what’s going on here? What happened is that there was a jump to the no specialization “special case”. That is, there is a point at which Crusoe’s absolute advantage is identical for both goods and thus there are no gains from trade. Because of decreasing returns in grape production, the gains from trade were eliminated by changing relative prices . This is a point that never gets discussed enough- the difference in the absolute advantage Robinson Crusoe has and thus the difference between the opportunity costs of production are changed under any situation that isn’t constant returns to scale. This is why the handwaving when discussing the situation where Crusoe’s absolute advantage of both goods in undergraduate economics classes are so misleading. Yes it is a “special case” but in a situation where some fundamental forces are driving changes in relative prices it becomes a point that all models will pass through. Thus as we’ve seen, if you assume “short run” maximization in a situation where relative prices aren’t constant (which is most situations) then eventually short run gains from trade will disappear or explode. As we’ve also seen however, in both cases “short run” optimization is inconsistent with intertemporal optimization.
The reason we get the result that output is actually lower in “equilibrium” even as the decreasing returns end is the nature of “maximum sustainable production”. The jump to no specialization led to production at the midpoint of both Crusoe’s and Friday’s production possibilities frontier. This led to no further decreases in natural resources but also not a return to the original “stock”.
What is truly galling about this result is decreasing returns to scale with regard to natural resources was an essential part of Ricardo’s rent theory. That following static comparative advantage when one good experienced diminishing returns not only eliminated gains from trade but lowers equilibrium output relative to the no specialization case makes discussions of comparative advantage infuriating to those with some knowledge of the history of economic thought and the inherent limitations of this perspective.
The point of this isn’t that professors should be using the Robinson Crusoe analogy to convince their students of protectionism and militate against specialization instead of convincing them of free trade and specialization. The point is, are you sure your students could follow either of these broadsides against the way the usual comparative advantage model is used? If not, and i suspect the answer is no, then this part of every undergraduate economics education is propaganda and not education as such. Students should be able to explain and use economic concepts and because the basic example isn’t intuitive and isn’t really connected to their lived experiences, they generally don’t. Instead they are rushed along to more baroque and mathematically complex versions of the same models that are also not very understandable. This leaves students in a mass of confusion, but they still remember the slogans long after which, to a cynical man, might appear to be the point.