The Comparative Advantage story is famous. It is an essential part of nearly every undergraduate economics education. It’s propagandistic benefit is also well known. To review, I’m going to run through a numerical example.
Here we see that Robinson Crusoe has an absolute advantage in everything. That is, he can produce more of either type of output than Friday can. Oh no! Poor Friday! But wait, David Ricardo is to the rescue! As long as Crusoe’s absolute advantage over Friday is different for producing Rice than producing Grapes, the opportunity cost (what else he could be doing with that time and resources) of Crusoe producing grapes is higher than Friday producing grapes! Boom, gains from specialization and trade.
You can see here that this is precisely what we find. The table is clearly telling us that Friday should produce grapes while Crusoe produces rice. However, what happens if there are increasing returns to scale? Below I run through such an exercise.
Below I’m assuming that for each year Crusoe spends producing rice with specialization he is able to produce 4 more rice meals the next year.Poor friday can only produce the same amount of rice year after year and he just continues producing grape meals. For each year Crusoe spends producing Rice without specialization, he can produce 3 more rice meals the next year. For each year Friday produces Rice without specialization, he can produce 2 more rice meals the next year. Of course you could do these assumptions in all different ways, that is sort of the overarching point with regard to how these models are used.
nonetheless, I chose these assumptions specifically. First, output isn’t growing by some percentage rate of the previous years output because recall that in this model all factors of production are fully employed and constant. There is no investment here. Thus the growing returns are relative to the underlying stock of capital and land and are thus exponential relative to them. There is no reason to think exponentially accelerating returns are possible under these conditions. However, there is reason to suppose that applying all factors of production will lead to returns growing more quickly than just applying some percentage of your factors of production. This is why rice output is growing faster for Crusoe under specialization than without specialization.
Second, Friday does not only start out less efficient but he is also less efficient at expanding output. I made this assumption to show that if you move to increasing returns there is a case against specialization even if Friday starts out less efficient at producing rice and is always less efficient at producing rice even if he focuses on it. I didn’t do the analysis here because it was obvious, but if you had perverse specialization- that is Friday specializes in rice- Friday produces 3 more rice meals every year, leading to the least total rice output of all the cases.
There are a number of interesting things here to say. This does a good job of making Cameron Murray’s point, which I’ve agreed with ever since I took a look at “Robinson Crusoe’s Economic Man”, that the Robinson Crusoe story is a great pedagogical tool for getting across a number of important concepts in economics. Here we have not only increasing returns and time but Baumol’s cost disease, inequality/distribution and intertemporal optimization. Relative prices are shifting in this economy because of labor productivity increases that exist in one good but don’t exist in another. Within an economy, those working in the low/no productivity growth sectors get wage increases to induce them to do these jobs. Hence the “cost disease” is the rising prices in these industries. This example clearly and easily expresses that idea. On the flip side, in other social contexts there may be no inherent reason for productivity increases to be shared.
If I felt particularly inclined to troll economists, I’d say that what they ignore in their arguments over comparative advantage is intertemporal optimization. That is a bit of a dig but it does get at an important truth. At each Individual point the traditional argument for comparative advantage applies. In fact, the gains to trade as conventionally measured are growing along with Crusoe's labor productivity! Yet taken together this is wildly suboptimal. The argument for protectionism in a very real sense has for a long time been about intertemporally increasing output by inducing production and investment decisions that seem perverse given current production possibilities and prices. The model also makes the important point that protectionism doesn’t have to ever give the protected country's protected industries absolute advantages in producing output over other countries for there to be an intertemporal maximization (or at least improvement) case for protectionism.
Then there is the issue of distribution which increasing returns under specialization brings to mind. If Robinson Crusoe and Friday were more conflictual, say because of property rights or because they represent different countries, in the specialization case Crusoe may not share any gains at all. After all Friday was gaining from specialization in the first year and should be willing to specialize for that benefit 25 years later. Of course the cost of not specializing to Crusoe is increasing all the time precisely because of his productivity increases. If the opportunity cost of not specializing for Friday was lowered by some probability of Crusoe giving in and sharing gains not specializing could be an optimal strategy for Friday for a sustained period of time. That is Friday may be well positioned to strike for higher wages and this example could be a case where striking improved overall welfare. After all economists typically say there is declining marginal utility to more of the same kind of output.
I hope you found this as interesting and entertaining as I did. I suspect that the different ways you can use the Robinson Crusoe story to express concepts in economics will become a running series on this blog.