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It does become absolute over time

By Daniel M. Ryan
web posted January 1, 2007

If you've gotten through economics, and are inclined to be pro-market, you probably finished the unit on The Law of Comparative Advantage with somewhat of a good feeling. It is nice to know that the supposedly inferior person, or country, can indeed gain from trade; it adds a humane cast to economics. Unsurprisingly, this Law is the one that the foes of the free market continually go after.

Yes, the assumptions embedded in the LoCA are restrictive; it says so in every professional-level explication of it. Most of those limits, as you might either remember or expect, do tend to make the free market look less humane if dropped. With respect to one of them, though - the one that hardly gets mentioned - the free market actually look better if it is dropped.

That assumption is that productivity levels are static. As assumptions go, this one, over very-long-term time, may very well be the most unrealistic of them all.

That's because of a finding in dynamic economics called the "learning curve," or the experience curve This curve, one backed up solidly by empirical research initially done by the Boston Consulting Group, identifies growth in productivity, including cost-cutting, that results from experiential learning. In its least optimistic form, it identifies a growth in productivity that, roughly, increases x% per subsequent doubling of experiential trials. If 10 additional trials, after the first, result in productivity growth of 15%, then another 15% growth will occur after 20, then another 15% after 40 (we're up to a total of 71 units as of now,) etc.

[I know that this interpretation of the experience curve is not the same as the standard one; it's actually the most pessimistic interpretation of the doubling effect. Sticking to the worser-case scenario makes for a stronger argument for comparative advantages eventually turning into absolute advantages. If this takes place under the more pessimistic interpretation, then it will do so in the standard case also, and will do so much more quickly.] 

What the experience-curve effect implies is, if A and B completely specialize in what offers each of them a comparative advantage, then the less productive party's comparative advantage will eventually become an absolute advantage. The comparative-advantage case is only temporary.

Here's an example: assume that A can produce 10 units of food, or 20 units of clothes, per day. B can produce only 5 units of food or 8 units of clothes per day. This disparity may bring a lot of comparative pride to A, but not to B.

Both A and B need both food and clothes, though. A has to alternate between food production and clothes production, as does B. In a 30-day month, A will have produced 150 (= 10 * 15) units of food and 300 (= 20 * 15) units of clothes. B will have produced 75 (= 5 * 15) units of food and 120 (= 8 * 15) of clothes. A, quite clearly, is wealthier than B.

But A and B aren't as wealthy as each could be. Should A decide to specialize in the production of clothes, and B specialize in the production of food, then A will produce 600 (= 20 * 30) units of clothes and B will have produced 150 (= 5 * 30) units of food. Had both A and B tried to be self-sufficient, both of them would have produced, in total, 225 units of food and 420 units of clothes.

It cannot be objectively said, at this point, that each is richer. The critics of the pro-market implications of LoCA have made much of "bargaining power" in this situation. Yes, there is a range of bargaining power, but the range has a hard floor and a hard ceiling to it: in order for trade to take place at all, each party must benefit. Why would B agree to a bargain that would result in owning fewer than 75 units of food or 120 units of clothes, and thus become worse off, with respect to one good, than under an exchangeless system? At the end of the month during which specialization has taken place, B has 150 units of food. Why would B give up more than 75 of them? And why would B take any less than 125 units of clothes in exchange for those 75 units of food? Doing either would be flatly irrational from B's standpoint. So, B has a floor price for the 75 units of food available for trade with A: no less than 5/3 (125/75) units of clothes per unit of food. Any lower price and no deal.

A faces a similar calculus: a maximum offer of 300 units of clothes. This is 300 over and above the number of clothes units obtainable by going it alone during the month. A will demand none less, in terms of food, than 150 units for the 300 units of clothes. For the same reason as B, A has an iron floor price of 0.5 units of food per unit of clothes, or 2 units of clothes per units of food.

So, going in to the negotiation round, A has a floor price of 0.5 units of food per unit of clothes and faces a ceiling of 0.6 units of clothes per unit of food, the reciprocal of B's ceiling price. B has a floor price of 5/3 units of clothes per unit of food and faces a ceiling price of 2 units of clothes per unit of food, the reciprocal of A's floor price. There is clearly scope for trade, a bargaining range, and any agreed-upon price that falls within this range will end up being mutually beneficial, leaving both better off than in the isolated-production case (unless the negotiation process falls apart.) Again, if one party winds up a loser with respect to either good, relative to what could have been produced in isolated splendor, then there will be no deal.

Interestingly enough, LoCA pre-dates the marginalist revolution. This means that the established ratios apply to any whole amount over and above the levels reached in isolation, for whatever goods are traded.

Let's add a (please, no guffaws) more reality-oriented assumption to this case: caution in specialization. After hearing of LoCA, A decides to spend only one extra day producing clothes and shaves off a day from food production. As a result, A winds up with 140 (= 10 * 14) units of food and 320 (= 20 * 16) units of clothes. B follows the same policy and ends the month with 80 (= 5 * 16) units of food and 112 (= 8 * 14) of clothes. B now has 5 extra units of food to trade, for which a minimum of 8 units of clothes will be demanded, giving a ratio of 1.6 units of clothes per unit of food, or 5/8 units of food per unit of clothes received. A has 20 extra units of clothes to trade, for which 10 units of food is the rock-bottom minimum, giving a ratio of 2 units of clothes per unit of food, or 0.5 units of clothes per unit of food received, as A's floor price. The slight difference in B's ratio is due to the discontinuity effect resulting from dealing in whole units – a kind of rounding error. (Note that the volume of trade will be determined by B's lower production of trade goods. In this particular scenario, A isn't going to give up more than 10 for B's 5.) Other than the discontinuity difference, which would melt away if each unit of food and clothes were each perfectly divisible into sub-units, the floor and ceiling ratios - the prices - are the same as they would be with the throw-the-caution-to-the-winds case. It's true that the total gains from trade will be less, in absolute amounts, than the case where both A and B decide to specialize completely, but such a limitation can be seen as a kind of insurance policy against one party leaning on the other.

Of course, the subsistence level for A and B will determine how much trade at all will be conducted, assuming no prior savings. The interesting thing about this factor, though, is that its initial limitation on the volume of trade, due to subsistence considerations, tends to melt away over time as total wealth increases. By sticking to a subsistence regimen, both A and B can save goods to use as a fallback hedge if the next trade round winds up in acrimony. As they both grow in wealth, and in reliability in trade, the total practicable volume of trade, and thus the total potential gains from trade, grow too, provided that consumption is limited to subsistence levels, or grows less than added production over time. Provided also, of course, that both food and clothes can both be saved for enough time to consume them later, with a First-Produced, First-Consumed regimen.

So, provided that common sense is brought to the decision to make, and put out, goods for trade, the LoCA works fine indeed – under the assumption that productivity levels are static over time. But what if they're not? What if the learning curve kicks in?

If B has a relatively modest gain of 10% productivity increase, per added doubling, when the full-specialization option is chosen, then B will never get any productivity improvements from clothes production, ever again. But, as B gains experience in food production, the 5 units of food per day will slowly creep up – and A's potential food production level won't budge at all.

If B has already produced a thousand units of food at this time, then B's productivity, by the time that 2000 further units have been reached, will be 10% more than it was at the time of shift to specialization. Assuming divisibility, A will be able to produce 5.5 units of food per day.

What if the units are not divisible? Then A will be stuck at 5 until the 6 threshold is crossed. Then, it will be six, and so on. Between the thresholds, A's still gaining, as the productivity improvement will be expressed in a shortened work day, but the gain comes in leisure, not in goods-wealth, until each threshold is crossed. If we assume perfect divisibility and a rigid 10% gain through an additional doubling, then B will be at the point of absolute advantage in food production long before the end of the 8th double, or after 510,000 units of food produced, subsequent to the first thousand food units. (Productivity at this specific point will have reached 10.7 units per day, using 3 significant digits rounded to the worse-case side, a rounding that I'll be using all through this article.) That is a lot of food.

Using the worser-case scenario of unit discontinuity, in which B stays stuck at 5 units until the 6 threshold is reached and so on up the curve, the first 3,760 food units after trade commences will be produced at 5 per day; the next 11,600 units will be produced at 6 per day; the next 30,500 will be produced at 7 per day; the next 72,000 units will be produced at 8 per day; and, the next 155,000 units will be produced at 9 per day. This approximation rounds down the productivity gains, in two ways; it's close to being the worst-case scenario under these constraints.

Under this assumption, it will take 752 days to move from 5 to 6 units of food per day; 1940 days to move from 6 to 7 units of food per day; 4360 days to move from 7 to 8; 9000 days to move from 8 to 9; and, 17,230 days to move from 9 to 10, making a total of 33,282 days for B to catch up to A, or about 91 years, 2 months and a week.

This is, of course, a very long time, but it is skewed by the assumption that B has an unusually low experience curve and a large base of prior learning under the belt. It's also quite damped with respect to the standard interpretation of the experience curve: according to it, 10 units of food per day will be reached after approximately 156,000 units of food have been produced in total, not 511,000. A doubling after 510,000 units, subsequent to the first 1000 units, implies, by the standard model, an experience-curve rate of 8.02%, not 10%. A standard 10% experience curve, with round-downs added due to unit-discontinuity and a 3-significant-digit knockdown of the case, implies that it will take A 52 years and 2 days to reach absolute parity with B, in terms of units of food produced per day.

Logically, though, the existence of the experience curve, period, implies that B will eventually surpass A in terms of productivity gains, provided that both A and B completely specialize in the good for which each has a comparative advantage. The only hole in it kicks in with the cautionary-trade scenario, provided that A produces more units of food than B per day, on average, because of incomplete specialization on A's part. This experience-curve advantage for A, with respect to food production, will melt away as trade becomes less risky. Given the scope for gains from additional trade, right up to full specialization for both A and B, there is a clear incentive for it to proceed to that level, as sketched out above. The closer A is to full specialization, the fewer food units A produces. Once A has gotten to producing less than an average of 5 food-units per day during the full month, the experience-curve advantage goes to B. These conclusions follow from the assumptions, no matter what numbers I use to give my calculator a workout. They also follow if "good X" and "good Y" are used, too.  

The picture for B, though, is better than it may seem in terms of catch-up time. There is such a thing as an atrophy curve, even if it hasn't been as studied as the experience curve. I know that it exists.

When I was ten, I could sing sufficiently well to rate a solo spot in a class rendition of "Silent Night." Nowadays, I can barely carry a tune, even with a music book in front of me. My singing talent has clearly atrophied.

With respect to that rendition, I was clearly the A, while someone in the chorus was the B. If that someone had gone down the experience curve while I was going down the atrophy curve, that B would have passed me in singing ability far quicker than an experience-curve-only calculation would imply. B's absolute advantage over me would emerge sooner than would have been the case had my singing ability stayed static.

As far as the no-atrophy case is concerned, it could be objected that the B may very well have a competitive advantage in the non-subsistence good, the clothes, instead of the subsistence good, the food. This objection is actually unrealistic, as poorer people, or nations, tend to acquire more relative experience in producing subsistence goods. Hungry cockerels don't gain experience hunting jewels, as Aesop knew; they acquire experience in hunting down food, first and foremost. This prior experience would make the trip down the food-production experience curve much more of a slow one for B, once trade commences, but it would all-but guarantee a prior comparative advantage in the production of goods that subsistence-level dwellers need. Why would the richer A have devoted more comparative time to learning how to better produce a subsistence good instead of a relatively luxurious good, anyway? And why would the poorer B gain the bulk of comparative experience-curve benefits in the production of a good farther away from fulfilling subsistence needs?

When these factors are considered, the "tyranny of international trade" argument melts down, except for unusual cases, into a mere bargaining tool. The supposed risks of poor B being entangled in a dependency relation with rich A (or vice versa!) melt away if we assume that B (or A) will act according to the dictates of common prudence – if B and A act sensibly, to put it more bluntly.

As far as common prudence is relevant to the negotiating process itself, B has an additional bargaining incentive to specialize in producing a subsistence good. "Fine; go back and tighten your magnificent belt" might very well make A more reasonable…ceteris paribus, of course.  ESR

Daniel M. Ryan is a regular columnist for LewRockwell.com, and has an undamaged mail address here.


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