Superior productivity of American industrial workers

Discussions on the economic history of the nations taking part in WW2, from the recovery after the depression until the economy at war.
KDF33
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Re: Superior productivity of American industrial workers

Post by KDF33 » 08 Jul 2021 02:10

Richard Anderson wrote:
07 Jul 2021 22:25
How is 19% of 36,527,000 "i.e. 12 million persons"? Why isn't it 6,940,130? Harrison's poorly defined "Group 1 Industry" has to be a subset of the NBER "Industry" doesn't it? Which would mean it is a subset of 10,998,000.
Hi Richard. 19% is the figure for the United States, not Germany. It is a subset of either 62.2 million (p. 16, for April), 62,026,000 (p. 65, for mid-year), or 63,490,000 (p. 126, as an annual average).

This gives us a range of 11,784,940 (mid-year) to 12,063,100 (annual average).
Richard Anderson wrote:
07 Jul 2021 22:25
Of course, the real problem is trying to compare two different labor accounting systems calculated at what were probably slightly different time periods.
At least in terms of what 'Group I' accounts for, Harrison made sure to compare apples-with-apples, as he explains here (paywall, but 100 free articles per month if one subscribes).

All the evidence points to the U.S. employing in 1943 ~12 million people in the metal, chemical and allied (i.e., 'Group I') industries.

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Re: Superior productivity of American industrial workers

Post by historygeek2021 » 08 Jul 2021 02:53

KDF33 wrote:
08 Jul 2021 02:10

Hi Richard. 19% is the figure for the United States, not Germany. It is a subset of either 62.2 million (p. 16, for April), 62,026,000 (p. 65, for mid-year), or 63,490,000 (p. 126, as an annual average).
Harrison gives the actual number of U.S. workers in Group I Industry in his book, Economics of World War II, page 104:

1939: 4,715
1940: 5,363
1941: 6,968
1942: 8,823
1943: 11,084
1944: 10,856
1945: 9,074

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Re: Superior productivity of American industrial workers

Post by KDF33 » 08 Jul 2021 03:44

historygeek2021 wrote:
07 Jul 2021 22:11
Thanks. It wasn't clear to me whether the chart was in percentages or raw numbers, but you've convinced me it is in percentages.
My pleasure. Filtering through the troves of data, and getting a firm handle on the definitions used - to say nothing of sometimes having to correct authors' mistakes - is quite a chore and I certainly have also experienced the occasional misreading.
historygeek2021 wrote:
07 Jul 2021 22:11
Harrison gives a (Economics of WWII, page 104), gives a figure for U.S. workers in Group I industry in 1943 as 11,084.
Here we face one such mistake, although not Harrison's. Harrison is only the editor of the book, with the chapter's author being Hugh Rockoff. Although Rockoff names his first column 'Group I', by looking at his own source material we find that he mischaracterizes his data.

First, let's look at Rockoff's work:

Image

Second, let's look at his source:

Image

Rockoff has committed an error of imprecision. He has conflated 'manufacture of durable goods' with 'manufacture of metal, chemical and allied industries' products'. But of course not all durable goods are made by 'Group I' industries, whereas many 'Group I' industries produce non-durable (i.e., consumable) goods, the latter being listed under series D132.

It is much better to use Harrison's figure of 19.0% for 1943, which amounts to almost exactly 12 million.
historygeek2021 wrote:
07 Jul 2021 22:11
USSBS Appendix Table 15 gives the number of German workers in Group I industry in 1943 as 6,863.
There are two problems with the table: first, it is for 5/31/43, rather than an average for the year. Second, there appears to be some distortion to 'Groups I and III' by the inclusion of handwork data for 1944, as can be seen here:

Image

Indeed, the USSBS figure for civilian employment on 5/31/43 is 320,000 higher than that of the Kräftebilanz, which it is built from. To correct for that issue, as well as to get a yearly average, I calculated revised figures by averaging out the following:

Image

I also included similar data for 11/30/42. Admittedly my average is somewhat skewed higher because of the concentration of late dates (9/30/43, 11/30/43 and 1/31/44), but then I miss a few hundreds of thousands of contributing handworkers. All-in-all my average of 6,242,667 workers is probably a sliver too low. Note that if we were to apply Harrison's share of 14.2% against 5/31/43, we'd get 6,543,928 'Group I' workers.

At the end of the day, it doesn't change much. Here is what we get if we use the latter figure:

Germany: $13,500,000,000 / 6,543,928 workers = $2,063
United States: $38,000,000,000 / 12,063,100 workers = $3,150

We get 65% of U.S. productivity instead of my original estimate of 68%. Even using the demonstrably inflated figure of 6,863,000, we'd still arrive at 62% of U.S. productivity.
historygeek2021 wrote:
07 Jul 2021 22:11
So the number of workers in Group I Industry in Germany in 1943 was 61.9% of the number of workers in Group I Industry in the United States.
As demonstrated above, it was somewhere between 51.8 and 54.2%.
historygeek2021 wrote:
07 Jul 2021 22:11
Where are you getting your valuation for total armaments production by each country?
Harrison, Resource Mobilization for World War II:

Image
historygeek2021 wrote:
07 Jul 2021 22:11
Since Group I Industry is more than just armaments (it also includes steel, aluminum and synthetic rubber), it would still seem to be the case that looking at the gross weight of steel, rubber and aluminum is a good basis for comparing the total industrial output of each country.
That would be a mistake. Metals manufacture was a small fraction of Group I industry - in the case of Germany, in 1943 it employed on average 577,333 out of 6,242,667 industrial workers. If a single metrics is to be used, it definitely should be the value of armaments output.
historygeek2021 wrote:
07 Jul 2021 22:11
In this case, the industrial output of the USA dwarfed that of Germany, despite Germany having 62% of the industrial workers of the United States.
'Dwarf' is an imprecise term. Practically speaking, the U.S. outproduced Germany 2.4-to-1 in 1942, 2.8-to-1 in 1943 and 2.5-to-1 in 1944. In 1943, the only year for which we have reasonably comparable labor inputs, its metal and chemical industry complex ('Group I') employed almost twice as many people as its German counterpart.

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Re: Superior productivity of American industrial workers

Post by Richard Anderson » 08 Jul 2021 04:45

KDF33 wrote:
08 Jul 2021 02:10
Richard Anderson wrote:
07 Jul 2021 22:25
How is 19% of 36,527,000 "i.e. 12 million persons"? Why isn't it 6,940,130? Harrison's poorly defined "Group 1 Industry" has to be a subset of the NBER "Industry" doesn't it? Which would mean it is a subset of 10,998,000.
Hi Richard. 19% is the figure for the United States, not Germany.
Oh, sorry, is Table 3 supposed to relate to Germany? I guess I'm confused. It appeared to be something you posted from NBER.
It is a subset of either 62.2 million (p. 16, for April), 62,026,000 (p. 65, for mid-year), or 63,490,000 (p. 126, as an annual average).
Ah, so you are making an approximation from a chart rather than from a data table.
At least in terms of what 'Group I' accounts for, Harrison made sure to compare apples-with-apples, as he explains here (paywall, but 100 free articles per month if one subscribes).
Okay.
All the evidence points to the U.S. employing in 1943 ~12 million people in the metal, chemical and allied (i.e., 'Group I') industries.
I see.
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Re: Superior productivity of American industrial workers

Post by historygeek2021 » 08 Jul 2021 05:50

KDF33 wrote:
08 Jul 2021 03:44
Filtering through the troves of data ...
Thanks for all the sources you provided. This is really helpful.

Starting with German Group I Industry. First, I don't see where USSBS Appendix Table 15 limits its data set to May 31, 1943. It just says 1943. Can you show where it says May 31, 1943? Second, Footnote 1 says it includes "related" handwork. I would think handwork directly related to the completion of a Group I product should be included in the worker count. Third, if you have a screenshot or link to Kräftebilanz, please share it.

If we use your method from Appendix Table 9, I get the same average as you for 1943 (6,242,667 workers).

What source/figure are you using to apply to Harrison's Group I percentage? Economics of WWII, p. 160, shows a German labor force of 36,174. If I multiply that by 14.2%, I get 5,136,708 Group I workers. If I use the same book's figure for the employed U.S. workforce, I get the same Group I number as you: 12,063,100.

I found the underlying source that Harrison uses for his 19% figure for Group I Industry, available here: https://books.google.com/books?id=jAc_Q ... &q&f=false

Page 35 of the underlying source gives us this breakdown of U.S. employment:
Harrison Source Page 35.png
I exclude non-Group I manufacturing in this spreadsheet:
American Industry p35 calc.png
Which gives us a lower bound of 10,910,000 Group I USA workers in 1943. Page 36 of that source states that the total U.S. manufacturing workforce devoted to war was 10,060,000. In comparison, USSBS page 37 states that 6.6 million German industrial workers were engaged in work for the armed forces by May 1943 (which is essentially the same as your estimate).

I have compiled all of the above estimates for the German and US Group I Industry workforce in this spreadsheet:
Group I Compilation.png
Taking the average of each of these estimates, I get a percentage of 54.83%. However, the Harrison % estimate of 5,136,708 Group I German workers seems to clearly be too low. If we exclude that estimate and only use the other 4, we get an estimate that the German Group I Industry workforce was 57.90% of the U.S. Group I workforce.

Turning to output, if we add the total tons of industrial material (steel, rubber and aluminum) made by each country, I get a U.S. to German output ratio of 2.70 to 1. This is probably too low a ratio to use since the work required to make a ton of aluminum and especially rubber was likely a lot higher than that required to make a ton of steel. If we follow your method and use Harrison's valuation of armaments, we get 2.8 to 1 for 1943. Given that the United States had 1.72 times as many Group I workers as Germany, this shows that the average American Group I worker was 1.62 times as productive as the average German worker, which is basically the same as what you arrived at.

Note that if we extrapolate from the data in Economics of WW2, pages 3 and 7 and 10, U.S. per capita GDP in 1943 was 1.72 times that of Germany's, suggesting our estimate is pretty close to accurate.
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Re: Superior productivity of American industrial workers

Post by historygeek2021 » 08 Jul 2021 06:56

In terms of trends, the United States appeared to drop its demand for war material in 1944, with the size of its Group I workers falling, while Germany's appears to have plateaued at roughly 6.6 million through the first half of 1944. The output of both countries increased that year, and I get a rough estimate of relative productivity that is about the same as what we got for 1943:
Group I 1944.png
Two factors that are hard to take into account quantitatively given calendar year figures for output are (1) decline in German production due to U.S. bombing and (2) decline in U.S. production due to the foreseeable end of the war. Both of these declines would have taken place in the latter half of the year. While it would be helpful to see monthly comparisons of output and Group I labor, I think our estimates have effectively captured labor productivity for both countries at their peak from late 1943 through the first half of 1944.

Another issue that KDF has identified is that Germany devoted a lower portion of its workforce to Group I industry, only 14%, compared to 19% for the USA. So there is an argument that Germany had more potential to grow its industrial output than the United States, if Germany had been able in certain counterfactual scenarios to reduce the size of its armed forces (which Harrison describes as "bloated" in Resource Mobilization - Harrison also blames Germany's incompetent federal bureaucracy for failing to effectively mobilize and organize the domestic working population). I guess our next set of calculations should show what Germany could have achieved if it devoted Allied style numbers to its Group I industry:

USA: 19%
UK: 23%
USSR: 31%
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Re: Superior productivity of American industrial workers

Post by historygeek2021 » 08 Jul 2021 14:57

If we assume Germany could maintain constant Group I labor productivity by adding more workers from the Wehrmacht, then I come up with the following if Germany had matched the mobilization levels of the Allied countries:
ATL German Industry and Armed Forces.png
The column on the right is an estimate of the size of the Werhmacht for each level of output. This assumes 1 million in irrecoverable losses to the armed forces by the time Germany is able to discharge members of the Wehrmacht, switch them to Group I industry and achieve a peak level of output. In the OTL, that casualty level occurred in the second half of 1942. Given that the OTL Wehrmacht peaked at about 9.5 million in 1943, a realistic level assuming an ATL with a "peaceful" eastern front is probably in the neighborhood of 7-8 million, theoretically allowing Germany to achieve 65-70% of the USA's armament output.

However, these output levels are excessive, given that Germany only had approximately 5 million Group I industry workers in 1939 prior to the outbreak of the war. It's unrealistic to assume that 2 or 4 million workers with no experience in Group I industry could simply be added and match the productivity of trained workers.

There is also the constraint of raw materials. Germany would have needed to devote significant labor to expanding its raw materials base in order to meet the level of production shown in this chart. Starting with coal as Germany's primary natural resource, significant effort would have needed to improve Germany's transportation network to be able to transport additional coal to its necessary outlets. With iron ore as the primary ingredient in armaments production, the question is whether Sweden could have supplied the additional ore necessary to support this armaments expansion. If not, Germany would have had to devote considerably more labor to mining and processing the low grade ore available in France and Germany. Likewise for aluminum, a greater effort would have been needed to mine bauxite before it could be processed into aluminum. Germany seems to have achieved most of its copper supplies through plunder, I'm not sure a sufficient level of copper production could have been achieved to sustain higher levels of armament production.

On the other hand, Germany likely would have had an adequate supply of manganese from the Ukraine and could have traded for chromium from Turkey. Synthetic production of oil and rubber appears to have been adequate and could have been expanded depending on the availability of coal.

The main question then seems to be whether Germany could have transformed Europe's economy in time to develop the raw materials base to support additional industrial output before the U.S. and British air force destroyed Germany's industry. And the limiting factor there is probably political: The incompetent German leadership would have been too busy celebrating another victory instead of mobilizing their economy to take on the U.S. and British air forces.
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Re: Superior productivity of American industrial workers

Post by Richard Anderson » 08 Jul 2021 17:25

KDF33 wrote:
08 Jul 2021 03:44
My pleasure. Filtering through the troves of data, and getting a firm handle on the definitions used - to say nothing of sometimes having to correct authors' mistakes - is quite a chore and I certainly have also experienced the occasional misreading.
Indeed, normalizing the data is one of the big problems when everyone uses a different definition.
Here we face one such mistake, although not Harrison's. Harrison is only the editor of the book, with the chapter's author being Hugh Rockoff. Although Rockoff names his first column 'Group I', by looking at his own source material we find that he mischaracterizes his data.
Good example.
It is much better to use Harrison's figure of 19.0% for 1943, which amounts to almost exactly 12 million.
Why is it "better"? Historygeek2021 finds where Harrison derived the figure of 19.0% from, but it isn't "19.0%", it appears to be 19.52%...and isn't "Group 1 Industry", but rather is "manufacturing, mining, and construction". It looks like that is "mischaracterized" too?
There are two problems with the table: first, it is for 5/31/43, rather than an average for the year. Second, there appears to be some distortion to 'Groups I and III' by the inclusion of handwork data for 1944, as can be seen here:
More problems than that. For example, BLS characterized employment data in the airplane industry by type of contractor, prime or sub, rather than by the type of work down, as in the German data sets.

Anyway, to take one comparison, USSBS Production of all German aircraft production in 1944 was 39,807 aircraft weighing 174,938 metric tons using 870,000 laborers. So 0.046 aircraft and 0.201 metric tons per laborer.

OMP Production of all U.S. military aircraft in 1944 was 93,588 aircraft weighing 948,883,000 pounds (430,406 metric tons) or 1,087,493,000 pounds including spares (493,279 metric tons) using an average of 1.964 million employees. So 0.048 aircraft and 0.219/0.251 metric tons per employee. However, all U.S. aircraft production - civilian and military - in 1944 was actually 96,318 weighing 962,441,000 pounds (436,556 metric tons) or 1,101,116 pounds including spares (499,458 metric tons). So 0.049 aircraft and 0.222/0.254 metric tons per employee.

Another way to look at US defense employment is that the figures included military personnel, civilian employees of the military, and employees of defense-related industries. 1944 was 40.3 percent of the labor force of 65.2 million minus 10.9 million in military = c. 15.3756 million non-military defense employment.
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Re: Superior productivity of American industrial workers

Post by TheMarcksPlan » 09 Jul 2021 06:32

historygeek2021 wrote:If we assume Germany could maintain constant Group I labor productivity by adding more workers from the Wehrmacht
As has come up numerous times, this is a most-ungenerous assumption. Germany was drafting extremely productive skilled workers, especially by 1943.

A more valid assumption would that, under certain ATL conditions, more returned Wehrmacht personnel would enable more foreign laborers under skilled German supervision - at overall productivity similar to OTL.
historygeek2021 wrote:download/file.php?id=486235&t=1
Your table retains 31% Group 1 for SU, which as I explained here is off by nearly 4x and can only be a typo or other error.
historygeek2021 wrote:download/file.php?id=486235&t=1
Your table also contains a common error/misconception about relative mobilization levels. See Harrison's graph from Resource Mobilization

Image

As you can see, from domestic resources US spent 53% on war in '43 and Germany 60%. What's the difference between these figures and yours? Net imports. US sent ~6% of its GDP abroad in LL, Germany stole 16% from Europe.

This actually provides a great argument you haven't yet used: That Germany's armaments productivity is artificially inflated by stealing from Europe and not considering European labor inputs (Tooze also makes this criticism of Wagenfuhr's table, cited earlier). This is distinct, btw, from military production in Germany by stolen Europeans.

To measure the impact of this dynamic on armaments productivity, however, we'd have to know how much non-armaments and armaments production Germany got from occupied countries. I know of no such data (does anyone?). Occupied Europe provided relatively little finished armaments but substantial armaments inputs and, presumably, non-armaments military production.

...which returns me to an over-arching theme I've been droning about; nobody seems interested: We have stats on total military spending and on armaments output; we don't have good stats on non-armaments military labor forces.

...which is why, although I have immense praise for KDF33's digging through the sectoral stats and trying to reconcile them, I'm not hopeful that we have any data set adequately distinguishing armaments and non-armaments labor force employment, even assuming we correctly identify total military spending, armaments output, and industrial sectors.
Last edited by TheMarcksPlan on 09 Jul 2021 07:17, edited 1 time in total.
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Re: Superior productivity of American industrial workers

Post by TheMarcksPlan » 09 Jul 2021 06:56

historygeek2021 wrote:significant effort would have needed to improve Germany's transportation network to be able to transport additional coal to its necessary outlets.
German rail traffic by t-km increased 57% between 1939 and 43 (Mierzejewski, History of the German National Railway, v.2 p.144). Germany built/rebuilt a massive rail network in the SU and elsewhere that, by '43, was operating far above '41 levels. Expansion wasn't a problem.
historygeek2021 wrote:The incompetent German leadership would have been too busy celebrating another victory instead of mobilizing their economy to take on the U.S. and British air forces.
By '42 the German economy was in competent hands, by comparative standards.

Have you read anything about US/UK economic management? Keep from All Thoughtful Men: How U.S. Economists Won World War II, which I'm currently reading, demolishes a lot myths about the US economy, such as:
  • To argue, as most historians have done, that President Roosevelt’s
    insistence on setting what at the time appeared to be both
    astronomical and impossible production goals inspired and provided
    impetus to American industry to reach record levels of production,
    ultimately burying the Axis under a tsunami of U.S. munitions, is
    also incorrect. I will show that Roosevelt’s ill-thought-out goals and
    his stubbornness about adjusting them came close to seizing up the
    entire production program and ending any practical chance of
    invading northern Europe in 1944. Furthermore, his insistence on
    producing what he called his “must items” threw U.S. production so
    out of balance that it endangered the conduct of military operations.
Just as in Germany, military and political leadership made unrealistic demands that threatened disastrous consequences. The difference was not the leaders - here FDR was as bad as Hitler - but that we had better economists. These men were Jewish, btw, a point that the press publicized and resulted in their being booted from government and forced into enlistment. Luckily they lasted long enough to correct the incompetent leaders. (though it makes one wonder how much full knowledge of the Holocaust would have changed things)

I'll be citing this book more; I found it recently after KDF33's remark that the US economy needs a "Tooze treatment." It's not exactly that but decisively deflates some patriotically-correct thinking.
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Re: Superior productivity of American industrial workers

Post by Tom from Cornwall » 09 Jul 2021 07:22

TheMarcksPlan wrote:
09 Jul 2021 06:32
As you can see, from domestic resources US spent 53% on war in '43 and Germany 60%. What's the difference between these figures and yours? Net imports. US sent ~6% of its GDP abroad in LL, Germany stole 16% from Europe.

This actually provides a great argument you haven't yet used: That Germany's armaments productivity is artificially inflated by stealing from Europe and not considering European labor inputs (Tooze also makes this criticism of Wagenfuhr's table, cited earlier). This is distinct, btw, from military production in Germany by stolen Europeans.
What I haven't also been able to work out is how much of Germany's exports during the war (including steel and oil) went to its allies or colonies in order to sustain either logistic support to its units in the field (Italian convoys to North Africa, for example) or industrial production in support of its war effort (French trucks, for example). Has anyone seen any figures that would help there?

Regards

Tom

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Re: Superior productivity of American industrial workers

Post by TheMarcksPlan » 09 Jul 2021 07:31

Tom from Cornwall wrote:how much of Germany's exports during the war (including steel and oil) went to its allies or colonies in order to sustain either logistic support to its units in the field (Italian convoys to North Africa, for example)
That's not an export, AFAICS. No more than is the tank used in Russia.
Tom from Cornwall wrote:industrial production in support of its war effort (French trucks, for example).
That would be contained in net imports. This book probably contains some stats on German capital investment in French truck plants.
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Re: Superior productivity of American industrial workers

Post by TheMarcksPlan » 09 Jul 2021 08:02

KDF33 wrote:U.S. outproduced Germany 2.4-to-1 in 1942, 2.8-to-1 in 1943 and 2.5-to-1 in 1944.
At the risk of being insufferable, we should be careful of the total armaments statistics as well. Harrison's source is a 12-page article written in 1946 whose entire analysis comparing US and German output appears below (highlighted):

Image

...hardly a body of scholarship on which to build precise productivity analysis.

That the prewar $/RM exchange rate is broadly in line with estimated production values (let's be honest - that's how Goldsmith got there) is the most reassuring part of the analysis.

...assuming no serious wartime differences in inflation/deflation, Germany vs. US, which is dubious.
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Re: Superior productivity of American industrial workers

Post by TheMarcksPlan » 09 Jul 2021 14:34

Just read an article by Tooze and Ristuccia, "Machine tools and mass production in the armaments boom: Germany and the United States, 1929–44."

Typically for Tooze at his best, it's dense, quantitative, and subtle. A few points bearing on our discussion:

1. The authors find unsupported, or needing serious revision, the typical (e.g. USSBS) narrative on fundamentally different German and American production techniques:
The US armaments boom, coming in the wake of the convulsive shock of the great
depression, pointed the way towards a far more selective and complex model of
production, which was capital- as much as labour-saving. There is every reason to
think that West Germany exemplified precisely such a complex strategy. But we are
once again reminded of how much more we have to learn about the history of
modern mass production after Fordism.
2. The authors find that German-US productivity grew at similar rates between 1929 and 44, indicating the persistence or slight increase of prewar American productivity edge (Table 1). The authors invoke factors we've mentioned here - e.g. slave labor and bombing - to suggest that these held back German wartime productivity growth, leaving room for "catch up" by West Germany after the war.

3. The authors endorse a 3.8:1 RM:USD exchange rate, whereas Goldsmith suggests RM was slightly more valuable than 2.5 : 1. This would indicate that US out-produced Germany in munitions by nearer to 4:1 than 2.5:1. Obviously a big revision of the picture.

Using the lower RM value implies even lower German labor productivity than we've been discussing, based on the disputed workforce statistics.

It also suggests, however, that the production costs of German weapons were even lower than commonly supposed, relative to their American counterparts. A Ju-88 cost ~130k RM in '43, for example ("Fixed Price Contracts" by Budrass, Scherner, and Streib). That's only ~$35k or ~28% of the $125k B-25. What's up with that?

I don't know exactly. Which, again, is why I'm not taking a strong position on who's right about the relative labor productivity stats. It's also why I'm concerned with concept of value vs. price, trying to explore it in speculative threads for example.

For my ATL purposes, this is why I usually focus on asking what Germany could have produced had she been able to demobilize 6mil workers and add millions more foreign laborers. I don't need international stats and their thorny problems to project that hypothetical...

Regardless of whose workers were more productive, a Germany producing twice as much ordnance, with ~75% of that going to planes (and sufficient fuel for training), would have been impossible to bomb conventionally. viewtopic.php?f=11&t=253448&p=2329160&h ... k#p2329160
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Re: Superior productivity of American industrial workers

Post by historygeek2021 » 09 Jul 2021 18:13

KDF33 wrote:
05 Jul 2021 23:45
historygeek2021 wrote:
05 Jul 2021 04:25
Thus, U.S. workers were orders of magnitude more productive than their German counterparts, due to superior capital and institutional experience in mass production and a vastly superior raw materials base. Even if Germany doubled the number of workers employed in industrial tasks, Germany would not have come close to matching U.S. war production. This is especially true when we factor in the law of diminishing marginal returns.
That's highly disputable. Although U.S. workers were, indeed, somewhat more productive, the gap was far narrower than is commonly assumed, and the vast majority of the differential in outputs is accounted for by larger U.S. inputs. Looking at aircraft production, for instance, we get:

Airframe weight produced, April/May 1943, compared to workforce employed in airframe assembly on May 1st of the year:

United States: 67,644 metric tons / 1,084,000 workers = 0.062 ton per worker
Germany: 19,368 metric tons / 373,000 workers = 0.052 ton per worker

German productivity is 84% of that of the U.S., at a time when a large part of the former's workforce was composed of coerced foreign labor. U.S. productivity was definitely higher at the margins, but it was not 'an order of magnitude' higher than that of Germany - or of any of the other main belligerents, for the matter.
Elsewhere, Richard gives us the total number of aircraft industry workers in each country:
Richard Anderson wrote:
29 Oct 2020 02:20

Okay, so then in 3Q43, the "final process of assembly" labor in the aviation industry (airframe, engines, and props) in Germany was 935,000 and the US was 910,851 (airframe), 296,949 (engines), and 157,593 (props), for a total of 1,365,393. Now do the productivity calculation.
If we use Richard's figures, then I get:
Productivity Air US v Ger.png
US aircraft industry workers were more than twice as productive as their German counterparts.

The numbers are slightly off, because Richard's numbers are for the third quarter of 1943, whereas KDF is using April/May 1943, but the data show that German aircraft production remained constant over this period, while U.S. aircraft production increased during the third quarter. So this is actually understating the U.S. advantage in productivity.
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