Fixed and variable costs

Fixed and variable costs are concepts that every economist knows very well, and over time I found them to be extremely useful tools for thinking about many things.

It goes like this:
You buy a machine that costs 1 Million €. Now you produce items that cost 1 € each to make.
Let's assume you buy that machine and produce exactly one item, then you forget about the machine. Your total costs of producing that one item was 1,000,001 €. 1 Million € fixed costs and 1 € variable costs.
Let's now assume you did not stop producing after one item; you produce a million items instead. Your total costs was 2,000,000 €. 1 million € fixed costs and 1 million € variable costs. The costs were thus two € per piece; 1 € fixed costs and 1 € variable costs per item.
The variable costs depend on the quantity, while the fixed costs are what costs you have to be able to produce any quantity at all.*

Fixed costs are often sunk costs, too; they incur anyway, regardless of whether you produce anything. A factory may consider the costs of the building as fixed costs in its production, but the building was probably built last year regardless of whether you continue to produce in it or not. Sunk costs should never influence decision-making, period.

These actually very simple concepts are very powerful mental tools. I've observed people having very confused thoughts about issues where resources allocation was of great importance. They lacked the economist's tools to make sense. Economic decisions driven by 'feelings' alone are all-too often poor decisions.

- - - - -

The fixed costs issue is pervading almost everything. Development costs and start of production costs are fixed, per copy costs are variable costs of a hardware program, for example.

One can also use the concept and transfer it. An interesting example in the military realm is about warships:

A warship needs a minimal crew for navigating and keeping it running. That's the fixed effort required for running a ship, regardless of what it's being used for.

The employment as a warship (excluding quite incapable patrol vessels) requires additional fixed effort, regardless of what specifically it's supposed to do: Extra communications gear, at least a multifunction radar, ESM, ECM, shock proofing, silencing, command centre, at least short range air defences, at least a 57 mm gun, at least basic anti-submarine hardware, propulsion power for higher speeds  - and the crew to make use of all this in at least a two-watch system.

HNLMS Tromp, a classic SARH missiles-armed AAW frigate
with obvious special AAW equipment ((c)Quistnix)
Why is this important? Let me show a hypothetical calculation:

Let's say the necessary basic equipment costs 100 coins.
The equipment needed to improve the ship to a dedicated air defence ship costs 50 units.
The equipment needed to improve the ship to a dedicated anti-submarine ship costs 50 units as well.

There are people arguing in favour of specialised ships. Let's look at that:

1 AAW ship costing 150 coins.
1 ASW ship costing 150 coins.
Meanwhile, one could have 1 general purpose (GP, AAW and ASW combined) ship for 200 coins with the same effectiveness in one package.** That's 1/3 less purchasing costs and even greater operating costs savings.

Now one could say all eggs in one basket is no good idea.

Well, let's look at a fleet of baskets to check this out:
We afford 10 AAW ships + 10 ASW ships OR 15 GP ships (purchasing costs each 3,000 coins).
The GP ships are 50% more capable. What do we have after 4 ships were lost in combat?

6 AAW + 10 ASW or 10 AAW + 6 ASW as extremely unfortunate scenarios, or evenly distributed attrition with 8 AAW + 8 ASW left. Meanwhile, the GP fleet is down from 15 to 11.
The GP fleet is still at least 37.5% more capable!

Let's say there are catastrophic losses; 10 ships sunk.
5 AAW + 5 ASW left. As are 5 GP ships. This is break even; GP ships and specialised ships have equal capability - but this requires 67.7% losses among the GP units! Instead, 10 ASW or 10 AAW ships could have been sunk, eliminating the ASW or AAW capability of the fleet. So why not think about the specialised approach as having the eggs in too many baskets?

"All eggs in one basket" was an irrational fear regarding GP warships in this hypothetical example. Feelings are a poor guide in resource allocation decisions.

HNLMS Kortenaer, a contemporary ASW frigate of the same navy
I write about this warship example because a warship is awfully expensive even if it has only basic equipment for self-defence against aerial threats including modern missiles, basic gun armament, mine avoidance sonar, SatCom, ESM (radar warning receivers, passive radio direction finders), seaworthiness, good endurance, crew quarters, redundant propulsion for well over 20 kts, helipad with related equipment, shock hardening, fire protection, boats and equipment for their recovery and so on. The huge basic ('fixed') cost leads to rather useless corvettes (which cannot afford much more than self defence***) and supports the case for GP warships over ASW or AAW warships.

The correct choice between specialised warships and general purpose warships isn't about personal preferences, or necessarily much about tactics. The correct decision-making method has to be dominated by the question how much of the costs is fixed for a basic, non-specialised and largely incapable warship capable of self-defence only. A resource allocation question should be answered with help of the appropriate economic tools.

Furthermore, the smaller the "extra" costs for either AAW or ASW capability become, the more likely is a GP ship the correct choice.****


(Some readers may have noticed that I deviated from the purely economic idea of fixed and variable costs, and transferred the concept to a different application. The analogy of "base+specialisation costs" is based on largely the same idea as the fixed+variable costs. The transfer of ideas to analogies is often useful - physics for example uses almost identical formula to describe a plethora of different waves. That's a tertiary point of the blog post; once you become educated with certain tools, you can be expected to make use of them, even transfer them to other areas.)

*: Not a textbook-grade definition.
**: Assuming no need for a larger hull and what higher order costs that causes. This simplifies the text. The moral of the story doesn't change if you assume 220 instead of 200 coins.
***: Hence they don't approach frigates in capability in anything but ship-to-ship missiles. Those can also be had even even much smaller (approx 1/10th the displacement of corvettes) fast attack craft. Corvettes are never high quality ASW or AAW ships. Corvettes are little but targets in a high end war.
****: This is why I wrote in the warship series in favour of GP warships (if warships at all). AAW better include AEW, and once you include (survivable) AEW you can largely do away with the expensive giant ship radars. The rise of surface to air missiles that need no illuminator radars eliminated their costs from the 'AAW extra expenses' list. An ASW ship can be an AAW ship simply by adding a console and a little more than a dozen VLS cells (which can even be retrofitted on superstructures!). The extra expenses for AAW capability (area air defence) have become tiny, so (near) future warships (escorts) should be GP warships.


  1. Very good post!

    You make your case with great clarity.

  2. I presume this post is directed towards the blog Navy matters. Don't bother, its author has got a proper bee in his bonnet and any attempt to critique his arguments leads to him creating a straw man argument, deleting posts and abuse.

    1. Among other things it was inspired by his obsession with specialised, smaller ships. His reasoning appears to be very incomplete. He appears to ignore just about every good case against specialisation of FFG and DDG.

      His behaviour was already mentioned in this month's link drop post and comments there.

  3. There are other considerations as well. If you build more of something, each successive iteration will cost a bit less (to a point).

    If you commit to a larger buy, there are all manner of economies from work sequencing, to steady funding for suppliers, to higher yard utilization.

    And if you can buy at a high enough rate (more relevant for the USN or other very large navy), you can split work across competing yards (e.g. DDG-51 class).

    1. Yes, this wasn't meant to be comprehensive. I used a ceteris paribus approach - one aspect and its effects at a time.

  4. Maybe next, you can do one on the stupidity of battleships.


    1. He obsesses about non-continental war with China, I obsess about almost exclusively continental deterrence & defence in Europe.
      Naval gunfire land attack is self-evidently nonsense in my scenario, and I don't really care about his scenario.

      Besides, I suppose the fanbois love the battleship talk anyway, and the non-fanbois understand that he's writing nonsense about 21st century battleships. I don't think I should wastetime on opposing him unless it's part of a bigger case to make.

  5. A question about your calculation:

    Are the costs of developing a general purpose ship further realy around 50 % of his main purchase costs (50 units adding to 100 units). I do not ask about exact sums / percentages, only about the direction ?

    What if the hypothetical calculation would be:

    1 Genereal Purpose Ship 100 units, AAW + 100 units and ASW + 100 Units

    and the costs for the more specialised smaller ASW and AAW ships would for example only 100 units.

    Then you have 1 GP ship with AAW and ASW for 300

    or 3 AAW / ASW ships instead.

    Your whole calculation / argumentation is based on this numbers, that to add on packages to an gp ship is much cheaper.

    But is this (always?) the case at all ?

    To include several specialised packages into one ship you need a bigger ship - a bigger hull and so on and the costs for the ship itself would increase. And to install ad ons is not everytime as cheap / cheaper as you suggest here. Sometimes it is even more expensive than an specialised system.

    Also: is the quality here then the same ? Many times a add on for a gp system has not the same abilities / quality than an more specialised system. And if it has the same quality, the costs are often higher.

    Moreover: if you use specialises smaller units, you could also construct a general purpose hull/ship which then can carry only one such module (AAW or ASW or ...) instead of having all such modules in one ship together.

    Such smaller modular ships would be perhaps even better because the costs per ship would be lower and they all share the same hull / basic ship design, but are smaller and therefore cheaper.

    What if your basic asumption, the hypothetical calculation is wrong ? Do you have an practical example and practical numbers for the costs available ?

    1. Have a look at my warships series from January/February. You'll see that my idea of a GP FFG is actually a ASW FFG that can do area air defence because missile tech (especially ESSM Blk II) and datalink to AEW enables this with little extra effort (no illuminators, no huge radars).
      I argued against the conventional AAW specialised units by pointig out that their huge investment in onboard radar tech has been of little use.

      To turn a ASW FFG into a GP FFG costs likely much less than +33% as in my abstract example.

      A valid criticism is that a dedicated ship may be better in its domain than a GP unit. This is very true regarding the crew unless the personel system is much smarter than a conventional one.
      I don't think it's really true in regard to hardware except maybe regarding the realistic munition stocks onboard. I think a worthwhile GP ship would have to be really good at ASW anyway (or else its ASW is near-useless). Meanwhile, the diminishing returns on investment in AAW render the difference between a modest AAW and extremist AAW unit rather moot. Neither will be of much use without really good AEW, and performance differences with really good AEW support would be near-negligible.

      Furthermore, have a look at the German F125; it has very basic equipment (neither true AAW nor any ASW to speak of) and awfully high costs. The relatively high costs of "corvettes" and "LCS" show how expensive the basics including incomplete self defence are on their own

  6. For the costs of the F-125: this is perhaps only the result of the german abnormal armament policy to choose nearly always the most expensive less capable plattform available - for example the very similiar Absalon class costs only around 50 % of the german f-125 as far is i am informed.

    But i can agree with your overall idea very much and especially the example of the f-125 / absalon class shows this very clearly because the costs per unit of the absalon class would sink very much if for example germany would have bought the absalon class instead of the f-125 (if you want such an colonial cruiser at all).

    Instead the germans bought this system. And this shows imo clearly, that corruption, nepotism, economical reasons, election battles, local policy, lobbyism and so on and so on are much more important in the question of the armament policy than logic, reason and military abilities.

    It is all nice and good, that at least some military thinkers like you have the right ideas, but it does not help anything. Because civilians with complete different aims decide about what is bought and what not. And because their aims are completly different, their target is neither cost-efficieny nor military abilities.

    Generally a last question: would you prefere smaller ships or ships with a bigger hull in this case? Because theoretically you could also include such add ons into a smaller hull at the cost of comfort for the crew, endurance etc but this factors are imo not so important for an german navy which would operate in the north sea and especially the baltic sea.

    Or should germany built such ASW FFGs with add ons as bigger units with big hulls which would then have place for further add ons and for acting as an blue water navy ?

    1. I concluded that a fairly large GP ship with a strong helo component would be appropriate for transoceanic convoying. That would be a kind of modern Giuseppe Garibaldi.
      The German navy shouldn't buy any such ship, though. I think it should be disbanded for evident uselessness and diversion of resources from the critical Heer. A navy bureaucracy wants to play with warships if you maintain it, even if having warships at the expense of the army is unreasonable in the context of the alliance.

      I don't see much of a role (if any) for warships in coastal warfare. Minehunting and minesweeping/-breaking can be done with drone boats, and in-service minehunters are effectively drone motherships anyway.
      Coastal ASW could rest on drones and helos as well. Coastal AAW is really a job for fighters & land-based AEW. Coastal ASuW is a job for land-based missile batteries and the air force where ASW helos might play a role in identifying surface craft.
      Accordingly, I suppose that MCM and drone ASW could be done by a border/coastal guard while helo ASW could be done by the air force in Germany. MCM could even be left to a purely civilian agency, as we had it in the early post-WW2 years before there was a West German military again.

    2. Do you see a role for a German Navy capable of maintaining (or assisting with maintenance of) global international trade routes in the face of hostilities?

      Or is continental Europe self-sufficient enough to weather a breakdown in the event of a major conflict?

      The EU still appears to be very reliant on imported oil, for example.

    3. I proposed a scheme for a secured coastal trade lane from Oslo/Copenhagen/Hamburg to Gibraltar. The assets to secure the lane would be provided by the countries with a coastline along the lane, including Germany.
      That's drones for minehunting, drones for minebreaking (simulating ships), ASW seeker and confirming drones and ASW helos with dipping sonars, maybe containerised land-based Sea Lance.

      "Pirates" can be dealt with with chartered cargo ships, quickly modified for the purpose and equipped with a helo.

      Transoceanic (transatlantic) convoying may involve warship escorts, but it may also be done with self-defending cargo ship convoys - kind of 'ARAPAHO 2'.
      I don#t think Germany should spend on transoceanic convoying; we are so close to the Eastern frontier of NATO and EU that we should first and foremost provide air base capacity in East Germany and an army Corps that's most effective and relevant if not decisive in the first two weeks of conflict.
      The British, Americans, Spanish and even French and Italians will take a long time to deploy substantial land power to Poland and Lithuania. Germany is more close and can react in time. Poland cannot be expected to race its land forces into Lithuania, as it would be concerned about securing Warsaw versus Kaliningrad forces and Belarus.

      This leaves French and Italian forces as the only feasible and powerful first weeks responders on land. They would be at least 12 hrs slower, have smaller economies and traditionally spend much on naval power. Germany has to step up with its Heer unless they improve their land forces a lot.

      German naval (and air/ground attack) spending is a distraction from the critical task.

    4. Moreover, even the USN cannot secure the U.S.' essential maritime import needs. Recently they admitted that they lack the capacities to even only escort the U.S.Armed Forces' own strategic sealift ships.

      Naval spending of the business as usual pattern does simply not make secure trade lanes affordable.

    5. Well.. To be fair, if the USN focused on maritime convoying, we have plenty of ships for it. However it would be at the expense of using them offensively.

      I'm thinking more of a scenario where the Russians decided to (or threaten to) interdict oil tankers coming to the EU using their SSN fleet.

      Or heck, they could enter into a pact with the Iranians to shut down oil from the Gulf.

      Germany would have to rely on other EU navies to either form convoys (vs Russian SSNs) or assist the USN in breaking the Iranian hold on the Gulf.

    6. There are 25 relevant SSN and SSGN in Russian service. Maybe 5...15 would be really operational with near-complete equipment.
      The Italian, Spanish, British, French and Dutch navies could very well escort tankers from the Persian Gulf (or Red Sea terminals) to the Suez Canal and to seal off the Med so Russian subs in there could not replenish.

      The bigger question would be how quickly would we set up the required government-sponsored ship insurance scheme (and how would we distribute the burden in Europe) and what would such a hot conflict mean for oil markets and economies in general.

      The idea that we would escort tankers with Arab and Iranian oil right to Rotterdam or Hamburg would be ridiculous imo. The German navy suffices on paper to run one convoy back and forth between Gibraltar and Rotterdam per week, but it would run out of lightweight torpedoes and SAMs real quick.

      Moreover, such a super-specific scenario would likely not happen at all. European Russia would be embargoed itself, their oligarchs would lose assets, Georgia and Ukraine could suddenly expect substantial Western support etc. Naval aggressions can be deterred with much more than just warships.

      "Germany would have to rely on other EU navies (...)"

      So what? Belgium relies on other allies for all of its defence, as its own forces are weak. EU ally Austria certainly doesn't secure its own maritime oil supply routes. Almost all NATO members rely on the UK and FRA for a nuclear deterrence umbrella.
      People have the urge to wish for a complete, all-round national defence military. That's nonsense, and has been nonsense ever since the death of Karl V. Ever since the late 16th century all Western governments have had incomplete military power and were more or less reliant on allies. It's extremely wasteful to try to be able to do it all (and outright impossible for almost all countries) by yourself even if you could instead to simply trust at least some allies.

      I fully understand the ideas of cooperation, trust and so on was eroded in American culture during the past 40 years or so, but most Europeans haven't lost these ideas (and abilities!) yet.

      I'm merely shedding the extant irrationality in the common approach and propose to be more consistent and forceful in the pursuit of efficient and effective collective deterrence and collective defence.

    7. I also disagree that the USN has plenty escorts to secure maritime trade. It has 65 DDG and 22 CG. Those ships would need to secure very long transpacific routes, long transatlantic routes, presumably even Red Sea/Indian Ocean/Mediterranean routes and so on unless the U.S. relies on others to secure U.S. maritime trade.
      I doubt they could provide satisfactory convoy security on the transpacific routes alone even if they docked all carriers and amphibious ships and focused on convoying. It would need 400+ escorts to properly and fully secure trade, especially with such ASW-inefficient ships as Ticos and early Arleigh Burkes. Those ships lack LFAS (Ticos, most Burke hulls) or no ASW helo component (all Flight I&II Burkes), so one would need 4...8 units to properly escort (screen) a single convoy.

      Then said escorted convoy would arrive at a port without secured entry point because there's little mine countermeasures capability (only 11 neglected mine hunters; the other MCM does not justify attention).

      So I have no illusions about the German navy not being relevant to the security of national maritime commerce - and I won't follow any request to join the delusional club, of become a fanboi who actually believes the national navy when it blathers about what it's doing for us. The USN is not securing U.S. trade, and the Deutsche Marine doesn't secure our trade.

    8. The USN certainly isn't large enough for protecting any and all maritime trade, even US trade. That would require thousands of ships.

      We could run a significant number of convoys, assuming we didn't do anything else.

      But, yes, my "plenty" characterization was an overstatement.

      Agreed on MCM capability. The LCS fiasco hasn't really added any capability here, at least not yet.

      I guess what I was really getting at was does Germany owe the greater EU (and/or NATO) a certain naval capability beyond what it might need simply for itself? And if so, what does that look like?

    9. Legally, we owe almost nothing (only some NATO bureaucracy support payments).
      Practically, we are the natural 1st or 2nd responders for Baltic defence. Warships don't matter to it. I suppose we should focus on the critical needs at the expense of de facto luxuries.