Complements in production

A colleague of mine is doing jury service; the case has dragged on for ages, because a jury member has fallen ill. The west coast main line will be closed over Easter because of engineering works in Rugby. The sale of my flat is taking forever, because my solicitor is so slow.  And despite the Bank of England's efforts, interbank markets are illiquid.
These four things are related.  They all show the troubles that happen when inputs into a production process are complements rather than substitutes. If a jury member falls ill or idle, you can't easily replace him halfway through a case; the 12 jury members are complements. If the line in Rugby is closed, trains can't easily be diverted through Coventry, and the track around Rugby is a complement to the track through to Manchester. I can't now substitute to a quicker solicitor. And the production of market liquidity is a complementary process. It's no use one bank being healthy and able to lend if others aren't perceived to be creditworthy. Market liquidity is like making a dream so real - it takes two baby.
In cases like these, single failures can badly hold up production - a chain is only as good as its weakest link - and substitution away from that link is difficult. We have Leontief production functions.
Now, Charles Jones has showed in this fantastic paper (pdf)  that such  complements in production processes help explain why poor countries stay poor.  But my examples suggest that they matter in richer countries too.
Could it be that  sectors have low productivity partly because they are riddled with complementarities in production, and so suffer from weakest link problems; think of transport, construction and the law, where Jarndyce vs Jarndyce is still an accurate description?
One of the tricks of good management is to try and overcome problems like these; remember, the assumption of conventional economics, that the production function is given, is false; such functions have to be discovered. A good manager asks: how can I avoid being dependent upon a weak link? Sometimes, the answer to this is to bring the complements under the same ownership. Other times, it's to increase potential to substitute between inputs, for example by replacing highly paid stars with cheap formats or by offshoring.
But what happens if managers lack incentives to find such substitution possibilities? Could it be that one reason for inefficiencies in the public sector - and even perhaps for  the collapse of the Soviet Union - is that managers lack incentives to minimize costs and hold-ups by finding technologies that permit substitution?

Comments

[Tim Worstall]

A story to add to this part:
"One of the tricks of good management is to try and overcome problems like these; remember, the assumption of conventional economics, that the production function is given, is false; such functions have to be discovered. A good manager asks: how can I avoid being dependent upon a weak link?"

We're the sole suppliers of a vital input to a huge production process in the US. Our part is very small (gross turnover of maybe $200,000 a year) while the total process is 100 million halogen bulbs a year.

We are reliant upon Russia as a source (although not one single point).

The customer has insisted that we research and then build a non-Russia based source so that the entire system is not based upon whatever Putin and Medvedev do to Russian exports.

Identifying and then avoiding a possible weak link, as you say.

[Scott Hughes]

I think that you are right to speculate that poor countries may be poor because they are too dependent on weak links. That's why I think poverty needs to be beaten at a very local level. We can't fix poverty with nation-wide solutions because that just makes these people more dependent on more links in a larger chain. Creating small, self-sufficient communities is key.

[kinglear]

Your last paragraph does not need any question marks. If your continued well-being only depends on not messing up, why would you try to make anything better. It's like the herd of investment managers. You won't get fired for being with the crowd - hey we all did it.

[Mark Wadsworth]

Isn't this a roundabout way of saying "A chain is as strong as the weakest link"?

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