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O-Ring Theory of Economic Development

ECON 450Development Economics

Contemporary Models of Development and UnderdevelopmentPart II

University of Illinois at Urbana-Champaign

Summer 2017

Henrique Veras de Paiva Fonseca ECON 450 Development Economics


Outline

1 Michael Kremer’s O-Ring Theory of Economic Development



Michael Kremer’s O-Ring Theory of EconomicDevelopment

Another innovative and influential model that provides importantinsights into low-level equilibrium traps was provided by MichaelKremer.The notion is that modern production requires that manyactivities be done well together in order for any of them toamount to high value.



Michael Kremer’s O-Ring Theory of EconomicDevelopment

The O-ring theory is interesting in part because it explains notonly the existence of poverty traps but also the reasons thatcountries caught in such traps may have such exceptionally lowincomes compared with high-income countries.



The O-Ring Model

The key feature of the O-ring model is the way it modelsproduction with strong complementarities among inputs.Suppose that a production process is broken down into n tasks.There are many ways of carrying out these tasks, which forsimplicity we order strictly by level of skill q required, where0 ≤ q ≤ 1.The higher the skill, the higher the probability that the task will be"successfully completed".



The O-Ring Model

Failure of any of these tasks will lead to lower output.Cannot substitute quantity for quality.Examples: Microchips, pizza, rock band.

We cannot trade an Eric Clapton with two or more mediocre guitarplayers!



The O-Ring Model



The O-Ring Model

Output is given by multiplying the q values of each of the n taskstogether, in turn multiplied by a term, say, B, that depends on thecharacteristics of the firm and is generally larger with a largernumber of tasks.Suppose also that each firm hires only two workers.



The O-Ring Model

Then the O-ring production function looks like

BF (qiqj) = qiqj

To make things simple, for this exposition we let the multiplier, B,equal 1.



The O-Ring Model

In addition to the form of the production function, we make threeother significant types of simplifying assumptions:

1 Firms are risk-neutral,2 labor markets are competitive,3 workers supply labor inelastically (i.e., they work regardless of the

wage).



The O-Ring Model

One of the most prominent features of this type of productionfunction is what is termed positive assortative matching.This means that workers with high skills will work together andworkers with low skills will work together.

E.g., the highest quality secretaries will work with the best CEOs.



The O-Ring Model

Figure: The Miles Davis Quintet – Miles Davis(trumpet), John Coltrane (tenor saxophone), Red Garland (piano), Paul Chambers(bass), and Philly Joe Jones (drums)

"They all had their own unique perspective on how tocompose and play, and when those unique componentscame together, they created an absolutely whole new sound.It is extraordinarily creative."



The O-Ring Model

To see this, imagine a four-person economy. Suppose that thiseconomy has two high-skill qH workers and two low-skill qLworkers.The four workers can be arranged either as matched skill pairs orunmatched skill pairs.

Total output will always be higher under a matching schemebecause

q2H + q2

L > 2qHqL



The O-Ring Model

To see this, imagine a four-person economy. Suppose that thiseconomy has two high-skill qH workers and two low-skill qLworkers.The four workers can be arranged either as matched skill pairs orunmatched skill pairs.Total output will always be higher under a matching schemebecause

q2H + q2

L > 2qHqL



The O-Ring Model

Because total value is higher when skill matching rather than skillmixing takes place, the firm that starts with high-productivityworkers can afford to bid more to get additional high-productivityworkers, and it is profitable to do so.

In economy-wide terms, high quality workers will earn higherwages when working with high quality co-workers.



The O-Ring Model

After the high-productivity workers pair off, they are out of thepicture. The less productive workers are then stuck with eachother.If there are many classes of skill or productivity, first the highestskill workers get together, then the next highest, and so on, suchthat skill matching results as a cascading process.



The O-Ring Model

The result in the business world is that some firms and workers,even an entire low-income economy, can fall into a trap of lowskill and low productivity, while others escape into higherproductivity



A Numerical Example

Suppose that there are six workers; three have q = 0.4 and aregrouped together in equilibrium, while the other three haveq = 0.8.Now suppose that the q of one of the workers in the first firmrises from 0.4 to 0.5 (perhaps due to training).Similarly, suppose the q of one worker in the second firm risesfrom 0.8 to 1.0.



A Numerical Example

In each case, we have a 25% increase in the quality of oneworker.As you might expect, a 25% increase in the quality of one workerleads to a 25% increase in output quality.



A Numerical Example

Notice that the first firm goes from (0.4)(0.4)(0.4) = 0.064 to(0.4)(0.4)(0.5) = 0.080;This is a difference of 0.080 − 0.064, which is a point change of0.016, or 25% increase;



A Numerical Example

For the second firm, we move from (0.8)(0.8)(0.8) = 0.512 to(0.8)(0.8)(1.0) = 0.640; the change in this case is 0.128, whichis again 25%.However, the point value of the increase is much greater - eighttimes greater - for a doubled point-value investment.



The O-Ring Model

If a firm can increase quality in percentage terms at constantmarginal cost or even a not too quickly rising cost, there is avirtuous circle in that the more you upgrade overall, the morevalue you obtain by doing so.Accordingly, wages would increase at an increasing rate as skillis steadily raised.



Implications of the O-Ring Theory

1 Firms tend to employ workers with similar skills for their varioustasks.

2 Workers performing the same task earn higher wages in ahigh-skill firm than in a low-skill firm.

3 Because wages increase in q at an increasing rate, wages will bemore than proportionally higher in developed countries thanwould be predicted from standard measures of skill.




4 If workers can improve their skill level and make suchinvestments, and if it is in their interests to do so, they willconsider the level of human capital investments made by otherworkers as a component of their own decision about how muchskill to acquire.

5 One can get caught in economywide low-production-qualitytraps.




6 O-ring effects magnify the impact of local production bottlenecksbecause such bottlenecks have a multiplicative effect on otherproduction.

7 Bottlenecks also reduce the incentive for workers to invest inskills by lowering the expected return to these skills.


econ 450 development economics - publish.illinois.edu · (bass), and philly joe jones (drums)...

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