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All posts by Dan Whalen,
Providence, RI (resume)

Friday, April 8, 2011

Marginality

           “Marginal” behaviors are as important to economics as they are to physics, math, natural sciences, engineering, etc.  If you’re not familiar with the idea of marginality, it can be a little confusing to get a grasp on.  But doing so is worthwhile, it’s pretty interesting stuff, and once you’ve got the idea, you will start to notice it everywhere.

When economists talk about a “marginal value,” they are referring to the value of the next unit (made, sold, consumed, whatever), irregardless of previous unit’s value.  This “value” can be anything: rates, time, prices, revenues, cost, whatever.

Often we won’t end up giving a marginal value a specific numerical value, as it can be a super difficult thing to accurately quantify.  Instead, we are just interested in the dynamic of the marginality.  Is it going up or down?   How drastically does it change?  Or does it just sit constant?

            Here’s an example.  Picture a marathon runner who’s just about to start their run.  We could consider that person to be a producer, and his product to be distance.  In order to manufacture this product, they have input and overhead to pay, which they “pay” in exertion.  As soon as the race begins, the runner doesn’t stop producing until they have manufactured their 26.2 miles. 

           The starting gun goes off, and the race begins. 

That first mile is a cinch.  The runner is well hydrated, they feel limber, and their exertion costs are very low.  Mile one will be very inexpensive for them to produce, no problem.   

            Our subject has now just passed the 13.1 marker (midpoint).  They’re starting to tire out.  Their body is fatiguing: their breathing is labored and their thighs and calves are starting to burn.  Now, the length of a mile has not changed during the race.  The physical space between the starting line and the mile one mark is the same as the distance between miles 13.1 and 14.1.  Their production cost per mile is rising fast.  

            A mile away from the finish line, the runner’s muscles have gone from sore to painful.  Every inhalation is a violent gasp, every step an act of will power.  That last mile will feel like an eternity.  The exertion expense per mile has skyrocketed to something many times its original value.

            The runner is an example of a producer with a rising marginal cost of production.  To ask simply “how much exertion will it cost to produce 1 mile?” doesn’t really make sense if we are aware of this marginality concept.  The most accurate response will always be: “I dunno.  Depends on how many you’ve already produced.”

These graphs show the marginal “cost” of two hypothetical marathon runners

You probably can already see how this ties in with economics.  Let’s say it costs Apple $10 million to produce 1 million iPads.  This does not immediately imply that 2 million can be produced for $20 million.  Costs could grow disproportionally fast as Apple pushes its supply and production chains to the brink of their capacity – or over capacity.        

That second million units might cost $11 million, or $30 million or $500 million to produce as Apple adds more laborers, factories, distributors, managers and materials to force out more units.  If the second million iPads happen to be more costly than the first million to produce, that second million would be a less profitable batch than the first million!   

Picture Steve Jobs trying to make a business plan for 2011.  He knows that in 2010, Apple made 1 million iPads, and was able to sell them for $100 a unit.  In 2011, Apple could just try to sell even more iPads, say 2 million.  Or they could make 1 million iPads, and 2 million iPods (which are going for, say, $50 a pop this year), for a total of 3 million items in the year. 

Both plans would net $200 million in revenue.  But if the iPad has a marginal cost of production that climes faster than the iPod’s, the 2nd plan would be the more profitable one (since Apple’s total production costs would be lower), and therefore be the one more likely to be adopted.   
               
OR this all could take us in the other direction!  Let’s say that a team of child psychologists and educators determine that children in a 5-student Kindergarten class with one teacher, learn, perform and retain just as well as a class of 10 students with just one teacher.

           Imagine two adjacent elementary school-districts, each with 5 kids per class, considering merging into one district.  The school administrators are concerned.  By merging, they will have to double the size of their production – from producing 5 educations to producing 10.  Won’t that intrinsically spell out a doubling of costs?

Sure, a class of 10 will cost more to run than a class of 5.  You’ll need twice as many books, finger paints, tables and tiny chairs.  But it that doesn’t necessarily mean that the total costs will double.  The merged class needs only one bus, one teacher, one class room, one heating bill and one tank of hamsters in the back.

Since this class’s marginal cost of educating is increasing at a decreasing rate, the merged school will end up with lower per student cost than the original component schools did on their own.  By internalizing expenses, the hybrid school can educate kids more cost effectively than the two districts operating on their own ever could.

Whenever we try to forecast a trend, be it in crime statistics, population growth, or stock prices, historical data is a great place to look for input and guidance.  But we should no lose sight of the fact that while the past may be known, but the future never can be.  The next value may well be influenced by the previous one, but ultimately, it is not determined by it.


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