March 22, 2013

Law of Diminishing Returns


\frac{1}{X}\sum_{i=1}^{X}\frac{1}{2^{i-1}}=\text{D}
Substituting 3 for \text{X} and expanding yields:
\frac{1}{3}\sum_{i=1}^{3}\frac{1}{2^{i-1}}=\text{D}
=\frac{1}{3}\cdot\left(\frac{1}{2^{1-1}}+\frac{1}{2^{2-1}}+\frac{1}{2^{3-1}}\right)
=\frac{1}{3}\cdot\left(\frac{1}{2^0}+\frac{1}{2^{1}}+\frac{1}{2^{2}}\right)
=\frac{1}{3}\cdot\left(\frac{1}{1}+\frac{1}{2}+\frac{1}{4}\right)

=\frac{1}{3}\cdot\left(\frac{7}{4}\right)
=\frac{7}{12}
=0.58\overline{3}\text{ t/kg}

I walked into my favorite coffee house this morning and was greeted with the sounds of Hawaiian music and Nathan's friendly smile asking me if I wanted my regular 2 shot Americano in the 16 oz cup.  I say, "yea but can you put it in a 12 oz cup?  I need my coffee stronger these days."  He says, "ah the law of diminishing returns".
 As defined by the oh-so convenient wikipedia: 
The law of diminishing returns states that in all productive processes, adding more of one factor of production, while holding all others constant ("ceteris paribus"), will at some point yield lower per-unit returns.[1] 

 So this starts me thinking about the concept and how relevant it is to much more than economics. How many times have we found ourselves in relationships at home, at work, with friends where we see ourselves constantly putting more and more into it when we feel the return becoming less and less. Like the lab rat in the cage pushing the button frantically as the reward becomes less frequent and unpredictable.  

 We might find ourselves going above and beyond at work, putting in longer hours only to find that then this is what becomes expected of us as our new baseline.  In relationships, we may find ourselves taking extra care to show the other person that they're special, that they are loved and appreciated only to find that over time those things are taken for granted. 

 So given this unfortunate Law of Diminishing Returns should we stop "adding more factors of production"?  I don't think so.  The important variable in all of this is finding yourself in a relationship, whether personal or professional,  where the other cog in the wheel (your partner, your boss, your co-workers, your friends) is of like mind, cognoscente of this concept and careful not to take things for granted.  The other key to not becoming a victim of Diminishing Returns is to "shake it up".  Add random variables to the equation to keep things fresh and interesting, to spark production, to keep love and happiness thriving. 

 As for my Americano?  Perhaps tomorrow I'll order a latte.

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