Wednesday, May 2, 2012

The case (for and) against frugality

Here is a mathematical proof for frugality:

  • Diminishing marginal utility of wealth.  Simply, each additional dollar you spend provides you less value than the previous dollar you spent.
  • Compound interest.  Deferring gratification now will enable you to exploit compound interest and enjoy more consumption in the future.  I like to think of 4% as a reasonable approximation of what the real (inflation adjusted) return on risky investments ought to be over my lifetime.
  • Progressivity of the US tax system.  Progressive is a fancy term which indicates that the more income you make, the higher RATE at which you are taxed on each incremental dollar.  Because we have a progressive tax system in the US, different chunks of income are taxed at different rates.  For example, in the US,  for a married filing jointly return in 2012:
    • For simplicity, a rough approximation of taxable income = gross income - (10.6k + 3.7k*#of_people_in_household) for a family filing jointly).
    • The US government hopes that you and I don't understand this stuff.  They think we are too stupid to understand the complexities of the US tax code and the association between gross income and net income.  For example, society would break down if all people realized and exploited this little loophole (with the assumption that everyone could live happily on 40k):  A family of 4 can make 0 dollars/year or 40k/year and be just as well off after accounting for government transfers, and bring home a net income of 40k/year.  Incentives to work are completely destroyed if a family of 4 learns to live well on 40k/year.
    • Democrats (and some republicans) will have you believe that you can raise marginal tax rates to 70% without significantly affecting behavior (  If the world were full of more people like me, this clearly wouldn't be the case.  But perhaps democrats are right and very few people think about this stuff...I certainly don't blame them.  It's somewhat convoluted.
  • Generally, people prefer leisure (not being at work) to work.  There is a certain amount of intrinsic value to working.  I agree with that.  But I think that most people would stop going to work if they were not paid for it.
    • If this assumption is invalid, then the argument for frugality breaks down.
I bring up taxes here because they distort incentives.  In economics, we say that leisure, or sitting at home and watching TV is costly because we forgo wages in opportunity cost.  How taxes effect us is that it lowers our net wages, and thus lowers our opportunity cost.  Raise taxes high enough, and leisure becomes pretty darn cheap.

The only compelling argument that I have ever encountered in opposition to a frugal lifestyle is found here: and  This is consistent with the research which shows that happiness is not correlated with accumulation of shiny trinkets, but rather using money to create good and lasting memories.

The authors describe memories as an investment that pays dividends over the course of your life.  The earlier you invest in these memories, the longer you can reap the benefits of dividends.

If I defer consumption (say a cruise to Hawaii) today, and let the magic of compound interest do it's thing, I should be able to consume more in the future (say two cruises to Hawaii).  Using the "rule of 72", and assuming a real return of 4%/year, deferring my trip to Hawaii today would grow to 2 trips to Hawaii in 72/4 = 18 years.  However, I will have missed out on 18 years of memory dividends along the way.

You can use the same analysis to evaluate whether going into debt to justify a vacation is warranted.  If your real interest rate on an outstanding loan is 8% (say on outstanding student loans, for example), and you plan a cruise to Hawaii, you will have to justify that 1 trip to Hawaii today is better than 2 trips to Hawaii in 72/8=9 years.

So there you go.  A mathematical proof for a frugal lifestyle followed by the most valid argument that I can think of against it.  Personal takeaway:  take the best of both frugally and find ways of producing fun/impactful memories in an economical manner, like those described here:  Some of my most vivid and lasting memories from my childhood were trouncing around the Sierra Nevadas with $50 of trail mix in my backpack at a cost of $100/week.

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