Give 'til it hurts...

This one's a stretch to fit into the environmental economics category, but given it was inspired by an historic environmental event, and it provides a valuable (yet simple) economic lesson, I decided to go ahead with it.  Sorry if this one reads like a principles of economics textbook but I'm starting to shift into teaching mode after a summer of research (and entertaining my fans!).

Faced with a large-scale event that affects many people we often see an amazing outpouring of contributions to charitable organizations.  For example after 9/11 its estimated that the thirty-five largest charities received over $2.7 billion in new donations.  Often at the forefront of these efforts are the wealthy and high-profile contributors.  Yesterday, Stephon Marbury of the New York Knicks donated $500,000 to hurricane relief.  Last week, Kobe Bryant pledged $100,000.  Both noble contributions but how much did it really set them back?   According to my calculations, Bryant's generosity is the equivalent of the median American household giving...$173.

Warning:  Back of the envelope calculations ahead.

When you give up money, you give up the opportunity to purchase other things that would make you better off.  So, in a sense, you are worse off. But, the more money you have, the less it hurts to give up a little of that money.  We economists refer to this as diminishing marginal utility of income.  The idea is simple.  The more money you have, the less utility you lose from giving up one dollar relative to someone who starts with less money.  Or put another way, an additional dollar is worth more to someone with an income of $20,000 than to someone with an income of $200,000. 

So how much utility did Kobe Bryant really give up when he gave $100,000?  Richard Easterlin at USC uses data from the General Social Surveys 1972-2002 administered by the National Opinion Research Center in Chicago to estimate the relationship between a persons perceived happiness (on a 5 point scale?) and their income in 1994.  He finds that relationship to be:

Happiness Ranking = .1255 ln(Income/1000)

I know, fancy math equation, but bare with me, hopefully the final point is worth it.  Let's assume this relationship still holds.  How much happiness did Kobe Bryant give up with his $100,000 donation?  Last year Kobe made $26,000,000.  So his income after the donation is $25,900,000.  Cranking through the math, that means his happiness ranking would fall by .000484 (from 2.1427... to 2.1423...) on a 5 point scale. 

Working backwards through the numbers, the median American household income is around $45,000.  For someone in that household to experience the same change in happiness as Kobe (.000484), they would have to give up $173. 

Hmmm...we applaud vigorously when a celebrity, athlete, public figure announces a sizable pledge to relief efforts.  But would you applaud your neighbor for giving $200?  I would.  Why?  Because they are probably sacrificing more than the celebrity.  At least my simple math tells me they are.

Comments

[John Whitehead]

ln = natural log

[Tim Haab]

Thanks.

[Jim Casey]

Question? Based on the following...

"When you give up money, you give up the opportunity to purchase other things that would make you better off. So, in a sense, you are worse off. But, the more money you have, the less it hurts to give up a little of that money. We economists refer to this as diminishing marginal utility of income. The idea is simple. The more money you have, the less utility you lose from giving up one dollar relative to someone who starts with less money. Or put another way, an additional dollar is worth more to someone with an income of $20,000 than to someone with an income of $200,000."

When we do contingent valuation - should people with lower incomes have their WTP scaled up? I don't think I have seen this done in the literature, but I most certainly could have missed it.

Peace, JC

[kaspit]

I can be as cynical as the next guy when it comes to sports millionaires (except Red Sox).

But what's the bottom line... How much would be raised if every family in the USA gave at this rate?

Another economics question: How much does this Katrina funding merely offset governmental monies (and potential foreign aid)?

[George Vogt]

Of course this was known thousands of years ago, though without the mathematical vocabulary:

Luke 21:1-4 1 And he looked up, and saw the rich men that were casting their gifts into the treasury. 2 And he saw a certain poor widow casting in thither two mites. 3 And he said, Of a truth I say unto you, This poor widow cast in more than they all: 4 for all these did of their superfluity cast in unto the gifts; but she of her want did cast in all the living that she had.