Tuesday, August 01, 2006

Defining Marginal Utility

by Ken Houghton

I've been trying to find a real-world example of the concept of Marginal Utility (in response to an e-mail) that can make the concept clear. While I keep coming back to the Starfish Analogy, this post from Bitch Ph.D. is eminently more usable. (It also has the advantage of being politics-neutral. I think.)

First, the Starfish Analogy, which is described here, among other places. Any action--this one is a positive--makes a marginal difference.

The downside of the Starfish Analogy is exactly the reaction of the kupuna is the story: for miles and miles of starfish, there will be no difference. The "upside" is that there are untold millions of other starfish who were not washed onto the beach. They, too, are unaffected by the actions of the keiki. Only those at the margin are directly affected.

(Our correspondent learned the term in context of famine relief, where even the sea change of lifestyle discussed--giving the monies you spend on luxuries to charity--would not eliminate famine relief. [Biblical passages: One can check out Matthew 26:11, for those who read the sequel, though I'm fonder of Deuteronomy 15 (note the parallel of 15:11 with Matthew).] But it would make a difference to the extent that those resources are re-allocated--that is, on the margin.)

I posted my personal working definition of economics in comments at Crooked Timber a few days ago (the subsequent discussion is worth a look):
If economics is a science, it is the science of optimal use of (definitionally scarce) resources.

I consider the above to be manifestly intuitive, primarily because of the concept of marginal utility.

As Tracy W. noted in the Crooked Timber discussion, "Economic growth is caused by improvements in knowledge. If we run out of oil, or must massively restrict economic development, we may take a massive hit to the level of economic activity, but that doesn’t mean that people will stop looking for better ways to do things." That includes better ways to make things (e.g., mass production/automation, substitution of materials), processing/efficiency improvements (time-motion studies, GUI design, handicapped-access ramps), and (most importantly in a consumption-driven society) innovations that offer choice.

The "problem," as it were, is that all of these options require trade-offs, which means there has to be a societal standard of comparison. Want to own that new 103" Plasma Screen television? So do I, but the $70,000 price tag makes it an unlikely choice.

This doesn't mean I don't have $70,000 available. I do, though it might mean living on the streets since selling things such as expendable stock holdings, a first edition of Naked Lunch, and the galleys of Snow Crash and The Diamond Age is unlikely to foot such a bill.

And that's where the question comes in, on a smaller basis. When the television is priced at $70,000, it means that someone considers it to produce $70,000 worth of value to a potential purchaser. In a "market-clearing transaction," I would agree and consider selling (or at least borrowing against) my house for that television.

That deals with the “Marginal” portion. For the “Utility,” let us suppose that I do have $70,000 available. Do I buy the television?

It still depends. For instance, I can buy the television immediately or I can look at the market and decide to wait a year and buy it then—likely at a different (presumably but not necessarily lower) price. At this point, the decision is one of the utility the purchase will provide against other options.

For the easiest comparative—remember, money is the commodity that standardizes the comparison of unlike items—I can put that $70,000 into a one-year CD and earn 5.00%. (For purposes of this example, assume that the effect of inflation is neutral and there are no tax considerations.) At the end of that year, I would have $73,500.

Now the comparison can be expressed as a relationship:

Utility(TV2007) >=< $3,500 + dPrice(TV)

That is, I place a value on the utility of having the television for all of next year (2007) by comparing it to the amount I would gain from the CD (5% of $70,000) plus the expected change in price of the television

1. If I believe the Utility value of the television is greater than (>)the right side of the equation and I have no doubt that I will want that same television next year, then I buy the television. (For purposes of this example, I've left out the optionality component of the equation above.)

2. If I believe the value will be less (<), I put the money into the CD.

3. If the estimations are exactly equal—that is, I really would be at the margin of the decision—I look for new information (a sale from a retailer, discovering that plasma screen maintenance will be a significant first-year cost, a bank offering a 5.50%, rate etc.) that changes the “equation” above.

In all cases, though, the key is estimation of the marginal utility of the expense. If you treat all comparatives as a decision tree (buy lunch or donate the monies to FINCA International, Oxfam America or Oxfam, the American Friends Service Committee, Heifer International, or another charity of your choice and go hungry; go out to a restaurant or prepare the food at home, spending more time but less money; buy a house or continue renting, etc.), then every decision--buy, spend, or wait--is a matter of Marginal Utility.

(This is what led some wag to comment that the rich are as free as the poor to sleep under bridges; it may be literally true, but the reverse--the poor are as free to sleep in mansions--is not.)

This brings me to the Bitch post referenced above, but that will have to be posted tomorrowat a later date.

(Continued on a following rock)
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