Decreasing Marginal Returns

A very interesting post just went up over at RortyBomb, all around awesome blog. I appreciated the chance to think about the topic presented, that some goods appear to have increasing marginal returns.

Anyways, interesting as it is I think it deserves rather harsh criticism for perpetuating some rather bad habits existant in what I guess I'd call new experimental economics (Unless, of course I'm totally wrong on all counts).

Without further ado, my reply to RortyBomb's post:

Interesting, but the greater the "wow" factor of a thought experiment, the more I'm suspicious.

Lets start with a more formal definition of decreasing marginal return. Decreasing marginal return says as x increases by a constant increment, y increases by a diminishing increment (y = f(x)). In other words, second derivate of f(x) is negative.

With your cake argument, it's all good. Each piece of cake is a constant increment - 1/10 of the whole. With the screaming argument I'm less sure. As you say the percieved incremental decrease in volume from one less screaming person is negligable at first and the whole cake at the end, to turn a phrase. To properly determine the curvature of this screamer data, you'd need to impute and determine a constant increment (denominator, x value) over which to measure your change in y (utility).

It's relatively confusing to try and work out how the above analysis effects our comparison of the cake and screamer model, and I think this is further evidence of the simpler point I'm trying to make: the cake and screamer examples are apples and oranges. The experiment is set up incorrectly. If you were to try a constant incremental decrease in decibel volume, I'm quite sure we'd start to see classic marginal decreasing return.

Anyways, I say perceived and that is strictly true, but for the basis of argument percieved means "real". Psychologically speaking, that is certainly true, and I'm bored by metaphysics. The theory of utililty functions seems to capture and subdue the difference between reality and perception, anyway.

Other thoughts:
A fundamentally confusing factor that gives this experiment extra sparkle is the increasing good in the cake example, and the decreasing bad in the screamer example. Graph these two and your blown away by the result - they are nearly opposite!. Well, of course they are - the cake example is the conceptual inverse reflection of the screamer example over x (increments) and y (utility). Graph the cake example against the screamer example reflected over the line x = y and you will see what I mean.

An economics way to accomplish this reflection might involve the use of Hicksian compensation for how much somebody would accept (dollars) to have an increasing number of people start screaming.

Anyways, the important part is the improperly constructed experiment. The new experimental econonomics is great because it involves a lot of interesting questions and though experiments. Again, though, you can "show" all sorts of really crazy things with improper conditions and mangled comparisons.

Once again on hoping I'm not massively horribly wrong. On the internet. God Forbid.