Indifference Curves: no Utility? Alex Gheg

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{\*\generator Msftedit 5.41.15.1515;}\viewkind4\uc1\pard\f0\fs24\tab Without getting too technical, I\rquote ll
show you the severe limitations of modern consumer theory, while we explore four things
that consumers value, which is quantity, quality, variety and convenience. By the end, any economics
student will know the problem with this theory in a way like never before. I'll also give
a glimpse of a simple solution, for sure. Indifference curve graphs: a geometric representation
of a consumer\rquote s rational preference relation characterized by completeness and
transitivity. Indifference curves are convex, downward sloping, everywhere in the plane
and they never cross. Is that really true? Let's see if we can generate indifference
curves that don't have these properties. If so, rational behavior can have absurd implications
in the standard model.\par \tab The Super Bowl tops ratings every year,
so we\rquote ll apply the theory to this common leisure activity. It\rquote s Bills Cowboys
III before economic suicide in Buffalo, and football fans must choose between one of two
viewing options. Option A is to watch the game alone in a room with exactly one television
of the highest available quality, in the subjective opinion of the viewer (good x). Option B is
to watch the game alone in another room on a specific lower quality television (good
y), but the viewer can choose an unlimited quantity of the relatively inferior television.
\par \tab In a college class, these indifference
curves are very flat or perhaps linear because the televisions are close substitutes. This
graph has nothing to say about quality. Factually, demand is sensitive to changes in the price
of close substitutes. These preferences are rigged to get a high cross price elasticity
of demand, and they possess the four properties of indifference curves. How should my curves
behave? Good x is the television that I want: a Trimaster. Good y is the relatively low
quality television that I have: a 46 inch XBR10. Let\rquote s look at the local behavior
of my indifference curve that has the point (1,1). If I had a Trimaster then any viewing
of my XBR would be irrational, so it becomes worthless. The indifference curves must be
parallel with the y axis in the interior of the plane. However, I have a corner solution
since I don\rquote t own a Trimaster. My optimal indifference curve must cross the y-axis.
It seems that a continuous indifference curve with these properties must be concave or upward
sloping. How can any interior point be on my optimal indifference curve when one Trimaster
is more than an infinite number of XBRs? The preference arrows point to cracks in the foundation.
\par \tab Digital music technology has gone in
two very different directions since 1983. The iPod makes listening to music more convenient.
Another direction is to improve sound quality with new formats. This is an audio only Blu
ray disk of Wagner\rquote s music, encoded with DTS-HD Master Audio. It is an exact bit
for bit copy of the master recording in 7.1 surround sound rather than compressed 2.0
stereo. Imagine that someone is considering if an iPod is a good gift for an owner of
a fully capable blu ray hometheater. For this example we\rquote ll use my subjective opinion
and say music on Blu ray is the inconvenient high quality good (Good x), and music on iTunes
is the convenient low quality good (Good y). The gift giver knows the listener\rquote s
piecewise continuous income expansion path of unique alternating corner solutions. The
iTunes corner solutions are justified because it would be irrational to buy blu ray if the
consumer is too busy for the inconvenient product. The blu ray corner solutions are
justified since blu ray can make an iPod a waste of time. Different incomes lead to different
lifestyles, so how does this technology fit in? Pieces A and C make the iPod a great gift,
but pieces B and D make it a wasted gift.\par \tab Let\rquote s assume this person has convex
and downward sloping indifference curves to see if these preferences are rational. This
broken path must be produced by crossing indifference curves that are not present in some parts
of the music plane. This is a violation of completeness and transitivity. The consumer
is simply irrational according to the standard model, but it can be rational behavior in
a different theoretical framework. If I were to listen to the same Beethoven for the next
12'08 then one blu ray audio system is better than an infinite number of iPods for listening.
On a hectic day, one iPod can be more valuable than an infinite number of blu rays. This
gift is lighter and smaller than an iPod but it\rquote s less convenient than the blu ray
disk, as the DVR also reveals, convenience is not really about mobility. \par
\tab This model does not tell me what convenience is, or why I would trade it for quality, which
is also a total mystery in this dead end. The key assumption of diminishing marginal
utlity didn't provide any useful insights. The possible local behavior of an indifference
curve for any quality vs. convenience point is problematically endless. This all important
equation will not help me understand why the higher quality Super Audio Compact Disc format
was crushed by the iPod. This model only predicts quantity responses when prices or incomes
change, and it vastly exaggerates the importance of variety. \tab\par
\tab Don't worry, this CES utility function is quick and easy to use for the Super Bowl
viewer's problem. A professional might use it, since the workhorse is perfectly suited
to order these kinds of preferences, right? Option A gives a finite amount of utility
for the consumer, for all parameters. Option B gives an infinite amount of utility by taking
the limit. Therefore, Option B is preferred to Option A. The CES approach completely failed.
In fact, everyone rationally chooses quality over quantity here.\par
\tab Suppose I have exactly one HDTV and two possible DVR arrangements. Option C is to
have exactly one Dish 922 DVR, which has 4 HD tuners and 100 hours of HD recording capacity.
Option D is to have any number of Dish 722k DVRs, with each one having 3 tuners and 55
hours of recording capacity. The 922 is more convenient than the 722k, but I prefer option
D, since it gives me unlimited recording and storage capabilities with identical image
quality. How did quantity lead to more convenience? The CES function predicted accurately, but
it wasn't illuminating.\par \tab We can study quantity, quality, variety
and convenience with one equation, while we model the choice between any finite number
of goods in two dimensions, with elementary calculus. Imagine measuring the rate of technological
change from the consumer\rquote s perspective. One way or another, things are going to change
dramatically. For how many more decades can economics professors tell their students that
the real wage has not advanced for the American worker since 1973? It's tougher when they
equate it to the marginal product of labor, and relate it to technology on the board.
The flawed consumer price index is measurement without comprehension. It's clear why economists
are in such a weak position when they measure technological advancement. The CES utility
function has dreamy properties, but it left us in the dark yielding the predictive accuracy
of a coin flip. Pop quiz, I don\rquote t know my lambda when I see this penny, what\rquote
s yours? \par \tab\par
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