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Suppose Our Tastes Can Be Represented by the Function u(x1,x2)=(αx1ρ+(1α)x2ρ)1/ρu \left( x _ { 1 } , x _ { 2 } \right) = \left( \alpha x _ { 1 } ^ { - \rho } + ( 1 - \alpha ) x _ { 2 } ^ { - \rho } \right) ^ { - 1 / \rho }

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Essay

Suppose our tastes can be represented by the function u(x1,x2)=(αx1ρ+(1α)x2ρ)1/ρu \left( x _ { 1 } , x _ { 2 } \right) = \left( \alpha x _ { 1 } ^ { - \rho } + ( 1 - \alpha ) x _ { 2 } ^ { - \rho } \right) ^ { - 1 / \rho } .It is often observed that people become more rigid --- more set in their ways --- as they get older.What parameter is changing as we get older --- and how is it changing? (Explain.)


Definitions:

Median

The middle value in a list of numbers, which separates the higher half from the lower half of the data set.

IQR

Interquartile Range, a measure of statistical dispersion, which is the difference between the 75th and 25th percentiles of the data.

Range

The difference between the highest and lowest values in a dataset, indicating the spread of the data.

Median

The middle value in a data set, which divides the set into two equal halves when the values are arranged in ascending order.

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