A. Comparison Analysis

For any y≥0, if losing utility is U( µ-y) , and profiting utility is U ( µ+y) , we have the following expression by using of (6), (7), (4) and (5),

That is U( µ-y)>U ( µ+y), and also means the losing utility is larger than the profiting utility when the losing sum is equal to profiting sum.

In virtue of the concept “losing aversion” in perception psychology, D. Kahneman depict the liability people is more impressionable to decrease of his boon himself than increase of the same boon [8], [10], and make use of the gradient of loss function divided by gradient of profit function at original point to measure the degree of “losing aversion”, and give, 2.0, an experience's estimate value.

This means that the utility of giving up something is as two times as that of getting it [5]. However, according to the profiting utility given by expression (6) and losing utility given by (7), we get the following conclusion: The losing utility is always larger than the profiting utility when the losing sum is equal to profiting sum, but the contrast value of loss utility to profit utility is determined by APL, the standard variance of APL and RL. We will see that in the following analysis.

B. The Examples

Let losing utility is U( µ-y), and profiting utility is U ( µ+y)

The curve of other comparison results of losing utility to profiting utility is shown in Fig. 4.

The curve of other comparison results of losing utility to profiting utility is shown in Fig. 5.

The curve of other comparison results of losing utility to profiting utility is shown in Fig. 6. From the above examples, we could get the conclusion: despite losing utility is anyway larger than the profiting utility when the losing sum is equal to profiting sum. when human’s prospect are very stable, the standard variance of fluctuation of PL is very small, people will accept loss or profit of same quantity as loss with the near utility; when human’s prospect are not stable, the standard variance of fluctuation of PL is very large, people will accept loss or profit of same quantity as loss with the big margin of utility.

 

Prof. Feng Dai, Prof. Song-tao Wu, Prof. Ya-jun Zhuang

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Summary: Index