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2016 | OriginalPaper | Buchkapitel

7. Measurement of Evaluation Rate of Public Pollution (Noise)

verfasst von : Hirotada Kohno

Erschienen in: Economic Effects of Public Investment

Verlag: Springer Japan

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Abstract

Generally, the more realistic, complicated policy decision-making problems have, the more objectives. For example, the road construction project has the objective to contribute to the effective development of the national economy/regional economy and at the same time to contribute to the preservation of natural environment/living environment, especially recently (hereinafter, depending on [1], [3]).

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Fußnoten
1
The permissible range of attribute is not necessary to be the inequality indicated the above. It will be \( {x}_i^w\leqq {x}_i\leqq {x}_i^b \), for the usual ordinary goods, and \( {x}_i^b\leqq {x}_i\leqq {x}_i^w \), for the environmental index.
 
2
Lottery is to be “a lot.”
 
3
Here, the \( {\overline{x}}_i \) of the conditional utility function \( {U}_i\left({x}_{i,}{\overline{x}}_i\right) \) is to be fixed at a certain value.
 
4
What is the certainty equivalent? It is the certain value of x i which gives the level of utility equivalent to the expected utility of lottery.
 
5
\( {k}_iU\left({x}_i^w\right)=0;{k}_jU\left({x_j}^w\right)=0. \)
 
6
\( E\left[U\left(\tilde{x}\right)\right] \) stands for the expected utility of lottery \( \tilde{x} \).
 
7
\( {k}_2{U}_2\left({\overline{x}}_i^w\right)=0;{k}_1{U}_1\left({\overline{x}}_i^w\right)=0 \)
 
8
The following can be said about the general form of U i  = U i (x i ). That is, the U i (x i ) according to \( \widehat{x}{}_{<}{}^{\geqq }p_i{x}_i^b+\left(1-{p}_i\right){x}_i^w \) for p i (0 ≦ p i  ≦ 1) takes the form of (1) concave function, (2) linear function, and (3) convex function, respectively; they are to be shown in Fig. 7.3.
 
9
The expected utility of these two lotteries can be obtained by using the additive utility function and the multiplicative utility function as follows:
1.
A case of additive utility function
$$ E\left[U\left({\tilde{x}}_{ij},{\overline{x}}_{ij}^{\kern0.5em w}\right)\right]=\frac{1}{2}\left({k}_i+{k}_j\right),\ E\left[U\left({\tilde{\tilde{x}}}_{ij},{\overline{x}}_{ij}^{\kern0.5em w}\right)\right]=\frac{1}{2}\left({k}_i+{k}_j\right) $$
 
2.
A case of multiplicative utility function
$$ E\left[U\left({\tilde{x}}_{ij},{\overline{x}}_{ij}^{\kern0.5em w}\right)\right]=\frac{1}{2}\left({k}_i+{k}_j+k{k}_i{k}_j\right),\ E\left[U\left({\tilde{\tilde{x}}}_{ij},{\overline{x}}_{ij}^{\kern0.5em w}\right)\right]=\frac{1}{2}\left({k}_i+{k}_j\right) $$
 
Due to k ≠ 0, this identifying method can be understood.
The expanding of equations is as follows:
$$ \begin{array}{c}\frac{1}{2}{\left.\left\{1\right.+kU(x)\right\}}_B+\frac{1}{2}{\left.\left\{1\right.+kU(x)\right\}}_D=\frac{1}{2}\left\{1+k{k}_1{U}_1\left({x}_1^b\right)\right\}\left\{1+k{k}_2{U}_2\left({x}_2^b\right)\right\}\\ {}=\frac{1}{2}\left\{1+k{k}_1\right\}\left\{1+k{k}_2\right\}=\frac{1}{2}\left\{1+k{k}_2+k{k}_1+{k}^2{k}_1{k}_2\right\}\\ {}=\frac{1}{2}\left\{1+k\left({k}_1+{k}_2+k{k}_1{k}_2\right)\right\}\end{array} $$
$$ \frac{1}{2}\left\{1+kU(x)\right\}=\frac{1}{2}\left\{1+k\left({k}_1+{k}_2+k{k}_1{k}_2\right)\right\} $$
$$ \therefore \kern0.5em \frac{1}{2}U(x)=\frac{1}{2}\left({k}_1+{k}_2+k{k}_1{k}_2\right). $$
 
10
On an earlier occasion, the questionnaire sheets of five attributes, i.e., X 1 = monthly income, X 2 = monthly residential expenditures, X 3 = monthly living expenditures, X 4 = commuting time, and X 5 = noise, have been made, for the pair of which the utility independent is verified, but preferentially independent was not verified.
 
Literatur
1.
Zurück zum Zitat Keeney, Ralf L. 1974. Multiplicative utility functions. Operations Research 22: 22–34.CrossRef Keeney, Ralf L. 1974. Multiplicative utility functions. Operations Research 22: 22–34.CrossRef
2.
Zurück zum Zitat Yoshida, Masatoshi (Translated). 1977. Tazokusei kōyō kansu (Multiplicative utility functions). Expressways and Automobiles 20(6): 58–66. Yoshida, Masatoshi (Translated). 1977. Tazokusei kōyō kansu (Multiplicative utility functions). Expressways and Automobiles 20(6): 58–66.
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Zurück zum Zitat Keeney, R.L., and Eric F. Wood. 1977. An illustrative example of the use of multiattribute utility theory for water resource planning. Water Resources Research 13(4): 705–712.CrossRef Keeney, R.L., and Eric F. Wood. 1977. An illustrative example of the use of multiattribute utility theory for water resource planning. Water Resources Research 13(4): 705–712.CrossRef
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Zurück zum Zitat de Neufville, Richard, and R.L. Keeney. 1972. Chapter 23: Use of decision analysis in airport development for Mexico City. In Analysis of public systems, ed. A.W. Drake, R.L. Keeney, and P.M. Morse, 497–519. Cambridge, MA/London: The MIT Press. de Neufville, Richard, and R.L. Keeney. 1972. Chapter 23: Use of decision analysis in airport development for Mexico City. In Analysis of public systems, ed. A.W. Drake, R.L. Keeney, and P.M. Morse, 497–519. Cambridge, MA/London: The MIT Press.
9.
Zurück zum Zitat Kohno, Hirotada, Yoshiro Higano, and M. Yoshida. 1977. Measurement of evaluation rate of public pollution using the multi-attributed utility function. In Studies in regional science, The 13th (s.51) annual meeting report, vol. 7, 225–245. Tokyo: Japan Regional Science Association. Kohno, Hirotada, Yoshiro Higano, and M. Yoshida. 1977. Measurement of evaluation rate of public pollution using the multi-attributed utility function. In Studies in regional science, The 13th (s.51) annual meeting report, vol. 7, 225–245. Tokyo: Japan Regional Science Association.
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Metadaten
Titel
Measurement of Evaluation Rate of Public Pollution (Noise)
verfasst von
Hirotada Kohno
Copyright-Jahr
2016
Verlag
Springer Japan
DOI
https://doi.org/10.1007/978-4-431-55224-6_7