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2017 | OriginalPaper | Buchkapitel

3. Introduction to Decision Theories

verfasst von : Shinji Yamashige

Erschienen in: Economic Analysis of Families and Society

Verlag: Springer Japan

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Abstract

In this section, we provide a brief introduction to decision theory to understand our theoretical arguments on the social transformation in Part II.

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Vorheriges Kapitel Markets, Communities, and Government: Analytical Framework

Nächstes Kapitel Formation of Families

Readers who are not interested in the mathematical theories can skip this chapter and Part II to read chapters in Part III where we discuss the public policies used to cope with the challenges of the social transformation in Japan and the lessons that other countries can learn from her experiences.

One of the most important perceptions in economics is that our time is limited and thus has a value. The monetary value of time for an individual can be measured by his/her wage.

Differentiation of a function is an act of calculating the derivative, that is, the slope of the function.

In order to find out whether or not the values are a solution to the maximization problem, we need to check the “second order condition.” See Remark 3.3.

In Fig. 3.1, there is a saturation point (H, M) where the utility is maximized. Hence, the utility function U(L, C) here is not increasing any more after \(L \ge H\) and/or \(C \ge M\). As consumers will not choose the bundle (L, C) beyond the saturation point, only the part below the saturation point of the indifference curves is usually plotted.

The mathematical symbol \(\in R^2_+\) means “in the two dimensional space of non-negative real numbers”.

The answer can be changed if we were assumed to have a billion yen. In such a case, we may challenge it. It is well known that the degree of “risk aversion” tends to decline as we have more wealth.

Such a utility function is known as the von-Neumann-Morgenstern utility function. When expenditures for consumption are coming from our wealth, the decreasing utility from each unit of consumption would mean decreasing utility from the wealth.

When we think of an individual who has two million yen and faces the risk of losing two million yen with a probability of 0.5, \(\rho ^*> 0\) is the maximum amount of money that he/she can pay in addition to the expected loss of one million yen (\(=0.5\times 2\) million yen), because \(0.5 u(2) + 0.5 u(0) = u(2-(1+\rho ^*))\) holds. The amount \(1+\rho ^*\) is the maximum “insurance premium” that he/she can pay to insure against the risk, which can be decomposed into the expected loss and the risk premium. The risk-averse individual’s willingness to pay certain amount of money makes the insurance business profitable.

We may be able to offset the loss of wealth by purchasing various types of financial assets in financial markets.

See Sect. 3.3.5.2 for a discussion on “morals.”

In economics, the moral hazard problem refers to the problem that occurs in an insurance system under incomplete information. Hence, it can be seen as an example of the free rider problems. See Sect. 9.2.1.2 for more discussion on the moral hazard problem.

As a good introductory textbook on game theory, see, for example, Osborn (2003), and for advanced concepts, see Osborn and Rubinstein (1994) and Fudenberg and Tirole (1991).

The notation \(\forall a_1 \in A_1\), say, means that “for any \(a_1\) in the set \(A_1\).”

See, for example, Maskin (1996) for game-theoretic consideration of the problem.

We use the Nash bargaining solution in analyzing how wives and husbands share the returns from marriage, as given in Sect. 4.3.2.

Johnson and Krüger (2004), for example, pointed out that supernatural punishment has played an important role as a psychological punishment mechanism to discourage selfish people from deviating from the social norm. There are numerous examples of selfish behaviors being discouraged by the fear of punishments by “god” in various religions or legends. They also pointed out that the reason why there are small differences among the religions and legends in different regions are probably because problematic behaviors differ.

A difficulty associated with this mechanism is the cost of creating and properly maintaining the markets. For markets to work well, property rights must be well defined and constantly monitored. Whether creating markets is worthwhile depends on its costs and benefits.

Axelrod, R. (1984). The evolution of cooperation. New York: Basic Books.

Buchanan, M. (1975). The Samaritan’s dilemma. In E. S. Phelps (Ed.), Altruism, morality, and economic theory. New York: Russel Sage Foundation.

Fudenberg, D., & Tirole, J. (1991). Game theory. Cambridge: MIT Press.

Gordon, R., & Varian, H. (1988). Intergenerational risk sharing. Journal of Public Economics, 37, 185–202.CrossRef

Hardin, G. (1968). The tragedy of the commons. Science, 162, 1243–1248.CrossRef

Kornai, J. (1979). Economics of shortage. Amsterdam: North-Holland.

Johnson, D. D. P., & Krüger, O. (2004). The good of wrath: Supernatural punishment and the evolution of cooperation. Political Theology, 5(2), 159–176.CrossRef

Maskin, E. (1996). Theories of the soft budget constraint. Japan and the World Economy, 8, 125–133.CrossRef

Osborn, M. (2003). An introduction to game theory. Oxford: Oxford University Press.

Osborn, M., & Rubinshtein, A. (1994). A course in game theory. Cambridge: MIT Press.

Shiller, R. J. (1999). Social security and intergenerational, intragenerational and international risk sharing. Carnegie-Rochester Series in Public Policy, 50, 165–204.CrossRef

von Neumann, J., & Morgenstern, O. (1943). Theory of games and economic behavior. Princeton: Princeton University Press.

Nash, J. F. (1950). The bargaining problem. Econometrica, 18, 155–162.CrossRef

Yamashige, S. (1997). Fairness in markets and government policies: A weak equity criterion for allocation mechanisms. Hitotsubashi Journal of Economics, 38, 61–78.

Titel: Introduction to Decision Theories
verfasst von: Shinji Yamashige
Verlag: Springer Japan
Buch: Economic Analysis of Families and Society
Print ISBN: 978-4-431-55907-8

Electronic ISBN: 978-4-431-55909-2

Copyright-Jahr: 2017
DOI: https://doi.org/10.1007/978-4-431-55909-2_3

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