General Notes on SWF (Mueller)

General Notes on SWF (Mueller) - CHAPTER 23 Social welfare...

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CHAPTER 23 Social welfare functions The interest of the community then is - what? The sum of the interests of the several membets who comDose lt' Jeremv Bentham Whereas one can speak ofrlepositive theory ofpublic choice, based upon economic man assumptions, one must think of normative theories of ptrblic choice, for there are many views ofwhat the goals ofthe state should be and how to achieve them. This potential multiplicity has been the focus ofmuch criticism by positivists, who have argued for a "value-ftee" discipline. For the bulk ofeconomics, it mightbe legitimate . to focus on explanation and prediction, and leave to politics the explication of the goals of society. For the study of politics itself, in toto, to take this position is less legitimate; thus the interest in how the basic"ralues ofsociety are or can be expressed through the political process. The challenge that normative theory faces is to develop theorems about the expression and realization ofvalues, based on generally accepted postulates, in the same way that positive theory has developed explanatory and predictive theorems from the postulates ofrational egoistic behavior. Part V reviews some efforts to take up this challenge. 23,1 The Bergson-Samuelson social welfare function The traditional means for representing the values ofthe community in economics is to-use a social welfare function (SWF). The seminal paper on SWI's is by Bergson (1938), with the most significant further explication by Samuelson (1947, ch. 8). The SWF can be written as follows: W = lT(2t,22,. ..,2,), where ll is a real valued frrnction of all variabies, and the z;s and I/ are chosen to represent the ethical values ofthe society or ofthe individuals in it (Samuelson, 1947,p.221). The objective is to define aW and set ofz;s, ard the constraints thereon, to yield meaningfrrl fust- and second-order conditions for a maximum IZ. Although in principle any variables that arc lelated to a societyt well-being (e.g., crime statistics, weather data, years of schooling) might be included in the SWF. economists have focused on economic variables. Thus, the SWF literature has adopted the same assumptions about consumers, production functions, and so
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564 Social welfare functions on, that underlie the bulk of economics and public choice and has made these the focal point of its analysis. The only value postulate upon which general agreement has been possible has been the Pareto postulate. This postulate suffices to bring about a set of necessary conditions for the maximization of Il, which limit social choices to points along the generalized Pareto frontier. The proof is analogous to thb demonstration that movement fiom offthe contract curve to points on it can be Pareto improvements, and the necessary conditions are also analogous. With respect to production, these conditions are \Xi/\hi :... : \Xi/\V-i _ T,r 0Xy/01\1, 0X1/0v6 - 7,1' where 3 Xi / 0 V*i is the marginal product of factor V^ tn the production of out- put Xi, and
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General Notes on SWF (Mueller) - CHAPTER 23 Social welfare...

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