In economic theory the individual well-being of a consumer i is represented by a utility function u (x, G), where x. stands for the individual consumption of so-called private goods (i.e., those that are individually acquired, perhaps in different quantities by every consumer), and G is the consumption of so-called public goods (by definition identical for all consumers). Since the mid-twentieth century, economic theory has applied the Bergson—Samuelson function of economic welfare W(xp . . . , Xk, G), where the consumers are numbered from 1 to k. No conditions are imposed on Wother than if all the consumers prefer one situation over another, Wmust indicate this universally preferred situation as superior. This concept can be formalized in the following way. If for every i = 1,. ..,ku(x',G')>u(x,G), then also Wx^,..,x'^G' )> W(xj, .. x^G). The general definition of the Bergson—Samuelson function does not indicate the effect on overall welfare when some consumers are better off while others are worse off. One has to make additional assumptions in order to draw further conclusions.
Many specific social welfare functions are considered in economic theory. Three of them are particularly well studied (see any advanced text of microeconomics, e.g., Mas-Collel et al. 1995:825-828):
Bentham function (utilitarian)
W(xp.. .,xk,G) =a1u1(x1,G) +... +akuk(xi,G), where a1v .. ,<<£>0
These functions differ in what they assume about how social welfare depends on the welfare of individual consumers.
Bentham's function asserts that social welfare increases even when a consumer j has experienced a decrease of utility as long as a consumer m has experienced a higher increase of utility (taking into account the relation </am). If one is guided by the Ben-tham function with identical coefficients < (< 1 = . . . = < k ), that is, no consumer is favored over another, then the social welfare is maximized when resources are allocated to the consumers who value them most. In contrast, the Rawls function asserts that social welfare is identical to the welfare of the worst-off consumers. According to Rawls, welfare changes among those who are well off do not affect the social welfare. The latter increases only when the welfare of the very worst-off consumers improves. Finally, the Nietzsche function (referring to the nonegalitarian convictions of the philosopher) asserts that social welfare is identical with welfare of the best-off consumers. If the Nietzsche function were preferred, resources would have to be allocated in order to improve the situation of the most privileged ones, even at the expense of the least privileged ones.
These examples of welfare functions demonstrate how flexible economic theory can be in analyzing social and economic changes. It can provide analytical tools irrespective of political convictions of the analyst. Bergson—Samuelson social welfare functions can model any system of resource allocation, both purely egalitarian and the opposite.
Economic theory can accommodate any relationship between the natural environment and social welfare. Thus, one can study how the environment affects the satisfaction derived from both individually consumed goods (x;.) and public ones (G). In particular, economic theory does not take an a priori position with respect to privatization or socialization of certain services provided by natural resources. For instance, the demand for clean water can be satisfied either by improving the quality of natural aquifers (i.e., providing public goods) or by developing the market for bottled water (i.e., providing private goods). The first way reaches all consumers because, by definition, everybody has access to a public good. The second way reaches only those who put the highest value on clean water first because the demand is satisfied through individual purchases; therefore, not all consumers need to purchase the same amount.
The most challenging questions refer to welfare impacts of the environment in the future. Some decisions are based on present preferences despite the fact that they will affect future generations of consumers whose preferences are not known. For instance, land use decisions, particularly those that determine proportions between built-up areas and natural ecosystems, are made without knowledge of whether they are consistent with the future generations' preferences.
Economists ponder whether the environment is a luxury good, that is, a good for which demand grows faster than consumers' income. There is some evidence indicating that indeed this might be the case. Nevertheless, a fully satisfactory and universal answer will remain unknown because we cannot predict the preferences of future generations.
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