- Joined
- Apr 20, 2018
- Messages
- 10,257
- Reaction score
- 4,161
- Location
- Washington, D.C.
- Gender
- Undisclosed
- Political Leaning
- Undisclosed
Social welfare is the aggregate expressed (by way of buying "this" mix of goods/services instead of "that" mix of the same goods/services) utility[SUP]1[/SUP] of a society's members. A social welfare function (SWF), then, merely describes a curve (the curve is called a "social indifference curve" (SIC)) that represents a specific quantity of utility an individual realizes from various combinations of a given mix of goods/services whereby every point on the curve represents the same quantity of utility. Of course, i has multiple SICs, and each curve represents a more or less utility.
The graph above shows four of one person's (A's) SICs. Each point on an SIC represents a unique mix of a set of goods and services (a bundle). All points on, say, curve W[SUB]1[/SUB] provide the same utility (W); however, any point on curve W[SUB]2[/SUB] corresponds to A being more satisfied than s/he is with any point on curve W[SUB]1[/SUB]. What allows A to realize the utility found on W[SUB]2[/SUB], or that found on W4? "Better" bundles, of course.
Q, R and all other points on W[SUB]1[/SUB] represent bundles containing varying quantities of two items: peaches and apples. Given that, S must necessarily include things that satisfy A more than do peaches and apples. S may include:
Obviously, myriad combinations of goods can be in a given set of bundles. For this thread, any bundle's contents don't matter because the topic/question is which social welfare function, IYO, best depicts satisfaction, not what be the actual components of and measures that produce a given quantity of satisfaction.
Thread question and discussion topic:
Which of the below social welfare models [functions] most obtains your approbation?
Variables listing:
Endnote:
The graph above shows four of one person's (A's) SICs. Each point on an SIC represents a unique mix of a set of goods and services (a bundle). All points on, say, curve W[SUB]1[/SUB] provide the same utility (W); however, any point on curve W[SUB]2[/SUB] corresponds to A being more satisfied than s/he is with any point on curve W[SUB]1[/SUB]. What allows A to realize the utility found on W[SUB]2[/SUB], or that found on W4? "Better" bundles, of course.
Q, R and all other points on W[SUB]1[/SUB] represent bundles containing varying quantities of two items: peaches and apples. Given that, S must necessarily include things that satisfy A more than do peaches and apples. S may include:
- peaches and apples, or
- peaches, grapes and no apples, or
- peaches, apples and water, or
- apples, condoms, housekeeping and a pet, or
- quantities of things that are neither peaches nor apples, or
- some other combination of goods and services that is "better" than is any combination of just peaches and apples.
Obviously, myriad combinations of goods can be in a given set of bundles. For this thread, any bundle's contents don't matter because the topic/question is which social welfare function, IYO, best depicts satisfaction, not what be the actual components of and measures that produce a given quantity of satisfaction.
Thread question and discussion topic:
Which of the below social welfare models [functions] most obtains your approbation?
[*=1]Benthamite/Utilitarian model
[*=1]W(u[SUB]1[/SUB], …,u[SUB]N[/SUB]) = Σ[SUB]i[/SUB]θ[SUB]i[/SUB]u[SUB]i[/SUB], where θ[SUB]i[/SUB]≥0 (the weights can, for example, be equal across individuals, or be proportional to income).
[*=1]Rawlsian model
[*=1]W(u[SUB]1[/SUB],…,u[SUB]N[/SUB]) = min[SUB]i[/SUB](u[SUB]i[/SUB]).
[*=1]Nozickian model (The linked content explains this model; however, I don't have an equation for it for it's more a philosophical thing than an empirical thing. Put another way, Nozick's model is basically "bitching and moaning" about what's wrong with Rawls' than it is an empirical depiction unto itself. That said, it's a model of sorts.)
[*=1]Commodity Egalitarian model
[*=1]W(u[SUB]1[/SUB],…,u[SUB]N[/SUB]) = Σ[SUB]i[/SUB]u[SUB]i[/SUB]- λΣ[SUB]i[/SUB][u[SUB]i[/SUB]-min[SUB]i[/SUB](u[SUB]i[/SUB])], where λ indicates the relative weight placed on equality.
Variables listing:
[*=1]W = social welfare
[*=1]N = # of people in Society (i=1, ...., N)
[*=1]x is a composite material good
[*=1]X=(x[SUB]1[/SUB], x[SUB]2,[/SUB] ...., x[SUB]N[/SUB]) is the set of individual consumption vectors
[*=1]u[SUB]i[/SUB](x[SUB]i[/SUB],e) is individual i’s utility function (a function of material goods and environmental quality)
[*=1]e is environmental quality, same for all agents
Math Note:
[*=1]If the "math" confounds you, click the "social welfare" hyperlink and watch the video. The lecturer does an excellent job of explaining each of the models. Not only does the video explain the functions, but it also calls attention to the key implications of each of them.
Endnote:
- Utility is the satisfaction, benefit, or welfare (in this post's/thread's context, they are synonymous) that a consumer gets from a given market. For example, if an individual prefers goods and services (GS) Bundle A (GSB-A)to goods and services Bundle B (GSB-B), then GSB-A gives more utility than BSB-B.
Last edited: