2a) Define \"social welfare function. 2b) What is a Rawlsian social welfare func
ID: 1166804 • Letter: 2
Question
2a) Define "social welfare function. 2b) What is a Rawlsian social welfare function? 2c) Suppose Mrs. Adams is handing out 100 identical pieces of Halloween candy to the children in her neighborhood. For each child, their utility is equal to their consumption (which implies there is no diminishing marginal utility). Mrs. Adams' social welfare function is utilitarian (the value of the welfare of society is simply the sum of all of the individual utilities). Is there any particular way to distribute candy that would increase or decrease the social welfare from Mrs. Adams' perspective?Explanation / Answer
2a) A social welfare function is a function of individual welfare function which represents the ranking of different allocations as per the preferences of all the individuals in the society. It basically determines the total welfare of a society from a given set of allocation.There are many forms of a social welfare function. The two functions i.e. classical utilitarian, Rawlsian welfare function are commonly used welfare functions.
2b) Rawlsian welfare function, which is also called minimax function is defined as follows:
W(U1, U2 . . . . . . Un) = min(U1, U2 . . . . . . Un)
Which means that the total welfare of society defined as W(U1, U2 . . . . . . Un) depends on the lowest utility value. This is the utility of the agent who is the worst off in the society. Therefore, according to the Rawlsian function, if any allocation is such that it improves the welfare of the worst-off (say the poorest) individual, then it means that it increases social welfare and is socially desirable.
2c) A utlitarian function is defined as:
W(U1, U2 . . . . . . Un) = U1 + U2 + U3 . . . . . . Un
Social welfare is the sum of individual welfare from the consumption of a given commodity.
In Mrs Adam's case, 100 identcal candy pieces are distributed and no matter how these are distributed, the sum will always be equal to total satisfaction of 100 pieces of candy. In an extreme case, the social welfare will give the same value if she gives all 100 pieces to a single person or she divides these 100 pieces uniformly among all indivuduals. Therefore there is no particular way to distribute candy that would increase/decrease social welfare.
Infact, this is the most important criticism of utlitarian social welfare function that the distribution of goods play no role in defining social welfare, which is ofcourse not true in real world.
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