Question:
Consider a social welfare function (SWF) defined as
\[
SWF=f(U_1,U_2,\ldots,U_m),
\]
where \(U_i\) is the utility function of the \(i^{th}\) person, given that there are \(m\) people in the society. Identify which one of the following statements is CORRECT.
Consider a social welfare function (SWF) defined as
\[
SWF=f(U_1,U_2,\ldots,U_m),
\]
where \(U_i\) is the utility function of the \(i^{th}\) person, given that there are \(m\) people in the society. Identify which one of the following statements is CORRECT.
Show Hint
Utilitarian social welfare maximizes the sum of utilities, whereas Rawlsian welfare focuses on improving the welfare of the least advantaged individual.
Updated On: Jun 5, 2026
- Jeremy Bentham and John Stuart Mill proposed \[ SWF=\sum_{i=1}^{m} w_iU_i, \] where \(w_i\) is the weight assigned to individual \(i\) for their unique characteristics and \[ w_1\neq w_2\neq \cdots \neq w_m \]
- Since SWF reflects value judgements, interpersonal comparisons can be made on scientific grounds.
- John Rawls proposed \[ SWF=\max\{U_1,U_2,\ldots,U_m\} \]
- If \[ SWF=\sum_{i=1}^{m}U_i, \] it is referred as the utilitarian function.
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The Correct Option is D
Solution and Explanation
Step 1: Recall the concept of Social Welfare Function (SWF).
A Social Welfare Function aggregates the utilities of all individuals in society into a single measure of social welfare.
\[ SWF=f(U_1,U_2,\ldots,U_m) \]
Step 2: Analyze option (A).
The classical utilitarian approach associated with Jeremy Bentham and John Stuart Mill gives equal importance to individuals.
The standard utilitarian SWF is
\[ SWF=\sum_{i=1}^{m}U_i \] and not a weighted sum with unequal weights.
Therefore, option (A) is incorrect.
Step 3: Analyze option (B).
Interpersonal comparisons in welfare economics involve normative value judgements and cannot be made purely on objective scientific grounds.
Hence, option (B) is incorrect.
Step 4: Analyze option (C).
John Rawls proposed the
maximin criterion, not the maximization of the maximum utility.
Rawlsian SWF is
\[ SWF=\min\{U_1,U_2,\ldots,U_m\} \] which focuses on maximizing the welfare of the least advantaged person.
Thus, option (C) is incorrect.
Step 5: Analyze option (D).
The utilitarian social welfare function is given by
\[ SWF=\sum_{i=1}^{m}U_i \] which simply sums individual utilities.
Therefore, option (D) is correct.
Step 6: Final conclusion.
Hence, the correct statement is
\[ \boxed{SWF=\sum_{i=1}^{m}U_i \text{ is the utilitarian function}} \]
Thus, the correct option is (D).
A Social Welfare Function aggregates the utilities of all individuals in society into a single measure of social welfare.
\[ SWF=f(U_1,U_2,\ldots,U_m) \]
Step 2: Analyze option (A).
The classical utilitarian approach associated with Jeremy Bentham and John Stuart Mill gives equal importance to individuals.
The standard utilitarian SWF is
\[ SWF=\sum_{i=1}^{m}U_i \] and not a weighted sum with unequal weights.
Therefore, option (A) is incorrect.
Step 3: Analyze option (B).
Interpersonal comparisons in welfare economics involve normative value judgements and cannot be made purely on objective scientific grounds.
Hence, option (B) is incorrect.
Step 4: Analyze option (C).
John Rawls proposed the
maximin criterion, not the maximization of the maximum utility.
Rawlsian SWF is
\[ SWF=\min\{U_1,U_2,\ldots,U_m\} \] which focuses on maximizing the welfare of the least advantaged person.
Thus, option (C) is incorrect.
Step 5: Analyze option (D).
The utilitarian social welfare function is given by
\[ SWF=\sum_{i=1}^{m}U_i \] which simply sums individual utilities.
Therefore, option (D) is correct.
Step 6: Final conclusion.
Hence, the correct statement is
\[ \boxed{SWF=\sum_{i=1}^{m}U_i \text{ is the utilitarian function}} \]
Thus, the correct option is (D).
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