Suppose that the utility possibilities set is a convex set...

Name: Problem 3, Chapter 33: Intermediate Microeconomics: A Modern Approach
Uploaded: 2021-02-27T11:23:25-08:00
Channel: Oluwadamilola Ameobi
Description: Suppose that the utility possibilities set is a convex set and that consumers care only about their own consumption. What kind of allocations represent welfare maxima of the Nietzschean welfare function?

Suppose that the utility possibilities set is a convex set and that consumers care only about their own consumption. What kind of allocations represent welfare maxima of the Nietzschean welfare function?

Key Concepts

Convex Utility Possibility Set

This concept refers to the idea that if two allocations (in terms of individual utilities) are feasible, then any weighted average of them is also feasible. Convexity is an important property because it guarantees that local improvements lead to global improvements and makes optimization problems, such as maximizing a welfare function, more tractable.

Social Welfare Function

A social welfare function aggregates individual utilities into a single measure that reflects the overall well?being of society. In social choice theory, different forms of such functions express different ethical or societal priorities, influencing which allocations are considered socially optimal.

Nietzschean Welfare Function

This specific form of welfare function is characterized by its focus on the highest individual utility in the distribution. Rather than seeking a balanced or equitable distribution of well-being, the Nietzschean function values the achievement of excellence by the best?off individual. It implies that allocations maximizing society’s welfare will be those in which one individual attains the highest possible consumption level, often at the expense of others.

Extreme (or Dictatorial) Allocations on the Pareto Frontier

When consumers care only about their own consumption and the utility possibility set is convex, maximizing a function that depends solely on the highest utility leads naturally to extreme allocations. These are allocations located on the boundary (or extreme points) of the utility possibility set where one individual’s consumption is maximized while the others receive as little as feasibly possible. Such outcomes are Pareto optimal in the context of the given welfare function because any reallocation that would lower the maximum utility would reduce the value of the social welfare function.

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