社会福利函数

General equilibrium analysis explores how markets interact and adjust to achieve balance. But does this equilibrium always lead to a desirable outcome for society? Defining what’s “desirable” can get tricky, so economists use specific standards to evaluate market performance.

One key tool for this evaluation is the social welfare function.

It is a measure describing the well-being of society as a whole in terms of the utilities of individual members.

One common type is the Utilitarian Social Welfare Function.

It adds up to the utility of every individual, giving equal weight to each person. Mathematically, it’s represented as shown. Here, W represents the total welfare of society.

Imagine an economy with only three people with the represented utilities. A utilitarian function would say the economy’s welfare depends only on the sum of its utilities, regardless of distribution. Utilitarianism prioritizes maximizing total welfare and not equity. 

For example, in this scenario, the utilitarian social welfare function would treat both outcomes as equally beneficial despite differences in utility distribution.