Continutiy of perfect complement Utilities Problem

완전 보완제의 효용함수(Utility function)가 불연속임을 밝힌다 :

A perfect complement(완전 보완제) utility function(효용 함수), also known as a "Leontief utility function", is not continuous.

 

Take u(＊) = min{ax₁, bx₂}

This utility function is not continuous because it contains sharp corners at the points where 

ax₁ = bx₂

ax₁ = bx₂ax₁ ​= bx

At these points, the utility suddenly jumps from one constant level to another, rather than changing smoothly. Therefore, it does not meet the criteria for continuity.