Is maximum of increasing concave functions quasi-concave?

Hallie Stanton

Hallie Stanton

Answered question

2022-11-06

Is maximum of increasing concave functions quasi-concave?

Answer & Explanation

Taniyah Lin

Taniyah Lin

Beginner2022-11-07Added 14 answers

Monotone functions are quasi-concave, the maximum of monotone functions is monotone as soon as they are all decreasing or increasing.
Let f and g two increasing function on I R . Then x , y s.t. x < y, we have f ( x ) f ( y ) and g ( x ) g ( y ). Thus :
max ( f ( x ) , g ( x ) ) max ( f ( y ) , g ( y ) ) .
That means that the function x max ( f ( x ) , g ( x ) ) is also increasing, hence quasi-concave by monotonicity.

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