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## Homework Statement

Show that a superadditive function has the following property:

For any superadditive function g on XxY (cartesian product):

f(x) = min { y' : y' = argmin g(x,y) }

is nonincreasing in x.

## Homework Equations

if g(x,y) is a superadditive on XxY, x in X, y in Y, x1 >= x2, y1 >= y2, then it satisfies the inequality:

g(x1,y1) + g(x2,y2) >= g(x1,y2) + g(x2,y1)

## The Attempt at a Solution

Let f(x1) = y', and suppose there is an x2 <= x1 such that f(x2) = y' then, g(x2,y1) - g(x2,y1) <= g(x2,y2) - g(x1,y2).

I am trying to find a contradiction, so that f is increasing in x for x2.