What this means: Hence, v(6,000) < v(4,000) + v(2,000) and v(-6,000) > v(-4,000) + v(-2,000). These preferences are in accord with the hypothesis that the value function is concave for gains and convex for losses

Jenny Schroeder

Jenny Schroeder

Answered question

2022-11-07

What this means: Hence, v(6,000) < v(4,000) + v(2,000) and v(-6,000) > v(-4,000) + v(-2,000). These preferences are in accord with the hypothesis that the value function is concave for gains and convex for losses

Answer & Explanation

Samuel Hooper

Samuel Hooper

Beginner2022-11-08Added 15 answers

The easiest way to think about examples is the following: f ( x ) = x a is (strictly) convex for a > 1 and (strictly) concave for a = .5 . Now try a = .5 for concavity, a = 2 for convexity.
The proposition given is just saying ( x + y ) .5 < ( x ) .5 + ( y ) .5 for positive x , y. Take squares and prove it on your own. The sign in inequality will reverse when x , y are negative.

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