Question

I'm having difficult understanding the concept of quasi-concavity. From my understanding, the concavity can be identified based on 3 dimensional graph, and also, it can be tested using the second-order partial derivative. If f11 is less than zero, it means x1 is concavity up in x1 direction and if f22 is more than zero, it means x2 is concavity down in x2 direction. However, my problem is that I am having a difficult time determining if the f(x,y) happens to be non-concave. Do you mind explaining how to test it? One more thing is that I would like to ensure that I do understand the concept of quasi-concavity. To identify the quasi-concavity means all level sets at a curvature but if it is not quasi-concavity, it means that some levels sets are not at a curvature. Am I correct? If so, how can I test it?

Answer 1