How to apply matrices, Jacobian, quasi-concavity, Hessian, Kuhn-Tucker conditions?© BrainMass Inc. brainmass.com March 4, 2021, 5:47 pm ad1c9bdddf
please refer to the attachment.
1. (a) Prove that quasi-concavity does not imply concavity.
The function f(x,y) defined by:
is quasi-concave, but not concave.
Here's the graph in two dimensions:
(b) Let ƒ be a C2 function on a convex subset D of R2. Assume that ƒ is strictly monotonic increasing. Prove that
(i) if the bordered Hessian determinant of ƒ is positive (negative) for all x Є D, then ƒ is quasi-concave (quasi-convex) on D; and
The bordered Hessian matrix for the function is
| f_11 f_12 ... f_1n f_1 |
| f_21 f_22 ... f_2n f_2 |
H = | ...
The expert prove that quasi-concavity does not imply concavity.