Purchase Solution


Not what you're looking for?

Ask Custom Question

How to apply matrices, Jacobian, quasi-concavity, Hessian, Kuhn-Tucker conditions?

Purchase this Solution

Solution Summary

The expert prove that quasi-concavity does not imply concavity.

Solution Preview

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 = | ...

Purchase this Solution

Free BrainMass Quizzes
Economic Issues and Concepts

This quiz provides a review of the basic microeconomic concepts. Students can test their understanding of major economic issues.

Economics, Basic Concepts, Demand-Supply-Equilibrium

The quiz tests the basic concepts of demand, supply, and equilibrium in a free market.

Elementary Microeconomics

This quiz reviews the basic concept of supply and demand analysis.

Pricing Strategies

Discussion about various pricing techniques of profit-seeking firms.

Basics of Economics

Quiz will help you to review some basics of microeconomics and macroeconomics which are often not understood.