2012-11-12, 06:37 PM
SolicShooter Wrote:I think your question is answered, so if you don't me hijacking your topic. How do you exactly determine if the critical points you find are a maximum or a minimum. I now have a solution to a problem, by using the langrange method, expressed through a few other symbols like this for example: x* = 3m / (3px + 2py), y* = 2m / (3px + 2py), where m is income, px is price of good x and py is price of good y. The question was to find the maximum, but how can I determine if this solution is the maximum?
I use the second derivative test. You'll have to translate the variables to work for that economics problem, but that shouldn't be difficult.
D = fxx(a,b)*fyy(a,b)-(fxy(a,b))^2 [Same thing as fxx cross fyy]
if D > 0 and fxx(a,b) > 0; f(a,b) is a local minimum
if D > 0 and fxx(a,b) < 0; f(a,b) is a local maximum
if D < 0 then test fails (saddle point I believe)