Mr_Elusive
New member
- Joined
- Sep 24, 2008
- Messages
- 1
Hey guys, I'm having trouble with this problem that I need to prove without differentiability:
Let m(a,y) be defined as a minimum value of ax subject to g(x) > y, where a, x for all R^n subscript ++, y for all R subscript +,and g(x) is strictly monotonic increasing and quasi-concave. Prove that m(a,y) is (i) non-decreasing in a and y and (ii) concave in a. Then, given that g(x) is homogeneous of degree k, derive the corresponding form of m(a,y).
Any help will be greatly appreciated
Let m(a,y) be defined as a minimum value of ax subject to g(x) > y, where a, x for all R^n subscript ++, y for all R subscript +,and g(x) is strictly monotonic increasing and quasi-concave. Prove that m(a,y) is (i) non-decreasing in a and y and (ii) concave in a. Then, given that g(x) is homogeneous of degree k, derive the corresponding form of m(a,y).
Any help will be greatly appreciated