ECO102 Lecture Notes - Lecture 14: Institute For Operations Research And The Management Sciences, Implicit Function Theorem, Fxx
Document Summary
Suppose we wish to solve the problem where (x, a) s and f is c 2 on s. here x is the choice variable and a is interpreted as a parameter. max x f (x, a) (1) Next assume the following: fxx < 0 for all x and a in the convex set s, i. e. , f is strictly concave in x on s and fa > 0 and fxa > 0 on s. Then the solution is x such that which yields a point of maximum because the su cient s. o. c. is satis ed, namely, fxx(x , a) < 0. The solution x is likely to depend on a so to indicate this we can write. F. o. c. fx(x , a) = 0 x = x (a) Note that the f. o. c. can be thought of as an equation in (x, a) and also as the equation of the level curve of the function fx.
