11. Show that the Cobb-Douglas type production function f(x, y) = Axαy1−α is always quasi-oncave, and it is concave if the degree of homogeneity is less than or equal to 1. 12. Consider the following problem: min f(x)gi(x) ≤ 0i = 1, ..., n Where all functions gi(x) are convex functions. Show that the feasible region S = {x ∈ Rn : gi(x) ≤ 0, i = 1, ..., n} is convex. Please explain as detailed as possible, step by step.

11. Show that the Cobb-Douglas type production function f(x, y) = Axαy1−α is always quasi-oncave, and it is concave if the degree of homogeneity is less than or equal to 1. 12. Consider the following problem: min f(x)gi(x) ≤ 0i = 1, ..., n Where all functions gi(x) are convex functions. Show that the feasible region S = {x ∈ Rn : gi(x) ≤ 0, i = 1, ..., n} is convex. Please explain as detailed as possible, step by step.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter14: Discrete Dynamical Systems

Section14.3: Determining Stability

Problem 13E: Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii...

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