Suppose agent has preferences given by the Constant Elasticity of Substitution utility function over two goods u(a, b) = (a^m + b^m )^1/m with m (0, 1).

a) Determine whether Ann's preferences have this property. If they do, prove this. If not, provide a counter example.

i. Rational

ii. Weakly Monotone

iii. Strongly Monotone

iv. Locally Non-satiated