(All Steps) Consider the following utility functions: U(x_1, x_2)=x_1+x_2^1 / 2 U(x_1, x_2)=x_1^1/3 x_2^2/3 U(x_1, x_2)=kmin;3 x_1, 2 x_2+3, k>0 U(x_1,

Question: Consider the following utility functions:

$U\left(x_{1}, x_{2}\right)=x_{1}+x_{2}^{1 / 2}$
$U\left(x_{1}, x_{2}\right)=x_{1}^{\frac{1}{3}} x_{2}^{\frac{2}{3}}$
$U\left(x_{1}, x_{2}\right)=\operatorname{kmin}\left\{3 x_{1}, 2 x_{2}\right\}+3, k>0$
$U\left(x_{1}, x_{2}\right)=25+\left(x_{1}+\sqrt{x_{2}}\right)^{2}$
$U\left(x_{1}, x_{2}\right)=\frac{1}{2} x_{1}^{2}+\frac{1}{2} x_{2}^{2}$

For each of the functions depict a typical indifference curve. Label your graph carefully (pay attention to the shape of the curve, slope and intercepts.) Are the preferences monotonic? convex? Answers should be precise.

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(All Steps) Consider the following utility functions: U(x_1, x_2)=x_1+x_2^1 / 2 U(x_1, x_2)=x_1^1/3 x_2^2/3 U(x_1, x_2)=kmin;3 x_1, 2 x_2+3, k>0 U(x_1,

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