(Solved): Suppose the expenditure function is given by the following equation: \\[ e(\\boldsymbol{p}, u)=\\le ...

Suppose the expenditure function is given by the following equation: \\[ e(\\boldsymbol{p}, u)=\\left(\\frac{1}{3} p_{1}+\\sqrt{p_{1} p_{2}}+\\frac{2}{3} p_{2}\\right) u \\] At a target utility of \\( u=1 \\), which of the following statements are true, where \\( x^{h} \\) is the Hicksian demand function? a. \\( x_{1}^{h}(\\boldsymbol{p}, u)>\\frac{1}{3} \\) and \\( x_{2}^{h}(\\boldsymbol{p}, u)>\\frac{2}{3} \\) b. \\( x_{1}^{h}(\\boldsymbol{p}, u) \\leq \\frac{1}{3} \\) and \\( x_{2}^{h}(\\boldsymbol{p}, u) \\leq \\frac{2}{3} \\) c. \\( x_{1}(\\boldsymbol{p}, u)=\\frac{1}{3} \\) and \\( x_{2}(\\boldsymbol{p}, u)=\\frac{2}{3} \\) d. None of the above. Hint: What Lemma connects Expenditure function with the Hicksian Demand? See Lec 3.