Suppose L $=3,$ and consider the demand function x$($p$,$ w$)$ dened by x$1($p$,$ w$)=$ p$2$ p$1+$p$2+$p$3$ w p$1$ x$2($p$,$ w$)=$ p$3$ p$1+$p$2+$p$3$ w p$2$ x$3($p$,$ w$)=$ p$1$ p$1+$p$2+$p$3$ w p$3($a$)$ Does this demand function satisfy homogeneity of degree zero and Walras' law when $=1?$ What about when in $(0,1)?($b$)$ Assume $=1$ and w $=1.$ Compute the substitution matrix. Show that at p $=(1,1,1),$ it is negative semidenite but not symmetric. $($c$)$ Show that this demand function does not satisfy the weak axiom.