Consider the $$two$-$by$-$two$$pure exchange economy. Denote the consumption bundle for each individual i $=\{1,2\}$as xi $=($xi$1,$xi$2).$Suppose endowments are $\backslash$omega i $=(1,1)$for each i$.$Further$,$ suppose preferences are characterized by the following utility functions:

U$1($x$1)=$min$\{$x$11,$x$12\}$

U$2($x$2)=$max$\{$x$21,$x$22\}.$

Characterize the equilibrium allocation$($s$)$x$$i in this economy, if any.