Bernice has the utility function U$($x$,$ y$)=$ min$[$x$,$ y$].$ The price of x used to be $3,$ but rose to $4.$ The price of y remained constant at $1.$ Her income is $12.$ The price increase was as bad for her as a loss of $3$ dollars in income, but she would need an income of $16$ dollars to be able to a$!$ord a bundle as good as her old one at the new price. True or false? Why? $[[$Ans: False. Given Px $=3,$ Py $=1,$ m $=12,$ and U$($x$,$ y$)=$ min$[$x$,$ y$],$ the optimal consumption requires x $=$ y$.$ By subsitution, one can write the budget equation as $3$x $+$ x $=12,$ yielding x $=3$; Hence, y $=3.$ The associated utility is U$!=3.$ When Px $=4,$ Py $=1,$ m $=16,$ then x $=$ y $=16/5$ and U$!!=16/5=3\mathrm{.}2>3.$ The utility is higher. $]]]$