(12 points) With the policy setting {H 2 TL, could it he the case that low-wage individuals\" optimal choices for both c and I are identical to the high-wage individuals\" optimal choices for c and I? More precisely, is it possible that the optimal values are such that boil: 6; = c: and I; = I; '? If so, clearly and carefully provide important algebraic steps explaining why. If not, clearly and carefully explain why not. If it is impossible to determine, clearly and carefully describe why it is impossible to determine. (Note: numerical analysis is needed and should not be included in your solution; the result is entirely analytic. Points will be deducted if the result relies on a numeric example.) Be as precise as possible in your results