$(10pts)$ Consider the three$-$period model $of$ early child education with a single school district con$-$

taining two schools, A and $B,$ where $F_{1A}>F_{1B}{Q}_{1A}>Q_{1B}ma{x}_{S_{2A},S_{2B}}U=Q_{2A}+Q_{2B}$

subject $to$ the budget constraint

$S_{2A}+S_{2B}\frac{?}{b}=ar(S{)}_2$

Explain under what conditions $(mathematicallyas$ well $as$ intuitively$)on$ the period $2$ EPF $,$ the

utility$-$maximizing strategy $of$ the school district $is$

Equality: $S_{2A}=S_{2B}$

Compensation: $S_{2A}>S_{2B}{S}_{2A}$

Reinforcement: $S_{2A}>S_{2B}$