$(10$ points$)$ Consider a monopolist that serves two separate market segments $($e$.$g$.,$ two geographic markets or two distinct demographic groups$)$ with demand curves given by $p_1=a_1-b_1{q}_1,$ and $p_2=a_2-b_2{q}_2,$ respectively. For tractability, we assume $b_1=b_2=b,$ and $a_1>a_2.$

Compare the social surplus under price discrimination $($DP$)$ versus uniform pricing $($UP$).$ Under which scheme do we observe a higher total output $($i$.$e$.,q_1+q_2)?$ How about prices in each market under the two different scenarios?$(10$ points$)$ Consider a monopolist that serves two separate market segments $($e$.$g$.,$ two geographic markets or two distinct demographic groups$)$ with demand curves given by $p_1=a_1-b_1{q}_1,$ and $p_2=a_2-b_2{q}_2,$ respectively. For tractability, we assume $b_1=b_2=b,$ and $a_1>a_2.$

Compare the social surplus under price discrimination $($DP$)$ versus uniform pricing $($UP$).$ Under which scheme do we observe a higher total output $($i$.$e$.,q_1+q_2)?$ How about prices in each market under the two different scenarios?