Q: A monopolist with TC=3q2+q+12 faces a demand curve of
Find CS and DWL.
A: First we need to determine Pm and Qm. From the information above we
MC=6q+1 and MR=81-4q. To find qm set MC=MR and you get 10q=80 or qm=8.
Pm is found by plugging qm into the demand curve: pm=81-2(8)=65.
To find CS we still need to know the P-intercept of demand which is P=81-2(0)=81.
Hence CS= (1/2) (81-65)(8)=64
To find DWL we need to know qe and the height of MC at qm.
To find qe set P=MC or 81-2q=6q+1 or qe=10.
At qm the height of MC is 6(8)+1=49.
Hence DWL= (1/2)(65-49)*(10-8)=16.