Graphical Analysis, Intuition In Figure 5.2, loss to steel firm of moving to Q is shaded triangle dcg This is the area between the mb and mPc curve going from Q1 to Q Fishery gains by an amount abfe This is the area under the Md curve going from Q, to Q. By construction, this equals area cdg Difference between fishery's gain and steel firms loss is the efficiency loss from producing Q, instead of Q
11 Graphical Analysis, Intuition • In Figure 5.2, loss to steel firm of moving to Q* is shaded triangle dcg. – This is the area between the MB and MPC curve going from Q1 to Q* . • Fishery gains by an amount abfe. – This is the area under the MD curve going from Q1 to Q* . By construction, this equals area cdhg. • Difference between fishery’s gain and steel firm’s loss is the efficiency loss from producing Q1 instead of Q*
Numerical Example: Negative Externalities Assume the steel firm faces the following mb and mpc curves MB=300-Q MPC=20+Q Assume the fishery faces the following MD curve MD=40+2Q 12
12 Numerical Example: Negative Externalities • Assume the steel firm faces the following MB and MPC curves: MB = 300 − Q MPC = 20 + Q • Assume the fishery faces the following MD curve: MD = 40 + 2Q
Numerical Example, continued The steel firm therefore chooses Q1 MB=MPC→300-Q=20+Q→C1=140 The socially efficient amount is instead Q MB= MSC= MPC+MD →300-9=(20+9)+(40+29)→g=60 13
13 Numerical Example, continued • The steel firm therefore chooses Q1 : MB = MPC 300 − Q = 20 + Q Q1 = 140 • The socially efficient amount is instead Q* : MB = MSC = MPC + MD 300 − Q = (20 + Q) + (40 + 2Q) Q = 60 *
Numerical Example, continued The deadweight loss of steel firm choosing Q1=140 is calculated as the triangle between the mb and msc curves from Q, to Q DWL=(e-0)MSCo-MBlo) DWL=7(140-60(480-160)=$12800 In Figure 5.2, this corresponds to area dhg 14
14 Numerical Example, continued • The deadweight loss of steel firm choosing Q1=140 is calculated as the triangle between the MB and MSC curves from Q1 to Q* . DWL = (Q − Q )( MSC Q − MB Q ) 1 2 1 1 1 * DWL = ( − )( − ) = 1 2 140 60 480 160 $12800 • In Figure 5.2, this corresponds to area dhg
Numerical Example, continued By moving to q the fishery reduces its damages by an amount equal to the trapezoid under the Md curve from Q, to Q GAN=(@@)MDe +MDla) GAN=7(140-60160+320)=19200 By moving to Q the steel firm loses profits equal to the triangle between the mb and mPc curve from Q, to Q LOSS=10-0)MB oMC Q LOSS=2(140-60240-80)=6400 15
15 Numerical Example, continued • By moving to Q* the steel firm loses profits equal to the triangle between the MB and MPC curve from Q1 to Q* . LOSS = (Q − Q )( MB Q − MC Q ) 1 2 1 * * * LOSS = ( − )( − ) = 1 2 140 60 240 80 $6400 • By moving to Q* the fishery reduces its damages by an amount equal to the trapezoid under the MD curve from Q1 to Q* . GAIN = (Q − Q )( MD Q + MD Q ) 1 2 1 1 * * GAIN = ( − )( + ) = 1 2 140 60 160 320 19200