ABSTRACT
Social welfare at each port is defined as a summation of net consumer surplus, producer surplus (or shipping lines’ profits), port profit, and tax revenue of the local government. Then, the pollution cost will be subtracted from the total value of social welfare so as to represent the environmental concern. Firstly, from Figure 1, we specify the consumer surplus as:
cs1 ¼ Ðzlj j 0
V � P1ðQ1;Q2Þ � 4tz½ �dzþ Ð~z 0 V � P1ðQ1;Q2Þ � 4tz½ �dz, and
cs2 ¼ ðð1�~zÞ 0
V � P2ðQ1;Q2Þ � 4tz½ �dzþ ððzr�1Þ 0
V � P2ðQ1;Q2Þ � 4tz½ �dz; (A:1)
where ~z ¼ 12 þ P2�P18t , zl ¼ � V�P14t , and zr ¼ 1þ V�P24t . Note that Q1 and Q2 do not depend on z, whereas ~z, zl, and zr depend on Q1 and Q2. Substitute Pi (Q1,Q2) from (6) into (A.1), then consumer surplus for each port can be written as:
csi ¼ t4 7Q 2 i � Q2j þ 2QiQj
� � þ t Qj � Qi � 1
� � : (A:2)
Note that total net consumer surplus for these two local cities is:
CS ¼ cs1 þ cs2 ¼ 3t2 Q 2 1 þ Q22
� �þ t Q1Q2 � 2ð Þ: (A:3) Then, the respective total shipping line profits, port profits, tax revenues, and total pollution costs can be expressed as follows:Pni
k¼1 πik ¼ Pni
k¼1 Pi � c� wi � sið Þqik ; �i ¼ wiQi: GovRevi ¼ siQi and PCi ¼ αQi þ βQj: (A:4)
Therefore, the local social welfare and regional welfare are expressed respectively as follows:
SWi ; ’i ¼ t4 7Q 2 i � Q2j þ 2QiQj
� � þ t Qj � Qi � 1
� �þ Pi � cð ÞQi � PCi; (A:5)
Regional cooperation and management of port pollution 465
PORTS AND THE ENVIRONMENT
Φ ¼ ’1 þ ’2 ¼ 3t2 Q 2 1 þ Q22
� �þ t Q1Q2 � 2ð Þ þXi Pi � cð ÞQi � PCi½ �: (A:6) The online supplement is available on the website of PolyU Institutional Repository https://repository.lib.polyu.edu.hk/jspui/.
