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P
P
(2)
P
(3)
Our main purpose is to get the maximum annual profit speed, so we define
as
the only variable in Equation (2) and recognize marginal profit equals zero. There-
fore, the maximum annual profit speed function is:
P
P
(4)
Applying Equation (4) to determine the optimal speed, we could investigate how
the motivation for profit maximization of shipping carriers influences ship speed
under the marine emissions trading scheme proposed above.
3.1
CO
2
Emissions
International containerships emit several kinds of exhaust gases, such as CO
X
, NO
X
and SO
X
. Among these types of emissions, the quantity of CO
2
is the maximum and it
is the one that influences global climate most. Therefore, this paper focuses on
calculating the quantity of CO
2
from international containerships.
Marine fuels are a petroleum byproduct with carbon segment which converts to
CO
2
after burning. Normally, fuel consumption is used to calculate the CO
2
emissions
rate. The fuel consumption of a ship is the sum of fuel used by main and auxiliary
engines and it is calculated by Equation (5).
(5)
The fuel consumption of a ship is then multiplied by the fuel's carbon fraction (de-
fined at 0.8645) and a conversion factor from carbon to CO
2
(equal to 44/12) in order
to calculate CO
2
emissions in tons per trip [12]. The CO
2
emissions of each trip from
to
then is:
0.8645
3.17
(6)
Inserting Equation (5) into Equation (6), we obtain:
3.17
(7)
3.2
Annual Profit of a Ship in the Marine Emissions Trading Scheme
As mentioned before, there are three basic measures to cut down exhaust emissions of
containerships, respectively, technical, operational and market-based measures. Usually,
technical measures need a long time to plan before their final implementation. For this
