# Chapter 4 Market Analysis

## 4.1 Introduction

We simulate every possible market structure governed by the 3 firms and evaluate the firms and the market’s response to the low sulfur fuel switching policy.

## 4.3 Pollution Stock

The industry’s BAU sulfur and carbon emission paths\(\overline{E^{CO_2}_{t}}\) ,\(\overline{E^{SO_x}_{t}}\) accumulate throughout the planning horizon and form a pollution stock such that:

\[\begin{equation} \begin{cases} \overline{E_t^{CO_2}} = \sum_{i=1}^{N^{ firms} } \overline{e^{CO_2}_{i,t}}\\ \overline{E_t^{SO_x}} = \sum_{i=1}^{N^{ firms} } \overline{e^{SO_x}_{i,t}}\\ \end{cases} \end{equation}\]

Pollution decays over time with a natural rate of decay\(\delta\). We assume\(\delta\) = 1, and we compute the industry’s BAU\(CO_2\) and\(SO_x\) emission inventory as the following:

\[\begin{equation} \begin{cases} \overline{S_{t+1}^{CO_2}} = \overline{ E_t^{CO_2}} + (1 - \delta) \times \overline{S^{CO_2}_{t}}\\ \overline{S_{t+1}^{SO_x}} = \overline{ E_t^{SO_x} }+ (1 - \delta) \times \overline{S^{SO_x}_{t}}\\ \end{cases} \end{equation}\]

## 4.4 Enviromental Damages

we consider a relatively small pollutant damage parameter\(\gamma_D = 1.5\) and approximate the global damages generated by the industry from the accumulation of pollution stock \(D_t (S_t )\) as: \[\begin{equation} \begin{cases} {D_{t}^{CO_2}} = \frac{\gamma_D}{2} \bigg(S_t^{CO_2}\bigg)^2 \\ {D_{t}^{SO_x}} = \frac{\gamma_D}{2} \bigg(S_t^{SO_x}\bigg)^2 \\ \end{cases} \end{equation}\]

## 4.8 Selected market structures for coalition analysis

Business Case | Firm 1 | Firm 2 | Firm 3 |
---|---|---|---|

\(1\) | \(s_1 = 90\%\) | \(s_2 = 5\%\) | \(s_3 =5\%\) |

\(2\) | \(s_1 =80\%\) | \(s_2 = 10\%\) | \(s_3 =10\%\) |

\(3\) | \(s_1 =70\%\) | \(s_2 =15\%\) | \(s_3 =15\%\) |

\(4\) | \(s_1 =60\%\) | \(s_2 =20\%\) | \(s_3 =20 \%\) |

\(5\) | \(s_1 =33\%\) | \(s_2 =33\%\) | \(s_3 =33\%\) |

The motivation;

proxy china case : big market share + high abatement cost + high pollutant

energy producing countries: low market share + high abatement cost + high pollutant

## 4.9 fleet size and market demand and occupancy % ???

Add more stuff analysing the # of vessels that were deployed and how much of these were full vs not full might expand the analsys to 5 % increase -later add the TEU on the x axis as well as the market share impact of higher fuel prices on vessel speeds, and emissions and the size of the fleet as demand grows …. also add 90 % and 100 to the analysi s just add the results to final data seprately probably fir firm 3 it was better go fast bite the cost of fuel than to add in another vessel to the fleet the # of vessels would allow to explain the calculation and remove any ambiguities … remove the second axis from the carbon analysis not worth it

**switch the bullet type on the NPV, if i want to keep in the same graph …**

graphical analysis 1. 3d graphs at the period level ; ?? x = market share, y = emissins / # vessel , z = period how full the vessel was ?