\documentclass[12pt]{article} %%%%%%%%%Packages%%%%%%%%%%%%%%% \usepackage{geometry} \geometry{verbose,tmargin=1in,bmargin=1in,lmargin=1in,rmargin=1in} \setlength{\parskip}{7pt} \setlength{\parindent}{6pt} %\setlength{\parindent}{0pt} \usepackage{setspace} \doublespacing \usepackage{amsmath} \usepackage{mathtools} \usepackage{amsthm} \usepackage{amssymb} \usepackage{thmtools, thm-restate} \usepackage{cleveref} %Add institute to title \usepackage{etoolbox} \makeatletter \providecommand{\institute}[1]{% add institute to \maketitle \apptocmd{\@author}{\end{tabular} \par \begin{tabular}[t]{c} #1}{}{} } \makeatother %%%%%%%%%%%%SETUP THEOREMS%%%%%%%%%%%%%%%%%%%%%% \declaretheorem[within=subsection]{theorem} %%%%%%%%%%%%FORMATTING%%%%%%%%%%%%%%%%%%%%% %Math formatting \newcommand{\bb}[1]{\mathbb{#1}} \newcommand{\parder}[3]{\ensuremath{ \frac{\partial^{#3} #1}{\partial #2~^{#3}}}} \newcommand{\likeli}[2]{\text{L}\left( #1 | #2 \right)} \newcommand{\induction}[3]{ \textbf{#1}\\ \underline{Basis Step:}\\ #2 \underline{Induction Step:}\\ #3 } \newcommand{\mle}[1]{\hat{#1}_{\text{MLE}}} \newcommand{\pr}[1]{\text{Pr}\left( #1 \right)} \newcommand{\thm}[3]{ \begin{restatable}[#1]{theorem}{#2} \label{thm:#2} #3 \end{restatable} } %These are some formatting/reminder commands \newcommand{\todo}[1]{ \textbf{\#TODO: \underline{#1}} } \newcommand{\define}[1]{%for now just highlight, in future, link. \underline{\textbf{#1}} } %%%%%%%%%%%%%%%Math Operators%%%%%%%%%%%%%%%%%% \DeclareMathOperator{\argmax}{argmax} \DeclareMathOperator*{\plim}{plim} \DeclareMathOperator*{\adj}{adj} %%%%%%%%%%%%%%INTERNAL REFERENCES%%%%%%%%%%%%%% \newcommand{\eref}[1]{Eq. \ref{#1}} %Already defined %%%%%%%%%%%%%%Bibliography%%%%%%%%%%%%%%% \usepackage[backend=biber,sorting=none,style=numeric]{biblatex} \addbibresource{References.bib} %%%%% Adjust this at some point. %This is how to perform citations. % Use \cite{ref} to get a numerical reference to the bibliography % Use \citetitle{ref} to get the title as a citation % Use \fullcite{ref} to insert the full reference. % Use \autcite{ref} to get formatted references %%%%%%%%%%%%%%Other commands%%%%%%%%%%%%%% \providecommand{\keywords}[1]{\textbf{\textit{Keywords:}} #1} \providecommand{\jel}[1]{\textbf{\textit{JEL Codes:}} #1} %%%%%%%%%%%%CUSTOMIZATION%%%%%%%%%%%%%%%%%%%%%% \title{Dynamic Launch Decisions for Satellite Constellation Operators} \author{William King} \institute{Washington State University} \begin{document} \maketitle \begin{abstract} Over the last 10 years new technology has make low earth orbits (LEOs) more accessible, and the resulting increase in LEO satellites has increased the risk of collision. Because debris in orbit generates more debris through collisions with objects in orbit and the debris created during launch and operation imposes a negative externality on other operators, optimal use of orbits is believed to not occur under free entry. This paper develops a dynamic model of satellite operation incorporating two effects not considered in previous models. The first effect is complementarity between satellites within the same operator's fleet (called a constellation). The second effect is collision avoidance efficiencies that exist within constellations. The primary result is a theoretical model and the resulting analysis of the difference in survival ratios between constellation operators and society. \end{abstract} \keywords{Orbits, Pollution, Economies of Scale, Externality } \jel{Q29, Q58, L25} \textbf{Acknowledgments:} I am the sole author and have recieved no contributions from others as of yet. This paper has been approved for dual submission in Econs 529 and Econs 594 by the instructors. \end{document}