stage various changes that I don't really rember before getting back into things.

Code/2Firm_vfi.jl

@@ -0,0 +1,58 @@
+#=
+The purpose of this is to set up a 2-firm, finite, dynamic orbit use model.
+
+# TODO LIST
+ - [ ] Set up loss functions
+ - [ ] Set up utility functions
+ - [ ] Set up State×Choice → Utility matrix
+ - [ ] Set up VFI
+ - [ ] Run it
+ - [ ] ?
+ - [ ] Profit!!!!
+=#
+
+#=
+Model Description
+
+V({sʲₜ}, Dₜ) = max{xⁱ} U(sⁱₜ) - F(xⁱ) + β V({sʲₜ₊₁}, Dₜ₊₁)
+
+Utility Function: Similar to Rao Rondina
+U(s) = ηs - ρ
+
+Laws of motion
+sʲₜ₊₁ = (1-l({sʲₜ},Dₜ))sʲₜ + xʲₜ
+Dₜ₊₁ = (1-δ)Dₜ + g(Dₜ) + γ⋅ ∑ⱼ sʲₜ⋅l({sʲₜ},Dₜ) + Γ⋅∑ xʲₜ
+
+Loss Function: Similar to Rao Rondina
+lⁱ({sʲₜ},Dₜ) = 1-exp(  -α₁⋅∑{i≠j}sʲₜ - α₂⋅sʲₜ - α₃⋅Dₜ  )
+
+Autofragmentation Function: See Rao Rondina for a description (pg48)
+g(Dₜ) = ζ⋅Dₜ⋅(1-exp(-α₄⋅Dₜ))
+
+Launch Costs
+F(xⁱ) = F⋅xⁱ
+
+=#
+
+#Setup Model Constants
+const α1 = 1e-2
+const α2 = 1e-2
+const α3 = 1e-2
+const α4 = 1e-2
+const ζ = 3
+const δ = 2e-2
+const F = 5
+const γ = 10
+const Γ = 2
+
+#=
+Potential Structs
+
+Maybe a view onto the state space?
+With methods which show own and other sizes as vectors?
+=#
+
+#Loss Function
+function loss(constellation_sizes::Vector{<:Int},debris::Float64,owner::Int)
+    1-exp(-α1*sum(constellation_sizes) + (α1-α2)*constellation_sizes[owner] - α3*debris)
+end

CurrentWriting/sections/03_SurvivalAnalysis.tex

@@ -31,8 +31,8 @@ The marginal survival rates when a given constellation $i$ changes size are:
     =& \sum_{i=1}^N \left[ \frac{R_i}{S_t} \right] - \frac{R}{S_t}
             +\sum_{i=1}^N \frac{ s^i_t}{ S_t} \parder{R_i}{s^i_t}{} \label{EQ:i}
 \end{align}
-Note that $ \sum_{i=1}^N \frac{ s^i_t}{ S_t} \parder{R_i}{s^i_t}{}$ is the weighted, average marginal survival rate-
+Note that $ \sum_{i=1}^N \frac{ s^i_t}{ S_t} \parder{R_i}{s^i_t}{}$ is the weighted, average marginal survival
-across constellation operators.
+rate across constellation operators.
 The derivation of \cref{EQ:i} is in Appendix \ref{APX:Derivations:SurvivalRates}.
 Direct comparison between the marginal survival rates of an individual operator and the social planner's fleet
 cannot proceed further without specifying the functional loss forms $l^i(\cdot)$