$\bf{SCOD: Social \ Cost \ of \ Orbital \ Debris}$

This is an accompanion app to the paper "On the Social Cost of Orbital Debris" by A. Bongers and J. L. Torres. This app is intended to be used to carry out a complete sensitivity analysis for all parameters of the IAM model developed to estimate the social cost of orbital debris (SCOD).

The IAM is solved for a centralized economy where the central planner maximizes social welfare by internalizing the social cost of the negative externality produced by orbital debris. The problem to be solved is:

$\max_{{c}_{t=0}^\infty} \sum_{t=0}^\infty \left(\frac{1}{1+\rho}\right)^tU(\hat{c}_t,N_t)$

where

$U(\hat{c}_t,N_t)= \frac{\hat{c}_t^{1-\sigma}-1}{1-\sigma} \times N_t$

subject to,

$c_t+i_t+h_t=y_t$

$k_{t+1}=(1-\delta_k) k_t + i_t $

$s_{t+1}=(1-\delta_s) s_t + q_th_t-x_t$

$y_t=a_t k_t^{\alpha_1}s_t^{\alpha_2}N_t^{1-\alpha_1-\alpha_2}$

$N_{t+1}=N_t \left(\frac{N^*}{N_t}\right)^\nu$

$a_{t+1}=a_t exp(g_{a,0}exp(-\delta_at))$

$q_{t+1}=q_t exp(g_{q,0}exp(-\delta_qt))$

$D_{t+1}= (1-\delta_d) D_t +Z_t$

$Z_t= \omega L_t + \gamma X_t$

$L_t=\frac{\mu q_t h_t}{\eta}$

$X_t=\theta D_t S_t$

$S_t=\mu s_t$

The Social Cost of Orbital Debris (SCOD) is defined as:

$SCOD_t=-\frac{\lambda_{Z,t}}{\lambda_{c,t}}$

where

$\lambda_{c,t}= \left(\frac{1}{1+\rho}\right)^t \hat{c}_t^{-\sigma}$

and

$\lambda_{Z,t}=\frac{1}{\frac{\mu \omega}{\eta}-\frac{1}{1-\delta_d+\gamma\mu \theta s_{t+1}+\frac{\mu \omega}{\eta}\theta s_{t+1}} \left[\frac{\mu \omega}{\eta}(1-\delta_s-\theta D_{t+1})-\gamma\mu\theta D_{t+1}\right]} \nonumber \\ \Biggl[\frac{\left(\frac{1}{1+\rho}\right)^t\hat{c}_{t}^{-\sigma}}{q_t}-\left(\frac{1}{1+\rho}\right)^{t+1} \hat{c}_{t+1}^{-\sigma}\alpha_2 \frac{y_{t+1}}{s_{t+1}} -\left[\frac{\left(\frac{1}{1+\rho}\right)^{t+1}\hat{c}_{t+1}^{-\sigma}}{q_{t+1}}\right](1-\delta_s-\theta D_{t+1})$ $+\frac{1}{1-\delta_d+\gamma\mu \theta s_{t+1}+\frac{\mu \omega}{\eta}\theta s_{t+1}}\frac{\left(\frac{1}{1+\rho}\right)^{t+1}\hat{c}_{t+1}^{-\sigma}}{q_{t+1}}\theta s_{t+1}\left[\frac{\mu \omega}{\eta}(1-\delta_s-\theta D_{t+1})-\gamma\mu\theta D_{t+1}\right]\Biggr]$

The parameters of the model have been divided in four groups:

• Preference parameters
• Technological parameters
• Exogenous growth parameters
• Orbital debris parameters

The default value for each parameter corresponds to the baseline calibration in the paper. Values for the different parameters can be changed inside the specified range. Then press the "Solve model" button to obtain the solution of the model. Results "Output" are presented as plots of the main variables. Results from simulations can be saved using the "Scenario menu" (up to the right).