Fossil Fuel Resource Depletion, Backstop Technology, and Renewable Energy

Abstract

In this chapter we will lay out how economic analysts became aware of the increasing side effects of the use of fossil fuel-based energy and the potential for disasters that could arise therefrom.

Appendix

We present the current value Hamiltonian, for the infinite horizon, with $\omega$ and $\gamma$ as co-state variables or shadow prices of capital accumulation and accumulated resource constraints, respectively:

$$\begin{aligned} H=U(C)+\omega \left( Q(K,S)-C-\delta K-H(m)S\right) +\gamma (S) \end{aligned}$$

(6.5)

with $Y=Q(K,S)=K^{\beta }S^{1-\beta }$. The necessary optimality conditions are obtained as

$$\begin{aligned} U^{\prime }(C)&=\omega \end{aligned}$$

(6.6)

$$\begin{aligned} \omega \left( Q_{S}-H(m)\right)&=- \gamma \end{aligned}$$

(6.7)

$$\begin{aligned} \dot{\omega }&=\omega (\theta -Q_{K}+\delta )\end{aligned}$$

(6.8)

$$\begin{aligned} \dot{\gamma }&=\gamma \theta +\omega H^{\prime }(m)S \end{aligned}$$

(6.9)

with $Q_{S}=\partial Q(K,S)/\partial S$ and $Q_{K}=\partial Q(K,S)/\partial K$.

Dasgupta and Heal (1974, pp. 10–11) showed the steps on how to derive the path for the consumption: $\dot{C}/C{=}(Q_{K}-\theta -\delta ) / (\varepsilon (C)$ where $\varepsilon (C)=-CU^{"}(C)/U^{'}(C)$.