Non-sustainable Growth, Resource Extraction, and Boom-Bust Cycles

Abstract

In this chapter, we study the perils of non-sustainable growth, which often take the shape of a boom-bust cycle. These frequently emerge from the high volatility seen in resource production, prices, over-leveraging, and from their impact on macroeconomic stability. The evolution of external debt is often related to short-termism in economic, financial, and policy decision-making. In fact, as resource-rich countries become more globalized, the economy becomes more vulnerable through increased commodity exports and fluctuations in their prices. Inevitably, the traditional simple models of a closed economy had to give way to extended versions which would allow for dynamic and open growth, driven by foreign trade, current and capital accounts, and external finance. We focus on countries that borrowed heavily from abroad and thus became vulnerable to external shocks. When resource prices decline sharply, many developing resource-rich countries experience a debt crisis and face a jump in borrowing costs; this, in turn, may trigger internal real and financial crises. We replicate those scenarios by employing numerical solutions of some model variants and trace out the impact of commodity boom-bust cycles, trade balances, and foreign debt. We emphasize those general features of exhaustible resources and their extraction dynamics since they are also inherited, as it were, by the extraction and use of fossil fuels; these will be dealt with in the next chapter.

Appendix

Following Dasgupta and Heal (1974, p. 10), the current value Hamiltonian with $\omega$ and $\gamma$ as co-state variables of constraints, K and R, respectively, is shown below

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

(3.7)

The necessary optimality conditions for the optimal control are obtained as

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

(3.8)

$$\begin{aligned} \omega Q_{S}&=\gamma \end{aligned}$$

(3.9)

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

(3.10)

$$\begin{aligned} \dot{\gamma }&=\theta \gamma \end{aligned}$$

(3.11)

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

Rearranging gives us $\dot{\omega }=U^{"}(C)\dot{C}$ or $\frac{\dot{\omega }}{\omega }=\frac{U^{"}(C)\dot{C}}{U^{'}(C)}$, and $\frac{\dot{\omega }}{\omega }=\theta -Q_{K}$. Based on these equations, Dasgupta and Heal (1974), pp. 10–11, showed the steps on how to derive the consumption: $\frac{\dot{C}}{C}=\frac{Q_{K}-\theta }{\varepsilon (C)}$ where $\varepsilon (C)=-\frac{CU^{"}(C)}{U^{'}(C)}$.

With $x=K/S$, (Dasgupta and Heal 1974, p. 11) derived the following elasticity of substitution between K and S that is used in the CES production function

$$\begin{aligned} \sigma =-\frac{q^{'}(x)\left( q(x)-xq^{'}(x)\right) }{xq(x)q^{"}(x)}\epsilon \left[ 0,\infty \right] \end{aligned}$$

(3.12)

According to Solow (1973), if the share of K exceeds the share of S in Cobb-Douglas production function, sustained consumption per capita would be a feasible objective. Dasgupta and Heal (1974, pp. 14–19), analyzed the case when $S=0$ with different values of $\sigma$ and showed that only in the cases when $\sigma =1$ and $\sigma <1$, non-renewable resource’s role in production becomes essential.