# Sustainable consumption and economic growth

**Human exploitation of the Earth’s resources is fast approaching planetary boundaries, and the closer we get, the greater the effects on human wellbeing. To aid the transition to a more sustainable path, the IIASA Advanced Systems Analysis Program is developing economic growth models, which inform green growth solutions. **

New economic models, now urgently needed, must take into consideration inherent uncertainties and nonlinear effects that change over time. In the search for green growth solutions, IIASA researchers and collaborators have furthered the theory of optimal control for infinite-horizon problems, addressing classes of problems that are typical for economic applications, in which traditional methods fail to deliver rigorous solutions [1][2].

The researchers examined some classes of optimal control problems, which are subject to the Pontryagin maximum principle, working to generalize them over infinite time horizons with unbounded controls [1]. They were able to derive sufficient conditions for the existence of an optimal control, as well as conditions guaranteeing the uniform local boundedness of optimal controls in a general, nonlinear case. In a further study, the team derived the necessary first-order optimality conditions of Pontryagin’s type for a general class of discrete-time optimal control problems on an infinite horizon.

To explore how renewable resources can be exploited sustainably, IIASA researchers considered a model of a logistically growing renewable resource. By applying the optimal control theory, they found that a consumption-based utility can increase or stay constant with the resource stock asymptotically non-vanishing only when the resource growth rate is higher than the difference between the discount factor and the technology growth rate adjusted to the elasticity of the production with respect to the resource [3].

To investigate the trade-off between consumption today and investment in the future, given the limited available natural resources, IIASA researchers used the Dasgupta-Heal-Solow-Stiglitz model. They showed that an optimal admissible policy may not exist if the output elasticity of the resource equals 1. In this case, an optimal solution does not exist for a sufficiently small initial stock of produced capital. This implies that it is impossible to formulate a welfare-maximizing policy at an early stage of economic development when produced capital is scarce and resources are abundant. An initial jump to the minimal stock of produced capital is therefore needed, followed by an optimal policy. The researchers characterized the optimal policies by applying a version of the Pontryagin maximum principle for infinite-horizon optimal control problems [4].

IIASA researchers also examined the effects of land ownership structures on population growth. Using a family-optimization model, where relative per capita wealth generates social status and wellbeing, they demonstrated that tenant farming is a major obstacle to escaping the Malthusian trap—a situation where technological advances that increase society’s supply of resources do not lead to an increase in standards of living because the population simply grows faster in response. Land ownership reform provides farmers with higher returns for their investments, encouraging them to increase their productivity and status rather than their family size. Consequently, the population growth rate slows down, and the productivity of land increases [5].

Population growth can also be influenced by efforts to shift production away from polluting industries, a new study found. IIASA researchers modeled an economy where output is produced by two sectors, dirty and clean. An air pollution emissions tax curbs dirty production, which decreases pollution-induced mortality and shifts resources to the clean sector. If the dirty sector is more capital intensive (i.e., requiring a lot of physical capital—such as machines or other equipment—but not so much labor) the results show that this shift increases labor demand and wages. This, in turn, means that rearing a child is more costly because of the wages one would lose (known as the opportunity cost); this therefore decreases fertility and hence the population size. Correspondingly, if the clean sector is more capital intensive, then the emission tax decreases wages and increases fertility. Although the proportion of production from the dirty sector falls, the expansion of population boosts total pollution, aggravating environmental mortality [6].

### References

[1] Aseev SM (2016). Existence of an optimal control in infinite-horizon problems with unbounded set of control constraints. *Trudy Instituta Matematiki i Mekhaniki UrO RAN* 22 (2): 18-27.

[2] Aseev SM, Krastanov MI, & Veliov VM (2016). *Optimality Conditions for Discrete-Time Optimal Control on Infinite Horizon**. *Research Unit ORCOS, Vienna University of Technology, Vienna, Austria.

[3] Aseev S & Manzoor T (2016). Optimal Growth, Renewable Resources and Sustainability. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-16-017

[4] Aseev S, Besov K, & Kaniovski S (2016). The Optimal Use of Exhaustible Resources Under Non-constant Returns to Scale. Österreichisches Institut für Wirtschaftsforschung, Vienna, Austria.

[5] Lehmijoki U & Palokangas T (2016). Land reforms and population growth. *Portuguese Economic Journal *15 (1): 1-15.

[6] Lehmijoki U & Palokangas T (2016). *Fertility, Mortality and Environmental Policy*. IZA DP No. 10465. IZA Institute of Labor Economics, Bonn, Germany.

### Collaborators

- Steklov Institute of Mathematics, Russian Academy of Sciences, Russia
- University of Sofia, Bulgaria
- Technical University of Vienna, Austria
- Lahore University of Management Sciences, Pakistan
- Austrian Institute of Economic Research, Austria
- University of Helsinki, Finland