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Firms, technology, training and government fiscal policies: An evolutionary approach
Environmental degradation and indeterminacy of equilibrium selection
1. | Department of Economic and Business Sciences, University of Sassari, Sassari, Italy |
2. | Department of Statistics, Informatics and Applications, University of Florence, Italy |
3. | INdAM (National Institute of High Mathematics), Group of Analysis and Probability, Rome, Italy |
4. | Department of Law, University of Naples, Federico II, Naples, Italy |
5. | Department of Finance, Faculty of Economics, Technical University of Ostrava, Ostrava, Czech Republic |
This paper analyzes an intertemporal optimization problem in which agents derive utility from three goods: leisure, a public environmental good and the consumption of a produced good. The global analysis of the dynamic system generated by the optimization problem shows that global indeterminacy may arise: given the initial values of the state variables, the economy may converge to different steady states, by choosing different initial values of the control variable.
References:
[1] |
A. Antoci, M. Galeotti and P. Russu,
Poverty trap and global indeterminacy in a growth model with open-access natural resources, Journal of Economic Theory, 146 (2011), 569-591.
doi: 10.1016/j.jet.2010.12.003. |
[2] |
A. Antoci and S. Borghesi,
Preserving or escaping? On the welfare effects of environmental self-protective choices, Journal of Socio-Economics, 41 (2012), 248-254.
|
[3] |
A. Antoci, L. Gori, M. Sodini and E. Ticci,
Maladaptation and global indeterminacy, Environment and Development Economics, 24 (2019), 643-659.
|
[4] |
A. Antoci, S. Borghesi, M. Galeotti and P. Russu, Living in an uncertain world: Environment substitution, local and global indeterminacy, Journal of Economic Dynamics and Control, 126 (2021), 103929.
doi: 10.1016/j.jedc.2020.103929. |
[5] |
G. Bella, P. Mattana and B. Venturi,
Shilnikov chaos in the Lucas model of endogenous growth, Journal of Economic Theory, 172 (2017), 451-477.
doi: 10.1016/j.jet.2017.09.010. |
[6] |
G. Bella and P. Mattana,
Global indeterminacy and equilibrium selection in a model with depletion of non-renewable resources, Decisions Economics Finance, 41 (2018), 187-202.
doi: 10.1007/s10203-018-0218-z. |
[7] |
J. Benhabib and R. E. Farmer, Indeterminacy and sunspots in macroeconomics, in Handbook of Macroeconomics, North-Holland, Amsterdam, (1999), 387–448. |
[8] |
A. Caravaggio and M. Sodini,
Nonlinear dynamics in coevolution of economic and environmental systems, Frontiers in Applied Mathematics and Statistics, 4 (2018), 1-17.
|
[9] |
O. A. Carboni and P. Russu,
Linear production function, externalities and indeterminacy in a capital-resource growth model, Journal of Mathematical Economics, 49 (2013), 422-428.
doi: 10.1016/j.jmateco.2013.04.002. |
[10] |
E. Fernández, R. Pérez and J. Ruiz,
The environmental Kuznets curve and equilibrium indeterminacy, Journal of Economic Dynamics and Control, 36 (2012), 1700-1717.
doi: 10.1016/j.jedc.2012.05.004. |
[11] |
J. M. Hartwick,
Intergenerational equity and the investing of rents from exhaustible resources, The American Economic Review, 67 (1977), 972-974.
|
[12] |
J. M. Hartwick,
Substitution among exhaustible resources and intergenerational equity, The Review of Economic Studies, 45 (1978), 347-354.
doi: 10.2307/2297349. |
[13] |
P. Krugman,
History versus expectations, Quarterly Journal of Economics, 106 (1991), 651-667.
|
[14] |
P. Mattana, K. Nishimura and T. Shigoka,
Homoclinic bifurcation and global indeterminacy of equilibrium in a two-sector endogenous growth model, International Journal of Economic Theory, 5 (2009), 25-47.
|
[15] |
K. Mino, Growth and Business Cycles with Equilibrium Indeterminacy, Advances in Japanese Business and Economics, Springer, Tokyo Japan, 2017. |
[16] |
P. Russu,
Mathematical analysis of an economic growth model with perfect-substitution technologies, Nonlinear Analysis: Modelling and Control, 25 (2020), 84-107.
doi: 10.15388/namc.2020.25.15733. |
[17] |
S. P. Sethi,
Nearest feasible paths in optimal control problems: Theory, examples and counterexamples, Journal of Optimization Theory and Applications, 23 (1977), 563-579.
doi: 10.1007/BF00933297. |
[18] |
A. Skiba,
Optimal growth with a convex-concave production function, Econometrica, 46 (1978), 527-540.
doi: 10.2307/1914229. |
[19] |
R. M. Solow, Intergenerational equity and exhaustible resources, Review of Economic Studies: Symposium of the Economics of Exhaustible Resources, (1974), 29–46. |
[20] |
R. M. Solow,
On the intergenerational allocation of natural resources, Scandinavian Journal of Economics, 88 (1986), 141-9.
|
[21] |
R. M. Solow,
An almost practical step towards sustainability, Resources Policy, 16 (1993), 162-72.
|
[22] |
F. Wirl,
Stability and limit cycles in one-dimensional dynamic optimizations of competitive agents with a market externality, Journal of Evolutionary Economics, 7 (1997), 73-89.
|
[23] |
A. Yanase,
Impatience, pollution, and indeterminacy, Journal of Economic Dynamics and Control, 35 (2011), 1789-1799.
doi: 10.1016/j.jedc.2011.06.010. |
show all references
References:
[1] |
A. Antoci, M. Galeotti and P. Russu,
Poverty trap and global indeterminacy in a growth model with open-access natural resources, Journal of Economic Theory, 146 (2011), 569-591.
doi: 10.1016/j.jet.2010.12.003. |
[2] |
A. Antoci and S. Borghesi,
Preserving or escaping? On the welfare effects of environmental self-protective choices, Journal of Socio-Economics, 41 (2012), 248-254.
|
[3] |
A. Antoci, L. Gori, M. Sodini and E. Ticci,
Maladaptation and global indeterminacy, Environment and Development Economics, 24 (2019), 643-659.
|
[4] |
A. Antoci, S. Borghesi, M. Galeotti and P. Russu, Living in an uncertain world: Environment substitution, local and global indeterminacy, Journal of Economic Dynamics and Control, 126 (2021), 103929.
doi: 10.1016/j.jedc.2020.103929. |
[5] |
G. Bella, P. Mattana and B. Venturi,
Shilnikov chaos in the Lucas model of endogenous growth, Journal of Economic Theory, 172 (2017), 451-477.
doi: 10.1016/j.jet.2017.09.010. |
[6] |
G. Bella and P. Mattana,
Global indeterminacy and equilibrium selection in a model with depletion of non-renewable resources, Decisions Economics Finance, 41 (2018), 187-202.
doi: 10.1007/s10203-018-0218-z. |
[7] |
J. Benhabib and R. E. Farmer, Indeterminacy and sunspots in macroeconomics, in Handbook of Macroeconomics, North-Holland, Amsterdam, (1999), 387–448. |
[8] |
A. Caravaggio and M. Sodini,
Nonlinear dynamics in coevolution of economic and environmental systems, Frontiers in Applied Mathematics and Statistics, 4 (2018), 1-17.
|
[9] |
O. A. Carboni and P. Russu,
Linear production function, externalities and indeterminacy in a capital-resource growth model, Journal of Mathematical Economics, 49 (2013), 422-428.
doi: 10.1016/j.jmateco.2013.04.002. |
[10] |
E. Fernández, R. Pérez and J. Ruiz,
The environmental Kuznets curve and equilibrium indeterminacy, Journal of Economic Dynamics and Control, 36 (2012), 1700-1717.
doi: 10.1016/j.jedc.2012.05.004. |
[11] |
J. M. Hartwick,
Intergenerational equity and the investing of rents from exhaustible resources, The American Economic Review, 67 (1977), 972-974.
|
[12] |
J. M. Hartwick,
Substitution among exhaustible resources and intergenerational equity, The Review of Economic Studies, 45 (1978), 347-354.
doi: 10.2307/2297349. |
[13] |
P. Krugman,
History versus expectations, Quarterly Journal of Economics, 106 (1991), 651-667.
|
[14] |
P. Mattana, K. Nishimura and T. Shigoka,
Homoclinic bifurcation and global indeterminacy of equilibrium in a two-sector endogenous growth model, International Journal of Economic Theory, 5 (2009), 25-47.
|
[15] |
K. Mino, Growth and Business Cycles with Equilibrium Indeterminacy, Advances in Japanese Business and Economics, Springer, Tokyo Japan, 2017. |
[16] |
P. Russu,
Mathematical analysis of an economic growth model with perfect-substitution technologies, Nonlinear Analysis: Modelling and Control, 25 (2020), 84-107.
doi: 10.15388/namc.2020.25.15733. |
[17] |
S. P. Sethi,
Nearest feasible paths in optimal control problems: Theory, examples and counterexamples, Journal of Optimization Theory and Applications, 23 (1977), 563-579.
doi: 10.1007/BF00933297. |
[18] |
A. Skiba,
Optimal growth with a convex-concave production function, Econometrica, 46 (1978), 527-540.
doi: 10.2307/1914229. |
[19] |
R. M. Solow, Intergenerational equity and exhaustible resources, Review of Economic Studies: Symposium of the Economics of Exhaustible Resources, (1974), 29–46. |
[20] |
R. M. Solow,
On the intergenerational allocation of natural resources, Scandinavian Journal of Economics, 88 (1986), 141-9.
|
[21] |
R. M. Solow,
An almost practical step towards sustainability, Resources Policy, 16 (1993), 162-72.
|
[22] |
F. Wirl,
Stability and limit cycles in one-dimensional dynamic optimizations of competitive agents with a market externality, Journal of Evolutionary Economics, 7 (1997), 73-89.
|
[23] |
A. Yanase,
Impatience, pollution, and indeterminacy, Journal of Economic Dynamics and Control, 35 (2011), 1789-1799.
doi: 10.1016/j.jedc.2011.06.010. |




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