Skip to main content
SpringerLink
Log in

Social optimality in the constructed-capital model

  • Original Paper
  • Published:
Central European Journal of Operations Research Aims and scope Submit manuscript

Abstract

In the constructed-capital model, the steady state is derived under the assumption that each individual behaves optimally. Contrasting to this decentralized approach, in this paper we derive the first-best outcome a central planner would choose. The results show that agglomeration is socially not optimal, irrespective of the level of trade barriers. Furthermore, the differences in the explicit solutions of both approaches are highlighted.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

Notes

  1. For other contributions considering public expenditures in the New Economic Geography literature we refer to Trionfetti (1997, 2001), Martin and Rogers (1995) and Brakman et al. (2008). Some empirical evidence can be found in Brülhart and Trionfetti (2004).

  2. Therefore capital is a production factor for the manufacturing sector as it determines the number of different machines (equivalent to the number of different products). The number of product varieties depends on the capital stock. However, the amount of each product variety does not depend on the capital.

  3. Trade costs are assumed to be equal for both regions. However, the model allows to generalize this assumption straightforwardly.

  4. A stable population is characterized by constant mortality and fertility rates over time. This implies that the demographic structure does not change.

  5. Note that this implies that the social planner treats each individual in the same way. Therefore a region with a higher population has a higher weight in the social welfare function.

  6. Due to concavity of the Hamiltonian with respect to the states also second-order conditions are fulfilled. As long as the states are positive that concavity is strict.

  7. The time points when a state touches, enters or exits the constraint.

  8. \(\tau ^{+}\) and \(\tau ^{-}\) denote the limit from the right and the left respectively.

  9. A complete list of all possible parameter ranges is provided in Appendix A in Wrzaczek (2010).

  10. For each parameter we have chosen very small steps within the possible parameter interval.

  11. Note that the difference in labor efficiency is due to differences in the demographic structure of the population. The productivity of individuals depends e.g. on age and on their health. However, the demographic structure is not modeled explicitely in our model and assumed as exogenous.

  12. Note that \(\dot{\lambda }^{H} =0\) if \(\dot{K}^{H} =0\), which is fulfilled.

  13. \(L^{H}=L^{F}=1,\,N^{H}=N^{F}=1,\,\rho =0.015,\,\delta =0.05,\,\xi =0.3,\,\sigma =2,\,\varGamma =2,\,\alpha =1,\,\beta =1,\,\varphi =2\)

  14. For clarification once again: \(\hat{K}^{d}\) denotes the equilibrium capital of the decentralized Baldwin model in the symmetric equilibrium, \(\hat{K}^{H}\) and \(\hat{K}^{F}\) denote the equilibrium capital of the centralized model of the home and the foreign country respectively.

  15. Note that this argument is not valid in Baldwin (1999), as it assumes an arbitrary number (e.g. one) of individuals who live forever. For a decentralized model with finitely living individuals we refer to the more sophisticated model proposed in Grafeneder-Weissteiner and Prettner (2008).

References

  • Baldwin RE (1999) Agglomeration and endogenous capital. Eur Econ Rev 43:253–280

    Article  Google Scholar 

  • Baldwin RE, Forslid R, Martin P, Ottaviano G, Robert-Nicoud F (2003) Economic geography & public policy. Princeton University Press, Princeton

    Google Scholar 

  • Barro RJ, Sala-i-Martin X (1998) Economic growth. MIT Press, Cambridge

    Google Scholar 

  • Brakman S, Garretsen H, van Marrewijk C (2008) Agglomeration and government spending. In: Brakman S, Garretsen H (eds) Foreign direct investment and the multinational enterprise. MIT Press, Cambridge, pp 89–116

    Chapter  Google Scholar 

  • Brülhart M, Trionfetti F (2004) Public expenditure, specialisation and agglomeration. Eur Econ Rev 48: 851–871

    Article  Google Scholar 

  • Commendatore P, Kubin I, Petraglia C (2008) Productive public expenditure in a new economic geography model. Int Econ 114:133–160

    Google Scholar 

  • Grafeneder-Weissteiner T, Prettner K (2008) Agglomeration and population aging in a two region model of exogenous growth. WU Vienna University of Economics and Business, Department of Economics Working Papers

  • Feichtinger F, Hartl R (1986) Optimale Kontrolle ökonomischer Prozesse. Anwendungen des Maximumprinzips in den Wirtschaftswissenschaften. Walter de Gruyter, Berlin

    Book  Google Scholar 

  • Krugman P (1991) Increasing returns and economic geography. J Polit Econ 99:483–499

    Article  Google Scholar 

  • Krugman P, Venables AJ (1995) Globalization and the inequality of nations. Q J Econ 110:857–880

    Article  Google Scholar 

  • Marshall A (1920) Principles of economics. MacMillan, London

    Google Scholar 

  • Martin P, Ottaviano G (1999) Growing locations: industry location in a model of endogenous growth. Eur Econ Rev 43:281–302

    Article  Google Scholar 

  • Martin P, Rogers CA (1995) Industrial location and public infrastructure. J Int Econ 39:335–51

    Article  Google Scholar 

  • Puga D (1999) The rise and fall of regional inequalities. Eur Econ Rev 43:303–334

    Article  Google Scholar 

  • Smith A (1776) The wealth of nations. Various reprints, e.g. Penguin Books

  • Tafenau E (2008) Can welfare be improved by relocating firms? The case of the constructed capital model. Working Paper No. 64–2008, Faculty of Economics and Business Administration, University of Tartu

  • Trionfetti F (1997) Public expenditure and economic geography. Annales dconomie et de Statistique 47: 101–120

    Google Scholar 

  • Trionfetti F (2001) Public procurement, market integration, and income inequalities. Rev Int Econ 9(1): 29–41

    Google Scholar 

  • Venables AJ (1996) Equilibrium locations of vertically linked industries. Int Econ Rev 37:341–359

    Article  Google Scholar 

  • von Thünen JH (1826) Der isolierte Staat in Beziehung auf Landschaft und Nationalökonomie. F Perthes, Hamburg

    Google Scholar 

  • Wrzaczek S (2010) Social optimality in the constructed-capital model, mathematical methods in economics, Research Unit ORCOS, Vienna University of Technology, Research, Report 2010–2008

Download references

Author information

Authors and Affiliations

  1. Department of Business Studies, University of Vienna, Vienna, Austria

    Stefan Wrzaczek

  2. Vienna University of Technology, Vienna, Austria

    Stefan Wrzaczek

  3. Wittgenstein Center (IIASA, VID/ÖAW, WU), VID/ÖAW, Vienna, Austria

    Stefan Wrzaczek

Authors
  1. Stefan Wrzaczek
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stefan Wrzaczek.

Additional information

This research was financed by the research project “Agglomeration processes in aging societies” funded by the Vienna Science and Technology Fund (WWTF).

I would like to thank Theresa Grafeneder-Weissteiner (University of Vienna), Ingrid Kubin (WU—Vienna University of Economics and Business), Klaus Prettner (University of Göttingen), Alexia Prskawetz (Vienna University of Technology and Wittgenstein Centre (IIASA, VID/ÖAW, WU), VID/ÖAW), Vladimir Veliov (Vienna University of Technology) and an anonymous referee for helpful comments and fruitful discussions.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wrzaczek, S. Social optimality in the constructed-capital model. Cent Eur J Oper Res 22, 211–232 (2014). https://doi.org/10.1007/s10100-013-0285-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10100-013-0285-8

Keywords

Search

Navigation