Economic Theory

, Volume 2, Issue 1, pp 43–68 | Cite as

On characterizing equilibria of economies with externalities and taxes as solutions to optimization problems

  • Timothy J. Kehoe
  • David K. Levine
  • Paul M. Romer
Research Articles


We characterize equilibria of general equilibrium models with externalities and taxes as solutions to optimization problems. This characterization is similar to Negishi's characterization of equilibria of economies without externalities or taxes as solutions to social planning problems. It is often useful for computing equilibria or deriving their properties. Frequently, however, finding the optimization problem that a particular equilibrium solves is difficult. This is especially true in economies with multiple equilibria. In a dynamic economy with externalities or taxes there may be a robust continuum of equilibria even if there is a representative consumer. This indeterminacy of equilibria is closely related to that in overlapping generations economies.


Economic Theory Planning Problem Equilibrium Model General Equilibrium Multiple Equilibrium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Abel, A.B., Blanchard, O.J.: An intertemporal equilibrium model of saving and investment. Econometrica51, 675–92 (1983)Google Scholar
  2. Arrow, K.J.: The economies of learning by doing. Rev. Econ. Stud.29, 155–73 (1962)Google Scholar
  3. Balasko, Y., Shell, K.: The overlapping generations model I: the case of pure exchange without money. J. Econ. Theory23, 281–306 (1980)Google Scholar
  4. Becker, R.A.: Capital income taxation and perfect foresight. J. Publ. Econ.26, 147–67 (1985)Google Scholar
  5. Becker, R.A., Foias, C.: A minimax approach to the implicit programming problem. Econ. Lett.20, 171–5 (1986)Google Scholar
  6. Braun, R.A.: The dynamic interaction of distortionary taxes and aggregate variables in postwar U.S. data. Unpublished manuscript, Carnegie-Mellon University 1988Google Scholar
  7. Brock, W.A.: Some results on the uniqueness of steady states in multisector models of optimum growth when future utilities are discounted. Int. Econ. Rev.14, 535–59 (1973)Google Scholar
  8. Brock, W.A.: A simple perfect foresight monetary model. J. Monet. Econ.1, 133–50 (1975a)Google Scholar
  9. Brock, W.A.: Some results on dynamic integrability. Center for Mathematical Studies in Business and Economics, University of Chicago Report 7551, 1975bGoogle Scholar
  10. Brock, W.A.: A polluted golden age. In: Smith, V.L. (ed.) Economics of natural and environmental resources. New York: Gordon and Breach 1977Google Scholar
  11. Burke, J.L.: Inactive transfer policies and efficiency in general overlapping generations economies. J. Math. Econ.16, 201–22Google Scholar
  12. Chang, F.-R.: The inverse optimal problem: a dynamic programming approach. Econometrica56, 147–72 (1988)Google Scholar
  13. Chang, L.-J.: Corporate taxes, disaggregated capital markets, and business cycles. Unpublished manuscript, Carnegie-Mellon University 1988Google Scholar
  14. Chipman, J.S.: Homothetic preferences and aggregation. J. Econ. Theory8, 26–38 (1974)Google Scholar
  15. Danthine, J.P., Donaldson, J.B.: A note on the effects of capital income taxation on the dynamics of a competitive economy, J. Publ. Econ.28, 255–65 (1986)Google Scholar
  16. Dechert, D.: Optimal control problems from second-order difference equations. J. Econ. Theory19, 50–63 (1978)Google Scholar
  17. Feinstein, C.D., Luenberger, D.G.: Analysis of the asymptotic behavior of optimal control trajectories: the implicit programming problem. SIAM J. Control Optimization19, 561–85 (1981)Google Scholar
  18. Foster, E., Sonnenschein, H.: Price distortions and economic welfare. Econometrica38, 281–97 (1970)Google Scholar
  19. Ginsburgh, V.A., Van der Heyden, L.: On extending the Negishi approach to computing equilibria: the case of government price support policies. J. Econ. Theory44, 168–78 (1988)Google Scholar
  20. Gorman, W.: Community preference fields. Econometrica21, 63–80 (1953)Google Scholar
  21. Hansen, T., Koopmans, T.C.: Definition and computation of a capital stock invariant under optimization. J. Econ. Theory5, 487–523 (1972)Google Scholar
  22. Howitt, P., McAfee, R.P.: Stability of equilibria with externalities. Q. J. Econ.103, 261–277 (1988)Google Scholar
  23. Irwin, M.C.: Smooth dynamical systems. New York: Academic Press 1980Google Scholar
  24. Jones, L.E., Manuelli, R.E.: A convex model of equilibrium growth. Unpublished manuscript, Northwestern University 1990Google Scholar
  25. Judd, K.L.: Useful planning equivalents of taxed economies. Unpublished manuscript, Hoover Institution 1987Google Scholar
  26. Kehoe, T.J.: The comparative statics properties of tax models. Can. J. Econ.18, 314–34 (1985)Google Scholar
  27. Kehoe, T.J., Levine, D.K.: Comparative statics and perfect foresight in infinite-horizon economies. Econometrica53, 433–53 (1985a)Google Scholar
  28. Kehoe, T.J., Levine, D.K.: Empirical implications of complete contingent claims. Unpublished manuscript, UCLA 1985bGoogle Scholar
  29. Kehoe, T.J., Levine, D.K.: The economics of indeterminacy in overlapping generations models. J. Publ. Econ.42, 219–43 (1990)Google Scholar
  30. Kehoe, T.J., Levine, D.K., Romer, P.M.: Determinacy of equilibria in dynamic models with finitely many consumers. J. Econ. Theory50, 1–21 (1990)Google Scholar
  31. Kehoe, T.J., Levine, D.K., Mas-Colell, A., Zame, W.R.: Determinacy of equilibrium in large-square economies. J. Math. Econ.18, 231–62 (1989)Google Scholar
  32. Koopmans, T.C.: A model of a continuing state with scarce capital. In: Bruckmann, G., Weber, W. (eds.) Contributions to the von Neumann growth model. Berlin Heidelberg New York: Springer 1971Google Scholar
  33. Kurtz, M.: Optimal economic growth and wealth effects. Int. Econ. Rev.9, 148–57 (1968)Google Scholar
  34. Kydland, F.E., Prescott, E.C.: Rules rather than discretion: the inconsistency of optimal plans. J. Polit. Econ.85, 473–91 (1977)Google Scholar
  35. Laitner, J.: Transition time paths for overlapping-generations models. J. Econ. Dynam. Control7, 111–29 (1984)Google Scholar
  36. Laitner, J.: Tax changes and phase diagrams for an overlapping-generations model. J. Polit. Econ.98, 193–220 (1990)Google Scholar
  37. Lucas, R.E., Stokey, N.C.: Money and interest in a cash-in-advance economy. Econometrica55, 491–513 (1987)Google Scholar
  38. Manuelli, R.E.: Notes on competitive equilibrium with distortions. Unpublished manuscript, Stanford University 1988Google Scholar
  39. McGrattan, E.R.: The macroeconomic effects of tax policy in an equilibrium model. Unpublished manuscript, Stanford University 1988Google Scholar
  40. Negishi, T.: Welfare economics and existence of equilibrium for a competitive economy. Metroeconomica12, 92–7 (1960)Google Scholar
  41. Romer, P.M.: Increasing returns and long-run growth. J. Polit. Econ.94, 1002–36 (1986)Google Scholar
  42. Romer, P.M.: Capital accumulation in the theory of long run growth. In: Barro, R. (ed.) Modern macroeconomics. Cambridge: Harvard University Press 1988Google Scholar
  43. Scarf, H.E.: The computation of equilibrium prices. In: Arrow, K.J., Intriligator, M.D. (eds.) Handbook of mathematical economics, II. New York: North-Holland 1982Google Scholar
  44. Spear, S.E.: Growth, externalities, and sunspots. Unpublished manuscript, Carnegie-Mellon University 1988Google Scholar
  45. Uzawa, H.: Walras' existence theorem and Brouwer's fixed point theorem. Econ. Stud. Q.13, 59–62 (1962)Google Scholar
  46. Whiteman, C.H.: Linear rational expectations models: a user's guide. Minneapolis: University of Minnesota Press 1983Google Scholar
  47. Woodford, M.: Stationary sunspot equilibria: the case of small fluctuations around a deterministic steady state. Unpublished manuscript, University of Chicago 1986Google Scholar
  48. Woodford, M.: Monetary policy and price level indeterminacy in a cash-in-advance economy. Unpublished manuscript, University of Chicago 1988Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Timothy J. Kehoe
    • 1
    • 2
  • David K. Levine
    • 3
    • 2
  • Paul M. Romer
    • 4
    • 2
  1. 1.Department of EconomicsUniversity of MinnesotaMinneapolisUSA
  2. 2.Research DepartmentFederal Reserve Bank of MinneapolisMinneapolisUSA
  3. 3.Department of EconomicsUniversity of CaliforniaLos AngelesUSA
  4. 4.Department of EconomicsUniversity of CaliforniaBerkeleyUSA

Personalised recommendations