Skip to main content
SpringerLink
Log in

The applications of control theory to economics

  • Economic Systems
  • Conference paper
  • First Online:
Analysis and Optimization of Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 28))

Abstract

Control theory has been applied to various problems of economics, specifically to problems of allocating resources over time. Four specific problems of this type have been presented. In three of them — those for optimal economic growth (involving the allocation between consumption and capital formation for the aggregate economy), for science policy (involving the allocation of scientists between teaching and research), and for military strategy (involving the allocation of missiles between different rates of fire and different targets) — the solutions for the optimal trajectories involve a shadow price interpretation of the costate variables. In the fourth problem, that of planning, five theorems on planning were presented, with uncertainty and the costs of planning determining the optimal horizon and period of the plan.

There have, in fact, been many other applications of control theory in economics. At the macroeconomic level control theory has been used to study problems of economic stabilization and regulation, fiscal and monetary policy, international borrowing, and the allocation of investment among different sectors of the economy. At the microeconomic level control theory has been used to study the employment decisions of an individual worker; the savings decisions of an individual consumer; and the production, sales, inventory, investment, employment, and financing decision of an individual firm, all of which entail decisions over time.

Control theory has been established as one of the principal working tools of economists, and these tools have been and will continue to be extremely valuable in analyzing many important problems involving the allocation of scarce resources over time.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Arrow, K. J. (1951), Social Choice and Individual Values, New York: John Wiley & Sons, Inc. (Second Edition, 1963).

    Google Scholar 

  • __ (1968), "Applications of Control Theory to Economic Growth" in Lectures in Applied Mathematics, Vol. 12 (Mathematics of the Decision Sciences — Part 2), Providence R.I.: American Mathematical Society.

    Google Scholar 

  • __ (1970), Essays in the Theory of Risk Bearing, Amsterdam: North-Holland Publishing Co.

    Google Scholar 

  • __ and F. Hahn (1971), General Competitive Analysis, San Francisco: Holden-Day, Inc.

    Google Scholar 

  • __ and M. Intriligator, Eds. (1981/82) Handbook of Mathematical Economics, Vols. I, II, III, Amsterdam: North-Holland Publishing Co.

    Google Scholar 

  • Bellman, R. (1957), Dynamic Programming, New York: John Wiley & Sons, Inc.

    Google Scholar 

  • Bolt, R.H., W.L. Koltun, and O.H. Levine (1965), "Doctoral Feedback Into Higher Education," Science, 148: 918–28.

    Google Scholar 

  • Cass, D. (1965), "Optimum Growth in an Aggregative Model of Capital Accumulation," Review of Economic Studies, 32: 233–40.

    Google Scholar 

  • __ (1966), "Optimum Growth in an Aggregative Model of Capital Accumulation: A Turnpike Theorem," Econometrica, 34: 833–50.

    Google Scholar 

  • __ and K. Shell, Eds. (1976), The Hamiltonian Approach to Dynamic Economics, New York: Academic Press.

    Google Scholar 

  • Chipman, J.S., L. Hurwicz, M.K. Richter, and H. Sonnenschein, Eds. (1971), Preferences, Utility, and Demand, New York: Harcourt, Brace, Jovanovich.

    Google Scholar 

  • Chow, G. (1975), Analysis and Control of Dynamic Systems, New York: John Wiley & Sons, Inc.

    Google Scholar 

  • Cournot, A. (1838), Recherches sur les principes mathématiques de la théorie des richesses, Paris: M. Rivière & cie., translated as Researches Into the Mathematical Principles of the Theory of Wealth, 1929, New York: Macmillan.

    Google Scholar 

  • Debreu, G. (1959), Theory of Value, New York: John Wiley & Sons, Inc.

    Google Scholar 

  • Deleau, M. and P. Malgrange (1974), "Information and Contrastochastic Dynamic Economic Policies," European Economic Review 5: 159–75.

    Google Scholar 

  • __ (1977), "Recent Trends in French Planning" in Intriligator, Ed. (1977).

    Google Scholar 

  • Dorfman, R., P.A. Samuelson, and R.M. Solow (1958), Linear Programming and Economic Analysis, New York: McGraw-Hill Book Co.

    Google Scholar 

  • Fuss, M., and D. McFadden, Eds. (1980), Production Economics: A Dual Approach to Theory and Application, Amsterdam: North-Holland Publishing Co.

    Google Scholar 

  • Gale, D. (1960), The Theory of Linear Economic Models, New York: McGraw-Hill Book Co.

    Google Scholar 

  • Heal, G.M. (1973), The Theory of Economic Planning, Amsterdam: North-Holland Publishing Co.

    Google Scholar 

  • Hestenes, M.R. (1966), Calculus of Variations and Optimal Control Theory, New York: John Wiley & Sons, Inc.

    Google Scholar 

  • Hickman, B., Ed. (1965), Quantitative Planning of Economic Policy, Washington, D.C.: The Brookings Institution.

    Google Scholar 

  • Hicks, J.R. (1946), Value and Capital, Second Edition, New York: Oxford University Press.

    Google Scholar 

  • Hildenbrand, W. (1974), Core and Equilibria of a Large Economy, Princeton: Princeton University Press.

    Google Scholar 

  • __ and A.P. Kirman (1978), Introduction to Equilibrium Analysis, Amsterdam: North-Holland Publishing Co.

    Google Scholar 

  • Intriligator, M.D. (1967), Strategy in a Missile War, Los Angeles: Security Studies Project, UCLA.

    Google Scholar 

  • __ (1971), Mathematical Optimization and Economic Theory, Englewood Cliffs, N.J.: Prentice-Hall, Inc.

    Google Scholar 

  • __, Ed. (1971), Frontiers of Quantitative Economics, Amsterdam: North-Holland Publishing Co.

    Google Scholar 

  • __ (1975a), "Applications of Optimal Control Theory in Economics," Synthese, 31: 271–88.

    Google Scholar 

  • __ (1975b), "Strategic Considerations in the Richardson Model of Arms Races," Journal of Political Economy, 83: 339–53.

    Google Scholar 

  • __, Ed. (1977), Frontiers of Quantitative Economics, Vol. III, Amsterdam: North-Holland Publishing Co.

    Google Scholar 

  • __ (1978), Econometric Models, Techniques, and Applications, Englewood Cliffs and Amsterdam: Prentice-Hall, Inc. and North-Holland Publishing Co.

    Google Scholar 

  • __ and D.A. Kendrick, Eds. (1974), Frontiers of Quantitative Economics, Vol. II, Amsterdam: North-Holland Publishing Co.

    Google Scholar 

  • __(1980), "Toward a Theory of Planning," Paper presented to Econometric Society World Congress, Aix-en-Provence, France.

    Google Scholar 

  • __ and B.L.R. Smith (1966), "Some Aspects of the Allocation of Scientific Effort Between Teaching and Research," American Economic Review, 56: 494–507.

    Google Scholar 

  • Koopmans, T.C., Ed. (1951), Activity Analysis of Production and Allocation, New York: John Wiley & Sons, Inc.

    Google Scholar 

  • __ (1957), Three Essays on the State of Economic Science, New York: McGraw-Hill Book Co.

    Google Scholar 

  • __ (1965), "On the Concept of Optimal Economic Growth," in The Econometric, Approach to Development Planning, Amsterdam: North-Holland Publishing Co.

    Google Scholar 

  • __ (1967), "Objectives, Constraints and Outcomes in Optimal Growth Models," Econometrica, 35: 1–15.

    Google Scholar 

  • Kornai, J. (1967), Mathematical Planning of Structural Decisions, Amsterdam: North-Holland Publishing Co.

    Google Scholar 

  • Lancaster, K. (1968), Mathematical Economics, New York: Macmillan.

    Google Scholar 

  • Morgenstern, O., Ed. (1954), Economic Activity Analysis, New York: John Wiley & Sons, Inc.

    Google Scholar 

  • Nikaido, H. (1968), Convex Structures and Economic Theory, New York: Academic Press.

    Google Scholar 

  • Pontryagin, L.S., V.G. Boltyanskii, R.V. Gamkrelidze, and E.F. Mischenko (1962), The Mathematical Theory of Optimal Processes, translated by K.N. Trigrogoff, New York: Interscience Publishers, John Wiley & Sons, Inc.

    Google Scholar 

  • Ramsey, F.P. (1928), "A Mathematical Theory of Saving," Economic Journal, 38: 543–59.

    Google Scholar 

  • Samuelson, P.A. (1947). Foundations of Economic Analysis, Cambridge: Harvard University Press.

    Google Scholar 

  • __ (1965), "A Catenary Turnpike Theorem Involving Consumption and the Golden Rule," American Economic Review, 55: 486–96.

    Google Scholar 

  • Scarf, H.E. (1973), The Computation of Economic Equilibria, New Haven: Yale University Press.

    Google Scholar 

  • Sen, A.K. (1970), Collective Choice and Social Welfare, San Francisco: Holden-Day, Inc.

    Google Scholar 

  • Shell, K. (1969), "Applications of Pontryagin's Maximum Principle in Economics," in H.W. Kuhn and G.P. Szegö, Eds., Mathematical Systems Theory and Economics, Berlin: Springer-Verlag.

    Google Scholar 

  • __ (Ed.) (1967), Essays on the Theory of Optimal Economic Growth, Cambridge: MIT Press.

    Google Scholar 

  • Takayama, A. (1974), Mathematical Economics, Hinsdale, Illinois: The Dryden Press.

    Google Scholar 

  • Theil, H. (1961), Economic Forecasts and Policy, Second Edition, Amsterdam: North-Holland Publishing Co.

    Google Scholar 

  • __ (1964), Optimal Decision Rules for Government and Industry, Amsterdam: North-Holland Publishing Co.

    Google Scholar 

  • Tinbergen, J. (1952), On the Theory of Economic Policy, Amsterdam: North-Holland Publishing Co.

    Google Scholar 

  • __ (1954), Centralization and Decentralization in Economic Policy, Amsterdam: North-Holland Publishing Co.

    Google Scholar 

  • __ (1964), Central Planning, New Haven: Yale University Press.

    Google Scholar 

  • Walras, L. (1874), Eléments d'économie politique pure, Lausanne: L. Corbaz, English translation by William Jaffé (1954) as Elements of Pure Economics, Homewood, Illinois: Richard D. Irwin.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Economics, University of California, Los Angeles, 90024, Los Angeles, CA, USA

    Michael D. Intriligator

Authors
  1. Michael D. Intriligator
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

A. Bensoussan J. L. Lions

Rights and permissions

Reprints and permissions

Copyright information

© 1980 Springer-Veralg

About this paper

Cite this paper

Intriligator, M.D. (1980). The applications of control theory to economics. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 28. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0004070

Download citation

  • DOI: https://doi.org/10.1007/BFb0004070

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10472-8

  • Online ISBN: 978-3-540-38489-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation