The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Cost Minimization and Utility Maximization

  • Peter Newman
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_476

Abstract

Consider the following standard problem in the theory of demand: Find x ≥ 0 so as to max u(x) subject to 〈x, p〉 ≤ ω where 〈x, p〉 is the inner product of the n-dimensional commodity and price vectors, and ω > 0 and u are the consumer’s income and utility function respectively; this problem is here labelled max(p, ω).

Keywords

Arrow corner Compensated demand Cost function Cost minimization and utility Duality Indirect utility function Linear programming Maximization 

JEL Classifications

D1 
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Bibliography

  1. Arrow, K.J. 1951. An extension of the basic theorems of classical welfare economics. In Proceedings of the second Berkeley Symposium on Mathematical Statistics and Probability, ed. J. Neyman. Berkeley: University of California Press.Google Scholar
  2. Arrow, K.J., and G. Debreu. 1954. Existence of an equilibrium for a competitive economy. Econometrica 22: 265–290.CrossRefGoogle Scholar
  3. Bergstrom, T.C., R.P. Parks, and T. Rader. 1976. Preferences which have open graphs. Journal of Mathematical Economics 3: 265–268.CrossRefGoogle Scholar
  4. Deaton, A., and J. Muellbauer. 1980. Economics and consumer behaviour. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  5. Debreu, G. 1959. Theory of value. Cowles commission monograph no. 17. New York: Wiley.Google Scholar
  6. McKenzie, L. 1957. Demand theory without a utility index. Review of Economic Studies 24: 185–189.CrossRefGoogle Scholar
  7. Newman, P. 1982. Mirrored pairs of optimization problems. Economica 49: 109–119.CrossRefGoogle Scholar
  8. Samuelson, P.A. 1947. Foundations of economic analysis. Cambridge, MA: Harvard University Press.Google Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Peter Newman
    • 1
  1. 1.