Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

2 results

  • 22 - Lagrangeans and the Consumer

  • Martin Anthony, London School of Economics and Political Science, Norman Biggs, London School of Economics and Political Science
  • Book:
    Mathematics for Economics and Finance
    Published online:
    24 May 2024
    Print publication:
    30 May 2024, pp 238-250

  • Summary

    A more general formulation of the Lagrange multiplier method is given: that in which there are many variables and possibly more than one constraint. The general theory of the consumer is presented, the problem being to maximise utility subject to a budget constraint. Applying the Lagrange method to this problem, it is shown that the tangency conditions encountered inreappear as a consequence; and also that, when optimising, the marginal rate of substitution is equal to the price ratio. The general solution of the problem reveals how to express the demand quantities in terms of the budget and the prices, giving what are known as the Marshallian demand functions. The corresponding (maximum) value of the utility function (depending on the budget and the prices) is known as the indirect utility and it is explained that the partial derivative of this with respect to the budget (known as the marginal utility of income) is equal to the value of the Lagrange multiplier.

  • Monotone utility convergence

  • Part of
  • Stefan Ankirchner
  • Journal:
    Journal of Applied Probability / Volume 43 / Issue 3 / September 2006
    Published online by Cambridge University Press:
    14 July 2016, pp. 622-633
    Print publication:
    September 2006
    • Article
      • You have access
    • PDF
    • Export citation

  • We show that the maximal expected utility satisfies a monotone continuity property with respect to increasing information. Let be a sequence of increasing filtrations converging to , and let un(x) and u∞(x) be the maximal expected utilities when investing in a financial market according to strategies adapted to and , respectively. We give sufficient conditions for the convergence un(x) → u∞(x) as n → ∞. We provide examples in which convergence does not hold. Then we consider the respective utility-based prices, πn and π∞, of contingent claims under (Gtn) and (Gt∞). We analyse to what extent πn → π∞ as n → ∞.