Indifference Curve Analysis

Author:
Nuno Baeta

Indifference Curve Analysis in GeoGebra Using the Marginal Rate of Substitution Represented by an ODE

Jorge Marques, CeBER and FEUC, Coimbra, Portugal Nuno Baeta, CISUC, Coimbra, Portugal

Indifference curve analysis is an analytical tool to study consumer behavior in Microeconomics. An individual consumer has a scale of preferences on the space of two goods, which could be represented by the marginal rate of substitution. We are interested in the representation of consumer’s preferences from the differentiable point of view. In this setting we consider the marginal rate of substitution to describe smooth preferences. The main goal is to provide a graphical method to design the indifference map. For this purpose, we use GeoGebra software for plotting the direction field for a first order ordinary differential equation (ODE). We then represent quasi-linear, separable, homothetic, Cobb-Douglas, and CES preferences. Our alternative approach to understand consumer behavior is connected with the formulation concerning the representability of preferences by utility functions. Keyworks consumer behavior, preferences, marginal rate of substitution, ordinary differential equations, GeoGebra References

  • Allen, R. G. D. (1938): Mathematical Analysis for Economists. Macmillan & Co. Limited.
  • Debreu, G. (1972): Smooth Preferences. Econometrica, 40 (4), pp. 603-615.
  • Hicks, J. R. and Allen, R. G. D. (1934): A Reconsideration of the Theory of Value: Part II - A Mathematical Theory of Individual Demand Functions. Economica, New Series, 1 (2), pp. 196-219.
  • Marques, J. (2014): An Application of Ordinary Differential Equations in Economics: Modelling Consumer’s Preferences Using Marginal Rates of Substitution. In N. Mastorakis, F. Mainardi & M. Milanova, editors: Mathematical Methods in Science and Mechanics: Proceedings of the 16th International Conference on Mathematical Methods, Computational Techniques and Intelligent Systems (MAMECTIS '14) and Proceedings of the 5th International Conference on Theoretical and Applied Mechanics (TAM '14), Mathematics and Computers in Science and Engeneering Series 33, WSEAS Press, pp. 46-53.
  • Mas-Collel, A.; Whinston, M. D. and Green, J. R. (1995): Microeconomic Theory. Oxford University Press.
  • Samuelson, P. A. (1959): The Problem of Integrability in Utility Theory. Economica, New Series, 17 (68), pp. 355-385.
GeoGebra file to support a presentation made at GeoGebra ICM 2018.