Continuous or Discontinuous? Estimating Indifference Curves Inside the Marschak-Machina Triangle using Certainty Equivalents.

This paper presents results of a study, which shed new light on the shape of indifference curves in the Marschak-Machina triangle. The most important observation concerns (possibly discontinuous) jumps in indifference curves at the triangle legs towards the triangle origin. Such jumps, however, do not appear at the triangle hypotenuse. This points out to discontinuity in the lottery valuation when the range of the lottery outcomes changes. This observation is confirmed by an econometric analysis of six decision-making models: those models, which correctly predict jumps at the triangle legs, offer the best fit of the data collected. Focusing attention to the range of lottery outcomes appears thus one of the most important factors driving decisions under risk. The study has been made using a novel method of estimating indifference curves, which is based on linear interpolation of certainty equivalent values between adjacent points representing the lotteries under consideration.