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

This paper presents results of a study that has shed new light on the shape of indifference curves in the Marschak-Machina triangle. The most important observation concerns jumps in indifference curves at the triangle legs towards the triangle origin. Such jumps, however, do not appear at the hypotenuse. This indicates discontinuity in lottery valuation when the range of lottery outcomes changes. This observation is confirmed by estimating the slopes of the indifference curves in the triangle sub-areas and by estimating six decision-making models under risk. Those models that correctly predict jumps at the triangle legs offer the best fit for the data. The study was performed using a novel method of estimating indifference curves: one based on the linear interpolation of certainty equivalence values between adjacent points representing the lotteries under consideration