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It is generally assumed that such curves are convex to the origin.
Now I-I is a particular indifference curve. We may think of the consumption of any bundle of goods on it as yielding a particular level of satisfaction, or utility, to the consumer. However there are indifference curves passing through every point on figure 2, each one negatively sloped and each one convex to the origin. Those which pass through points above and to the right of D. link
Indifference curves that cross are incompatible with the assumption that consumers order bundles of goods consistently.
Up bundles of goods that yield higher levels of satisfaction than those on I-I and those below and to the left yield lower levels of satisfaction. Such curves can never cross one another, for this would violate the rationality assumption....
Consider figure 3 in which two indifference curves have been drawn to cross and consider their interpretation. The consumer is indifferent between points H. And J. On curve 1 and between R. And Q. On curve 2. However, bundle H. has more of both X and Y than does R. And hence must be preferred to it; for exactly the same reason, point Q. must be preferred to J. There is clearly an inconsistency here that violates the rationality assumption, and it obviously arises because the curves cross one another.
References
Bailey, M.J., The Marshallian Demand Curve, Journal of Political Economy, June 1994, reprinted in Breit and Hochman (op. cit).
Hicks, J.R., Value and Capital (2nd edition), New York (Oxford University Press) 1946, Chs 1-3.
Marshall, A., Principles of Economics (8th edition), London (Macmillan) 1936, Book 3.
Skurski, Roger. New Directions in Economic Justice. University of Notre Dame Press, 1983.
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