Each indifference curve is a set of points each representing a combination of quantities of two goods or services all of which combinations the consumer is equally satisfied with. The further a curve is from the origin the greater is the level of utility. The slope of the curve (the negative of the marginal rate of substitution of X for Y) at any point shows the rate at which the individual is willing to trade off good X against good Y maintaining the same level of utility. The curve is convex to the origin as shown assuming the consumer has a diminishing marginal rate of substitution. It can be shown that consumer analysis with indifference curves (an ordinal approach) gives the same results as that based on cardinal utility theory i.e. consumers will consume at the point where the marginal rate of substitution between any two goods equals the ratio of the prices of those goods (the equi-marginal principle). Revealed preference

Revealed preference theory addresses the problem of how to observe ordinal preference relations in the real world. The challenge of revealed preference theory lies in part in determining what goods bundles were foregone on the basis of the being less liked when individuals are observed choosing particular bundles of goods.1 2 Ordinal utility functions

An ordinal utility function describing a consumer's preferences over say two goods can be written as u(xy)

where x and y are the quantities of the goods consumed. Both partial derivatives of this function are positive if the consumer prefers more of both goods. But the same preferences could be expressed as another utility function that is a monotonic transformation of u:

where f is any globally increasing function. Utility functions g and u give rise to identical indifference curve mappings. Thus in ordinal utility theory there is no concept of diminishing marginal utility which would correspond to the second derivative of utility being negative. For example even if u has a negative second derivative with respect to x the equivalent utility function g may have a positive second derivative with respect to x. See also consumer theory cardinal utility marginal utility References Chiaki Hara (6-June-1998). "Revealed Preference Theory". 7th Toiro-kai meeting (1997/1998). http://www.societies.cam.ac.uk/cujif/ABSTRACT/980606.htm.  Botond Koszegi; Matthew Rabin (May 2007). "Mistakes in Choice-Based Welfare Analysis". American Economic Review Papers and Proceedings 97 (2): 477481. http://elsa.berkeley.edu/botond/mistakeschicago.pdf.  External Links Ordinal utility vs. Cardinal utility Murray N. Rothbard "Towards a Reconstruction of Utility and Welfare Economics"