Y is complementary with X in the consumer's budget if an increase in the supply of X (Y constant) raises the marginal utility of Y; Y is competitive with X (or is a substitute for X) if an increase in the supply of X (Y constant) lowers the marginal utility of Y.To put this in familiar terms, one could think of hotdog franks and buns as being an example of a pair of complementary goods. Conversely, one might think of french fries and onion rings as being substitutes.
With the above definition, the complementary-competitive relationship is symmetric or reversible: If Y is complementary with X, then X is complementary with Y, and similarly for competitive goods. Also if the marginal utility of money is constant, this definition implies that, for complementary goods, a fall in the price of X, increasing the demand for X, will raise the marginal utility of Y, which will lead to an increase in demand for Y. Similarly, if X and Y are substitutes, a fall in the price of X will lower the demand for Y.
Hicks then goes on to describe Pareto's difficulties in trying to translate the definitions of complementary and competitive goods into the terms of indifference curves. Pareto was able to find a connection between the case of complementary goods (according to the definition above) and the case of indifference curves that are highly bent, as in Figure 12.
But as Hicks explains, Pareto was not able to discover what degree of curvature corresponds to the distinction between complementary and substitute goods. In addition, Hicks notes that the definition above violates Pareto's principle of not assuming utility to be measurable. Hicks will show in the next section how these difficulties can be overcome.
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