“The Geometrical Representation of Complementarity.” Review of Economic Studies 10 (1942–1943): 122–125.
“Geometrical representation of complementarity encounters difficulties because complementarity involves a relationship between the three commodities and three-dimensional diagrams are notoriously difficult to handle. A family of indifference surfaces for three commodities is, indeed, most difficult to represent in a drawing. But complementarity, as now defined by Prof. Hicks, refers to changes in the marginal rates of substitution during movements on one indifference surface. And an indifference surface, of course, can be fully described by contour lines in the same manner in which we represent a production function. The only inconvenience of this method is that such a diagram looks misleadingly like a family of indifference curves for two commodities, although it shows for three commodities merely what a single indifference curve shows for two.”