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Early results by Antonelli (1886) and Nataf (1953) had shown that, assuming all individuals face the same prices in a market, their income consumption curves and their [[Engel curve]]s should be parallel straight lines. Gorman's first published paper in 1953 developed these ideas in order to answer the question of generalizing a society to a single individual.
In 1961, Gorman published a short, four-page paper in ''Metroeconomica'' which derived an explicit expression for the functional form of preferences which give rise to linear Engel curves. Briefly, an individual's (<math>i</math>) resulting expenditure function (<math> e ^ i \left ( p , u ^ i \right ) </math>) must be [[affine transformation|affine]] with respect to utility (<math>u</math>):
:<math> e^i \left (p,u^i \right ) = f^i(p) + u^i g(p) </math>,
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