Consider a consumer whose preferences over consumption bundles of non- negative amounts of each of three distinct commodities can be represented by a modified Stone-Geary utility function of the form U (91, 92, 93) = { (91-71) (9272) 2 (93 - 73) - 1-a1-92 if (91, 92, 93) , if (91, 92, 93) , where q is the quantity of commodity one, 92 is the quantity of commodity two, q3 is the quantity of commodity three, and = {(91, 92, 93) E R 91 > 71, 92 > 2, 93 > 73}. Note that 91, 92, and q3 are choice variables, while V1, V2, V3, a and a2 are fixed preference parameters. Typically, we would assume that > 0,