On the exploitation of additional duality relationships in consumer demand analysis

This paper advocates more extensive use of the (Frisch) profit function in static consumer demand studies and intorduces its inverse, the price of utility function, paralleling the well-known relationships between indirect utility and expenditure functions. An examination of the relationship between these four functions suggests: (i) a fourth 'system' complementing Marshallian, Hicksian and Frisch demand systems; and (ii) a fourth 'theorem' complementing Roy's Identity, Shephard's Theorem and Hoteling's Lemma.