CONSTRAINED INDIRECT UTILITY FUNCTIONS

Recent years have been marked by an extensive empirical testing of profit, cost, expenditure, and demand equations based on duality theory and the development of specific functional forms as approximations compatible with any neoclassical production or utility function. In estimating systems of demand equations, the approach taken is almost always to assume consumers maximize utility of current period consumption subject to a budget constraint (or combined time‐budget constraint). There are many times that consumers face other constraints on their purchases. Many of these cases are associated with price discrimination and other market imperfections that result in several products being sold in packages (or, equivalently, several characteristics being contained in one product). This constraint on the proportions in which commodities must be purchased presents some significant problems for using an indirect utility function, particularly if one is interested in testing if the proportions are equal to or differ from what consumers would desire. One example of this problem is whether merged charities allocate funds in accordance with donor's preferences. Franklin Fisher showed, using a Stone‐Geary utility function, that there were reasonable cases where a merged charity could increase contributions by allocating funds differently than donors prefer.