Indirect Preference Research Articles

The effects of gender control on fertility and children's consumption.

The authors analyzed the effects of preference for children of a particular gender upon fertility and children's welfare, with and without sex selection or gender control. The impacts upon investments in children's human capital, bequests, and fertility are studied in a model based upon parental altruism. Both pure sex preference, a feature of the parental utility function, and indirect preference resulting from price effects are modelled in this paper. When there is no gender control, the impact of pure sex preference is seen in smaller consumption for daughters than for sons. However, when gender control is employed, sex preference increases the sex ratio and it is possible that sisters may on, average, consume no less than their more numerous brothers. Parents who practice gender control have larger families than if sex selection techniques were unavailable. The effect is magnified if sons' earnings opportunities are better than daughters.

Duality between direct and indirect preferences

This paper develops a duality theory for preference orders, and highlights important differences with respect to the cardinal utility approach. Our main result is a symmetric duality theorem, under the minimal hypotheses, between direct and indirect preferences. In contrast to the cardinal theory, we also find that these conditions do not completely characterize the class of indirect preference orders.

The Structure of Constant Elasticity Demand Models

AbstractThe demand model with constant price and income elasticities has been used extensively in applied agricultural economics. This paper analyzes the structure of incomplete systems of constant elasticity demand functions. It is demonstrated that there is a duality theory for incomplete demand systems that is analogous to the duality theory for complete systems. This theory permits the recovery of that portion of the direct and indirect preferences pertaining to the goods of interest, and we can calculate exact welfare measures for changes in income and in the prices of these goods. For an incomplete system of constant elasticity demands, the Slutsky symmetry restrictions for integrability are presented and the implied structure of the direct and indirect preferences with respect to the prices and goods of interest is derived.

Budget preferences and direct utility

This paper extends a result of Sakai, who presented conditions for indirect preferences from which a utility function can be deduced if demand is single valued. It will be shown that—adding a “partial Lipschitz condition”—Sakai's theorem can be extended to multi-valued demand. Our result follows from the extension of a theorem of Hurwicz and Richter, who have shown that, under certain hypotheses on demand correspondences, an upper semicontinuous utility function f exists, so that the set of utility maximal elements μ f ( B) is contained in the choice set h( B) for every budget B. By our partial Lipschitz condition h( B) ⊂- μ f ( B) also follows.

Indirect preference for risky prospects

Indirect preference for risky prospects

Indirect preferences

Indirect preferences

The Ideal Log-Change Index Number

RICE and quantum indexes (P, Q) are dual to each other if PQ = E where E is the expenditure index. They satisfy the weak factor reversal test.' If they share an identical weighting formula as weighted averages of price and quantity relatives, they satisfy the strong factor reversal test, that is, they are ideal. The most celebrated ideal economic index is the one associated with the name of Irving Fisher though it was discovered before him. No ideal index as simple as Fisher's has been discovered since. Log-change index numbers have become increasingly popular in recent years, particularly as an approximation to the theoretically desirable Divisia index. Theil (1973) proposed a new log-change index number that alhnost satisfies the strong factor reversal test. I derived several alternative formulas that improve in the degree of approximation (Sato, 1974b). But neither Theil nor I was able to obtain the ideal log-change index. In section II, I report its discovery. Our pessimism has proved premature. Indeed, the formula was self-evident from the very beginning -we simply failed to see it.2 There are dual dualities between economic indexes and homothetic preferences (Samuelson and Swamy, 1974). A price or quantum index is associated with a homothetic indirect or direct preference ordering. If P and Q are dual to each other, so are the direct and indirect preference orderings corresponding to them. If P and Q are ideal, the latter are not only dual but also share an identical mathematical form. They are strictly self-dual as I call them elsewhere.3 An obvious example is the association of Cobb-Douglas indexes and preferences. A less obvious example is the association of Fisher's ideal indexes and quadratic preferences. The association itself was discovered by Konuis and Buscheguence a half century ago in 1926.4 Note that homothetic quadratic preferences are self-dual. Then, what is the selfdual preference ordering that corresponds to our ideal log-change index? We shall show in section III that it is the CES function that has become so popular in the economic literature, originally discussed by Bergson (1936), rediscovered by Solow (1956), and popularized by Arrow et al. (1961). The CES function is known to be self-dual (Samuelson, 1965) and yet the economic index associated with it has eluded discovery until now. Economic indexes are useful because they apply even when underlying preferences are not homothetic.5 We shall show in section IV that the ideal log-change index corresponds to the addilog preference ordering introduced by Houthakker (1960).