On the Elasticities of Substitution and Complementarity

Estimating the Effects of Family Background on the Return to Schooling

“…One possible explanation for this finding is that better educated fathers increase children education through transmission of innate ability, whereas better educated mothers raise children education by enhancing the "family learning environment." This finding can also be stated in terms of the characteristics of the production function (1): Own education and father's education are q complements, whereas own education and mother's education are q substitutes (see Sato and Koizumi 1973). Interestingly, the differential impact of father's and mother's education on educational attainment and labor market earnings is also noticeable in Tables 2 and 3.…”

International Migration

“…Following Hicks (1970; see also Sato and Koizumi, 1973), i and k are called q-complements if ς ik > 0 and q-substitutes if ς ik < 0. 49 Because it is easier to interpret the quantity elasticities of inverse input demand, ln , ln…”

Elasticities of substitution and complementarity

“…The idea was that the HEC would 7 Similarly the Morishima and factor ratio ES's do not discriminate between p-substitutes and be dual to the Allen-Uzawa ES and would reflect the change in the price ratio for a change in the input ratio holding the quantities of the other inputs constant and the output price constant. It can be shown (Sato and Koizumi 1973), therefore, to be:…”

“…It is, in fact, the dual of the gross version of the AES -the HLES (Kim 2000). An interesting conclusion of Hicks (1970) and Sato and Koizumi (1973) is that in the two input case the HEC and AES must take the same sign.…”