unemployment or productivity effects, or unless the extent to which wage changes compensate price changes differs systematically across income levels.
Expression (12.12) yields(12.A1) We substitute (12.2), (12.4), (12.10), and the definition of the social weight βu = λu∂W/∂Vu into (12.A1). This yields (12.A2) Next, from the definition of compensated demand responses and the symmetry property of Slutsky terms, (12.A3)
where, and .
Substitution of the above and of definition (12.5) allows (12.A2) to be rewritten as(12.A4)
At an interior optimum, where dH/dpi = 0, the above expression yields (12.13).