On the path independence conditions for discrete-continuous demand

We consider the manner in which the well-established path independence conditions apply to Small and Rosen's (1981) problem of discrete-continuous demand, focussing especially upon the restricted case of discrete choice (probabilistic) demand. We note that the consumer surplus measure promoted by Small and Rosen, which is specific to the probabilistic demand, imposes path independence to price changes a priori. We find that path independence to income changes can further be imposed provided a numeraire good is available in the consumption set. We show that, for practical purposes, McFadden's (1981) ‘residual income' specification of the conditional indirect utility function offers an appropriate means of representing path independence to price and income changes.