A statistical interpretation of a market demand curve for a commodity obeying the law of demand

In this note we provide a statistical interpretation of the Marshallian market demand curve of a commodity that obeys the law of demand and which has a finite and positive level of satiation. A consequence of our approach is that in the context of two goods, we are able to obtain demand functions which are very similar to those obtained by “budget-constrained Cobb–Douglas utility maximization”, but now as a result of a “budget-constrained linear utility maximization” exercise, although our budget constraint is “slightly different” from the one that would be used for the former optimization problem.