On the basic assumption that individual consumption of a good is a stochastic phenomenon, the first part of this article shows that under general conditions market quantity demanded is asymptotically (as n, the number of individuals in the market, increases) distributed as normal with mean and variance a function of own price given all other prices and individual incomes. Next, by the use of integral transforms, it is shown that the unknown mean market demand function can be approximated by a specific functional form. The estimation problems involved with such a model are discussed in the last part of the paper.