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On the Law of Demand. - A mathematically simple descriptive approach for general probability density functions

By Lars-Göran Larsson

Abstract

In this paper we assume that choice of commodities at the individual (household) level is made inside the budget set and that the choice can be described by a probability density function. We prove that law of demand()0xExpis valid for one(x) or two choice variables (x, y)*. The law of demand at the market level is valid by summation. We use general probabilistic density functions p(x), p(x, y) defined over the bounded budget set to calculate E(x) and prove law of demand. The expected demand functions are homogeneous of degree zero in prices and income(,,)xyppm.The commodities x and y are normal goods**. The present approach is less complex in a mathematical sense compared to other approaches and is descriptive in its nature. Why not keep descriptions as simple as possible? Entia non sunt multiplicanda praetor necessitatem Beings ought not to be multiplied except out of necessity âOccam´s razorâ Encyclopedia BrittannicaLaw of Demand and other properties of consumer demand; Microeconomics; Consumer theory; Consumer behaviour; Choice described in random terms; Expected individual and market demand

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